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Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent dtre filmds i des taux de reduction diff6rents. Lorsque le document est trop grand pour dtre reproduit en un seul cliche, il est film6 d partir de Tangle sup6rieur gauche, de gauche 6 droite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagramnies suivants illustrent la mdthode. 1 2 3 32X 1 2 3 4 5 6 FO F ■ i4 I 0. BEi ,1^ ; A COMPENDIUM / OP MENTAL ARITHMETIC FOR -THE- USE OE^SCaOOLS BY F. E. JTJNE-A.TJ, Esq. , ^ _ ^ Member of the Board of Examineirs^' rwsko.- ■ ■ , .**■ I i mu W M we^^iW MONTREAL Printed for the author by I 0. BEAUGHEMIN & VAL0I8, BooKSELLEBrj^aBJPWMXERS 237 and 239, St. Paul Street 1868 Price : 20 Cents mM ^y. ' -t'^.^'*- ■•■■ ■ -"- . V"-" ■ -Wii: ''>■/*■ f:-'^ . . . , > H ,r r - '■ -^ '".-^ ■ 'i ' ■< ■ '■■.(% V . il'^«J v V , yM> ■■■^\ :i .^ :■' .•/ ..»^^'■ .•<■■s «Mpi ' Entered, according to the Act of the Parliament of Ganad in the year one thousand eight hundred and sixty-eight, F. E. Juneau, Esq., in tho Qffice of the Minister of A|pnculti ^•»';.v-rf, .' ',' '-f ».; •«i, .■ ;<-*'-;:-^.'^ ■■■ i; 'V'i'^:f ■...•i:..,,,;-^-::;;A,t- .,.^;;.?^.■,:;^ ■•:'■"■■■'•'-■'>''• .'■^- . '-i^ "i^ ,' ,• ;,i' iV'-.;,i.., ;^ .,;'-H V ..:|iS';V' •!'•*•'■- I -.i^^-AVi:,.^!..;:^-* ■'■ *"--"^v,tt>i.>vfiaS'y"''i;",' ■ y ■ • y'^''~' ' '*■'-•♦- <£...■.*'.• |.>i' v?"**^. ■ U'.*.^^^,.» vy^-^fK-^;-*"'*"' "'— J^'>^'=^'*''-! .'■" "-tV •.<*■''' :. -^ ,,v-' • -■'*■- ' -. ■-'■' ''■'■ ■iy-r:::-Ky'^«y^ 'V. vrv *.■■;; '■'?.,«"":"" ' ;.."<•)"■■,. ",.1 • \ ' .;.•..'.■- mm iiont of Ganad sixty-eight, of Agriculti >■ ^»f. • U?/ ^'-^ ,*. 1 >'..*•; .1; .•■'^ vi- ■(■.■;• I'Ji'Vl^tV:-,' 'f A. DEDICATION. ... ■ y •' ' ' N ),. . • • v.. \V; f, •- J' (.. -•o»- .•■ .- V-:.- .':„ -'• >'''^ TO THE HONORABLE + ;.■•/*■ .'uV HERRE-J.-0. CHAUVEAU,! f .. '.""^ *.;.-. -.-.. ....■,■-.--!,-■' -'!v/A> . ..;,.> ■'■.'.-■■.■.i,v;. "-?.■ V ;> ■•?:' *■,<;' - • P Provincial Secretariat' 'I Minister of Public Instructioa &c.^ cscc. &c. -;*:•:;-. .■; ,. ■ • ..■ ■;■■■■/ - .. . ., . _ •;*.?■ ■ *•'■;* 'v'l- THIS LIlrrLE "WORK RESPECTFULLY DEDIGATEP - BY THE AUTHOR la k^ M ^-v. -\.hr.J:iti- ii. Quebec, 28th March, 1868. ^ I have looked over the manuscript copy of a ICompendium of Mental Arithmetic for the use of litishand Canadian Schools," by F.-E. Juneau, ''A -■?' I It is full, sufficiently varied, well adapted for both irrencies, and abounds in examples and exercises, le rules are ingenious and ' ntirely practical. I The original work, in French, has been some time use and is generally used in the country schools. im ijleased to find that he has decided *''■• :, •f" w^ ,\i '/.,■■■■ : '•- /( ..' V, ;i , . KM ■ ■' ■■ :yP': ■'■■ '"/U.C'' ... jr J.. Quebec, April 2^th, 1868. \'t:.:-^:-: f "■■*;'^>vv.f Dear" Sir, '*^^. I ■^' ~ With best wishes, 4 * ■''■/'^^■^yy'C:^'.,^ '-^i' 'vv;;-.4-r-\ I am, dear Sir, ^ ^'^r«<^^ ',-" Si ' . iKj- . %V* *,■ F.^. JUNEAU, Esq., J; Wi^ Inspector of Schools, etc Youjtruly, H.-H. MILES, M.A., LL. vn-fo; '-.'il- ■•'^■y;: -ti:'. u.-yf' /Ac^ /:'i-j'}:;;ci.^ ■■■■ :"■;■'. ^-f' ■ -ir'v/;. >'''"' ■/'.'l ijka.^'-:: oV/HjV *■/;. <<' >K .>->'.^ ^■ 'v'^''\:x Mv; >.l' >>■- ' .• : '>-»'■'' .-■ ( 'Hi" PREFACE. '''V^vi^:^ '*. -**^ '■r-,-;;M . "V. :,:<' Every one iinclerstands &e advantage of Mentol I Arithmetic, I therefore need not demonstrate its utility : I shall only say that our best farmers un- derstand it so well, Ihat they are all capable of find- ing, mentally, the amount of a sale of the products of their farms. '^^^■:- As I have remarked more th^n once during my visits of inspection to different schools that children are not generally instructed in this kind of arith- I metic, I thought it might be useful to compile this " Compendium of Mental Arithmetic," which, if thoroughly committed to memory, will considerably I facilitate the study of this science. I feel assured also that the progress of the pupil in written arith- I metic will be doubly rapid by this means. The third part of the work is intended to be taught I to those pupils only who have made some progress in writfeg' arithmetic. This last part contain- ing several methods, short and easy to remem- ber, will render the pupil capable of finding, mentally, the amount of any sale or purchase, like- wise the computation of interest and percentages I generally, ^b^^^i- #' ■ •i>;-:^&'k:;i/ -t^^-.-: ■^'--'- '■:.9'-': The pupil should perform on his slate what he [has already reckoned mentally. :>^:,^i ■I'*.: ri't I:- . ;, . ■■:{ ' J; ,!■ 'W There can ho no doubt, that thus accustoraod, young men who engage hi commercial business or in any other branch of industry will bo enabled to find promptly and without having recourse to a pencil the solution of any question. Mental arithmetic teaches a child to compare and reason, before he commits himself to an answer which he wishes to bo correct. It is thus that, with- out perceiving it, he forms his judgment. Persons intrusted willi primary instruction should therefore induce all their pupils to enter on mental arithmetic ; even yon ng children may do so as soon as they can read freely, for they cannot too soon learn to count correctly. V. H.u iHE Author. .;r»' . ''^ ''■■■\ V V .■ ... ;'..,!r. .. Y:!l ■\. i+ .V. ' .-' '\^:\ ourso to a tion should on mental I so as soon )t too soon EXPLANATION > •' ■ " \ f'v'.ir 07 I \ •< '■';■ >.(' ARITHMETICAL CHAEACTERS OR ■^'■\: •;<;^V 'T* ' SIGNS USED IN THIS WORK. ,/■■*■ ■>-! ■'*■ - ^<7wa< io. The sign of Equality ; as, 4 qrs.=^ 1 Ctrl. signifies, that 4 ^rs. are equal, to 1 cwU + Plus^ or wore. The sign of Addition ; as 4 + 4 = 8, that is, 4 added to 4, is equal to 8. — Minus^ or less. The sign of Suhtraction ; as, 8 — 4 ■- 4, that is, 8 diminished by 4, is equal :',..,/" if'":'' X Multiplied by. The sign of Multiplication ; as, 4 x 2 = 8, that is, 4 multiplied by 2, is equal to 8. ■■ ;■■. -..■v-, , . ,-_ -■■H^.; ■'•:>., •T- Divided by. The sign of Division ; as, 8-^2 = 4, that is, 8 divided by 2, is equal to 4. !■; .'iiiSS': :''?>-■:■, '".;,■<';.'?, «t 1. MENTAL AEITHMETia FIRST PART. Mental Atithmetic is the art or science of com- puting in tutj mind by numbers, and consists of five principal rules: .lamely, Numeration, Addition, Subtraction, Multiplication and Division. Numbers are denoted by the following characters: i^ "l 5. 4. 5. 6. 7. a 9. a NOTATION AND NUMERATION. Notation is the method of writing down a number in figures, thus : three hundred and thirty-three, are expressed by the figures 333, etc. Numeration is the art of reading a number ex- pressed in figures, and we read them from the left to the right hand. The fij;«t figure tov/ards the right hand is units^ and the next to that is so many tens^ as 36, thirty-six. Where 6 is in the place of unlts^ ajad 3 in the place of tens^ consequently 3 tens are properly called thirty ; the next figures to tens is called hundreds^ as 365, three hundred and sixty- five. (Number of days in a common year.) / MENTAL NUMERATION. The cipher (0) serves to bring figures to their pro- per places, by supplying vacant places ; thus : 7, (seven ;) 70, (seventy ;) 700, (seven hundred ;f 770. jseven hundred and seventy;) 777, (seven hundred and seventy-seven.) ft ■ :. ■ . ■■ ■■■■ * ■■*, , < ..'■ • \ ' . -., '■■-■. :ii- NUMERATION TABLE. : Vv ■ ■■■.^. ■■ ^ ' - . "' ■' , ■, -,. ^y - ■ ■ , ■ .- ,' " . '■.»• ■ •, •-■ ' ■' v^;,;-v;' '-..^i,,-. :. :■!■■■ ■'./ ,■"'■[_.:. :;. ■„' '. ■ ;■: ■ . ., ./ ■ ' .■ ■ ,;. . ^ r/ •/-■•-•v:^ •#.■'■" 'S \ ■^ .; ■■> Q ■ '** to .••■ . . *S a • •$ g . • ,■ ;:':K' M r-*^ ia i3 0^ '^ 5 ^"^^ i5 9 8 7 6 5 4 3 2 1 Units, one ; tens, twenty-one ; hundreds, three hundtea and twenty-one ; thousands, four thou- sand, three hundred and twenty-one ; tens of thou- sands, fifty-four thousand, three hundred and twen- -ty-one ; hundreds of thousands, six hundred and fifty-four thousand, three hundred and twerty-one ; raiihoiis, seven millions, six hundred and fifty-four thousand, three hundred and twenty-one ; tens of millions, eighty-seven millions, six hundred and fifty-four thousand, three hundred and twenty^one ; hundreds of millions,nine hundred and eighty-seven millions, six hundred and fifty-four thousand, three hundred and twenty-one. MENTAL NUMERATION. .1 Units. 21 Tens. - 321 Hundreds. ^ 4,321 Thousands. 54,32 1 Tens of thousands. -■'-^ 654,321 Hundreds of thousands. : > 7,654,321 • Millions. 87,654,321 Tens of Millions. 987,654,321 Hundreds of MUhons. ""'ii'Kii;- «r",' vW^'iter;; • - MENTAL i^UMERATlOK. Exercises in Numeration. ; 10, 20, 30, 40, 50, • 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160. 170, 18a, 190, 2U0, 212, 224, 236, 248, 256, 272, 288, 299, 310, 355, 377, 388, 404, 505, 606, 707, 808, 909, 918, 927, .936, 945, 954, 960, 972, '984, 996, 1000, ^ ' 1868. No. 1. 11,111,111 22,222,222 33,333,333 44,444,444 No. 2. 55,555,555 66,666,666 77,777,777 88,888,888 99,999,999 No. 3. 10,000,000 , 20,202,020 30,303,030 40,404,040 No. 4. 50,050,050 60,606,060 77,000,700 80,240,506 99,990,001 No. 1. 11,234,567 22,345,678 - 33,456,789 44,567,890 55,678,900 Nq. 2. 66,789,000 77,890,000 88,900,000 99,123,456 100.000,000 No. 3. 100,000,100 .200,200,200 300,800,300 400,400,400 550,550,550 No. 4. 606,060,606 700,777,700 880,880,880 910,910,910 1,000,000,000 ss^ *', iC^;' ,\ t EXTBNDlBD NUMERAtlON TAPLB. \ 4^2 3, 4 5^, a, 3 9, poo, 10 1 ■''■■■'4^: , OvC: H. CO • o : WHCd i-g! iri 9 * • pi <5 >^co o g •*• P — ICO =^: o • P : P-: ■'■'-' ■■rr- ■■■ ' .■ ■,. ■ ■,■--*'■*•. .'f ' 'tK o3 a o e^cjo ,-■ \. ^■■ ;v?v • * • ...,..9B 7, 6 5 4, 3 2 1, :9 a 8, 5 5 4 1 2 3 ,.-■'■> ^' ' ' :"- ' 5 5 4 6 -v^^ 7 8 : ■" , " ':-' ^ 9 1 10 11 12 13 14 15 '.';■ 16 '.- 17 18 v>^"-r A v^:./; r :'"^^^: .-it i t; ■1|:-? 01 5 S B. 3 co^ 1 =L a • » • • • • • • • • I •• • • • 5 5 4 'i-"r MENTAL ADDITION. 1^-' ■!?'■<'■ Mental Addition consists in finding, mentally, two lor more numbers taken together in one sum, and Ithis number is called jjigir %uja l^^t^us, 2 and 3^ are 5 j i5 and 4 are 9. ./:;^:-.->-->-^- -^^^p^m^-^,^^ And ADDITION TABLE. 1 ^ 3 4 5 6 7 « 9 10 11 12 2 = 3 = 4 = 5 = 6 = 8 = 9 = 10 = ir = 12 = 13 = 14 = 15 = 16 = 17 = 18 = ••••••••• •••••• •■• ••#•••••••••••• •••••• •••«••••• •••••• #••••• ( k — 10 11 12 10 11 12 8 12 13 13 14 15 16 14 15 16 13 14 15 16 17 13 iO 11 12 9 10 8 9 10 II 12 13 14 15 10 16 14 15 II 12 [6 11 12 in 10 11 12 13 11 12 13 15 14 10 10 17 17 18 17 18 19 18 19 20 19 20 19 17 18 19 18 19 16 17 18 19 10 14 15 16 12 13 14 15 13 14 15 16 17 18 20 20 21 20 21 21 22 21 22 23 19 20 20 21 22 22 23 24 23 24 21 22 18 19 20 21 19 20 21 16 17 18 19 17 18 19 20 20 21 22 22 22 23 23 23 24 25 24 25 26 24 25 21 22 23 23 24 25 26 24 25 26 27 26 27 28 25 26 27 27 28 29 28 29 30 ■M'': M 9 -• — 6 •/ - ' . .• ^ » * MENTAL ADDITION. \ . First Exercise. ' ■ ." ■ • 1 and 1 ai cc 1 c " 1 ' 2 " 2 ^ cc 1 c 3 " 2 ' cc 1 c 4>,cc 2 * 3 " 3 ' cc 1 c 5 " 2 ^ 4 " 3 ' •e2 ' 3 ' 4 ' 4 ' 5 ' 5 ' 6 ' 6 ' 6 ' 7 ' 7 ' 7 7 and 1 or 6 " 2 " 5 " 3 " 4 " 4 are 9 and 1 or 8 " 2 " 7 cc 3 (c 6 " 4 " 5 " 5 are 11 and 1 or 10 " 2 " 9 " 3 " 8 " 4 " 7 " 5 " 6 " 6 are 8 and 1 or 7 " 2 " 6 " 3 " 5 " 4 are lU lOandlor 9 " 2 " 8 " 3 " 7 cc 4 cc 6 " 5 are li 12 and i or 11 " 2 " 10 " 3 " 9 cc 4 ci 8 " 5 " 7 " 6 are 9 #• 11 ■ lii ! Second Exercise. 2 + 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 '98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132| 134 136 138 140 142 1^ A 146 148 150 152 154 7 — MBN-TArL ADDITION r- •:'' . ■ Third Exercise. ' ^' r • ^ . ■ ■ ..,■;;(+) _. •;. J ;■:=;;:;■,';: and 1 or a 2 ^' " 3 " a 4 u " 5 " " 6 are 13 ai 12 ' 11 ' 10 ' 9 ' 8 ^ 7 * id 1 or ( 2 " c 3 a i 4 a i 5 « * 7 are 14 and 1 or 13 *' 2 " 12 " 3 " 11 " 4 " 10 " 5 " 9 u 6 a 8 " 7are 15 and 1 or 14 " 2 " 13 " 3 " 12 " 4 " 11 " 5 " 10 " 6 " 9 " ^ 7 " 8 " 8 are 16 and 1 or 15 " 2 " 14 " 3 " 13 " 4 " 12 " 5 " 11 " 6 " 10 " 7 " 9 " 8are rz ■~14 15 and 1 or a 2 ^^ ct 3 « 16 17 Fourth Exercise. - u 4 *"; ■,. ■ '■'.' ■■', . ■-•• ; ; .^.:a 17 and 1 or 16 " 2 " 15 " 3 " 14 " 4 " 13 " ^ " 12 " 6 " 11 " 1 " 10 " 8 " 9,i" 9 are 18 and \ or 17 " 2 " 16 " 3 " 15 " 4 " 14 " "5 " 13 " 6 " 12 " 7 " 11 " 8 " 10 " 9 are 19 and 1 or 13 u 2 " 17 " 3 " le " 4 " 15 " 5 " 14 " 6 " 13 " 7 " 12 " 8 " 11 " 9 " !^0 and 1 19 " 2 " 18 " 3 " 17 " 4 " 16 " 5 ^' 15 " 6 " i4r*f 7 " 13 " 8 '' 12 " 9 " 18 19 10 " lOarell " lOar^ ' ^i) ^1 1 ' 1 . ■ ■- ■1'. " Sixth Exercise^ ";■::;..;':.. 4 + 4 -^-^ f an( JO " 19 (( 18 (C 17 u 16 a 15 C( 14 (C 13 cc 12 a 11 (( '-^ ■■ * it 8 12 16 20 24 28 32 36 40 44 43 52 56 60 64 68 72 5 76 80 84 88 92 96 100 104 108 50 112 116 120 124 128 132 136 140 144 95 148 152 15a 160 164 168 172^ 176 180 140 184 188 192 196 200 204 208 212 216 185 220 224 228 232 236 240 244 248 252 230 256' 260 264 268 272 276 280 284 283 275 292 296 300 304 3q8 312 316 320 324 320 328 332 336 340 344 348 452 3§6 360 365 ^^ ■■■}:"! ■■■:•■: ^. ^'■.'■•t-i'" 9 MENTAL ADDITION. Seventh Exercise. 'J: w 20 and 1 or a 2 " 5r 21 and 1 or cc 2 " w 22 and 1 cc 2 or 23 and 1 01 " 2 " ^ and 1 19 " 2 " 19 u 3 cc 20 cc 3 cc 21 " 3 22 cc 3 cc 18 " 3 « 18 " 4 " 19 c« 4 cc 20 cc 4 21 cc 4 cc 17 " 4 " 17 « 5 ct 18 cc 5 cc 19 " 5 20 C( 5 cc 16 " 5 " 16 " 6 " 17 cc 6 cc 18 " 6 19 cc 6 cc t5 "6 " 15 " 7 *» 16 cc 7 cc 17 cc 7 18 cc 7 cc |4 u 7 a 14 " 8 " 15 cc 8 cc 16 " 8 17 cc 8 cc 13 " 8 '^ 13 " 9 " 14 cc 9 cc 15 "9 16 cc 9 cc 12 " 9 " 12 " 10 " 13 cc 10 cc 14 " 10 15 cc 10 cc 11 " 10ar( 11 " Hare 12 " Hare 13 12 cc 11 cc " 12 are 14 13 cc 11 cc " 12ai6 "11 """ n ■'■■*,*•■, •....;■ "" 24 - 25 1 • \-H /^'*t Eighth Exercise. tv *■ -• M. 32 36 68 72 104 108 40 144 76 180 ^12 216 :48 252 84 288 ^0 324 56 360 5 10 50 55 95 100 140 145 185 190 230 235 275 280 320 325 365 370 15 20 25 60 65 70 105 110 115 150 155 160 195 -200 205 240 245 250 285 290 295 330 335 340 375 380 385 30 35 75 80 120 125 165 170 210 215 255 260 300 305 345 350 390 395 40 45 85 90 130 135 175 180 220 225 265 270 310 315^ 355 360* 400 405 ft I .''■'■JT-Jk' Vi^^;M:< :t^r ^..v::^l?-y'- . —10 — MENTAL ADDITION, Ninth Exercise. • .'.'L"< ' '.".'iV/ii' ZTamTl' "5^ and 1 "or TT and 1 or [28 aL d 1 0) 24 " 2 // 25 .u 2 26 " 2 " 27 2 " •23 " 3 " 24 " 3 25 u 3 cc 20 3 " 22 *' 4 tt 23 " 4 24 cc 4 cc 25 4 " 21 " 5 22 '^ 5 23 cc 5 cc -24 5 " 20 " 6 ,, 21 " 6 22 " 6 '^ 23 6 " 19 " 7 20 u 7 21 cc 7 cc 22 7 '' 18 " 8 19 " 8 20 '' 8 '' 21 8 " 17 " 9 18 '^ 9 19 cc 9 cc 20 9 " 16 "40 17 " 10 18 cc ^Q CC 19 10 '' 15 " 11 " IG a 11 17 CC 11 c. ,3 11 '' 14 '' 12 15 " 12 16 cc 12 '' 17 12 ": 13 " 13i ire 14 " 13i ire 15 14 cc ^3 cc " 14 are 16 15 13 " 1 4 ar( 2e ■ ^7 28 li\ Tenth Exercise. ■li. 6 12 18 60 66 72 114 120 126 168 174 180 222 228 234 276 282 288 .330 336 342 '384 390 396 -438 444 450 ^ 6 + 6 24 30 78 84 152 133 186 192 240 246 294 300 348 354 402 408 456 462 36 42 90 96 144 150 198 204 252 258 306 312 360 306 414 420 468 474 43 54 102 103 156 162 210 216 264 270 318 324 372 373 426 432 480 430 20 19 18 17 16 15 * ^ •- ■ 02 103 56 162 10 216 64 270 18 324 72 373 23 432 ^0 430 — 11 — MPNTAL ADDITION. ««f ** * ■ ' 1 1 M AiA 1 ■■ II ' nlM tm 1' J ■1 1 and 1 0) '"* v'TW"i' .» J".-Jt7r *■^■■^T">-»^^^I*^.ctT»w".■^^'-M■••raL»Tw* i"-""*-*"***-- fai->^i Hiji.m.twpi 'i u 2 " 29 and 1 or 30 and 1 or 31 and 1 or 32 and 1 or u 3 u 28 " 2 " 29 " 2 " 30 " 2 " 31 " 2 " u 4 u 27 " 3 " 28 " 3 " 29 " 3 " 30 " 3 " a 5 u 26 " 4 " 27 " 4 " 28 " 4 " 29 " 4 " a (J a 25 " 5 " 26 " 5 " 27 " 5 " 28 " 5 " u 7 u 24 " 6 " 25 " 6 " 26 " 6 " 27 " 6 " cc 8 u 23 " 7 " 24 " 7 " 25 " 7 " 26 " 7 " u 9 a 22 " 8 " 23 " 8 " 24 " 8 " 25 " 8 " cc 10 a 21 " 9 " 22 " 9 " 23 " 9 " 24 " 9 " ^'11 " 20 " 10 " 21 " 10 " 22 " 10 " 23 " 10 " a .J2 »' 19 " 11 " 20 " 11 " 21 " 11 " 22 " 11 " ' " 13 " 18 " 12 " 19 " 12 " 20 " 12 " 21 " 12 " " 14 ah 17 " 13 " 18 " 13 " 19 " 13 " 20 " 13 " 2<) 16 " 14 " 17 " 14 " 18 " 14 " 19 " 14 " Ai'i.' 15 " 15 are 16 "15 are 17 "15 " 16 "16 are 18 " 15 " 17 "16 are : - -' -■■■ "/"■ - I^^HpMi 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 1133- tt40 '147 .154 161 168 175 182 489 8 + 8 0-. jii 8 16 80 88 152 -^60 24 ^2 40 48 56 64 72 96 104 112 120 1^8 136 144 176 184 192 200 208 ?16 ■ . Ji>r.ik V ■ --■ ■■'■"^-'i:, ;::;.. ,,rr^ • ., MENTAL ADDITION. . V Thirteenth Exercfse. . . ; t 1 :■ : .,/ ■ ... .)... ^ ■ '"'. 1 ? and 4 8 and 8 7 and 7 are 6 " 6 arc 16 "4 are 14 " 5 are cc j u 12 " 8 u 20 " 7 " 19 " 3 ^ « 20 " 9 a 27 " 8 cc 22 " 8 / / " 29 " 7 " 35 " 6 cc 30 « 7 A ( < *' 36 " 5 u 41 u 5 cc 37 cc 9 t cc ^ " 41 " 9 " 46 " 7 cc 46 cc 5 cc B « 50 " 3 " 53 " 9 " 51 " 8 A' 53 " 7 " 62 " 8 '' 59 <^ 9 CC ( " 60 " 8 " 70 " 5 cc 68 cc 7 cc 1^ " 68 " 9 " 75 " 4 " 75 " 6 " 1 u 77 " 4 cc 79 cc 3 cc 81 " 8 1 1 ** 81 " 5 " 86 " 6 cc 82 " 7 " 83 " 4 " 89 ^* 5 ' 94 " 9 u 94 u 6 cc 93 cc 7 " 103 " 5 '•'y^ *^ 100 " 8 " 100 " 9 " 108 " 6 41 " 108 " § " 109 " 5 cc 114 cc 4 + 1 *" 117 " 3 cc 114 cc 6 " 12Q i.... cc 118 cc 2 " 120 * 1. X ff tJ " 120 ,^.« Are 4i 25 + 25 €1 "^ ? Fourteenth Exerpise^ ^ 'CO 5( '^M 9 18 27 36 "^45 54 % % 81 ^0 99 108 117 126 135 .44jfc i53 162 11 110 -i'.; ; 10 20 30 40 50 60 70 1^0 ^0 10 n^^ 11041Q i3p m m 460 iTp dso m 20 120? -MI^'>?^^-^-i;:rv' ■'^'"■'■^"■^■■^.-^■:¥"^/^ Oi' v'- "•-- .:.:■-;:..•;';';:,;' v . . ' . -.^•t'.rC; :;;^^;' --k:.^;-;^-';.-S.-::' ■ . ^_-....:^^..:^.l^^ '.■'■', Z^-'' '- » 'v 7 and 7 4 " 5 u u (( u a u u 3 8 7 9 5 8 9 7 6 8 " 5 " 6 " 4 2 u "72 81 53 162 ^0 10 ) Sl^P 20 .#■• -13 — MBNTAL ADDITION. ■.^^.:' {'>" •^xrt 3 Fifteenth Exei '^ise. •'■.■'-■'••'*■... , ' ' ''■■• ',•; 11.; 2 nnd i are 5 a 12 '.c i^O ( ■ 30 (( 42 u 56 u 7? a 90 c; 110 C( 132 't it iC u 10 12 14 16 18 20 22 are 8 " 15 u 24 35 48 63 80 99 " 120 " 132 u If (C u u and 5 9 11 13 15 17 19 21 12 u u u u u a u 5 are 13 19 and 8 " 6 (( u ,-,V 26 34 45 54 66 86 " 107 " 132 u u u u u u u a u u u 7 8 11 9 12 20 21 25 ■>.C Sixteenth Exercise. ,v.; 41 40 39 38 37 36 35 34 33 32 12 3 4 5 6 7 8 9 10 Are 42 42 42 42 42 42 42 -42 42 42 25 24 23 22 21 -20 19 18 17 16 + 25 26 27 28 29 30 31 32 33 34 «:'• '^ ;:j 50 50 50 50 50 50 50 50 m 50 " 11 + 11 -^^ '^ • ^■•■^-^ 11 22 33 44 55 66 77 88 99 S 110 121 132 143 154 165 176 187 198fP 12 + 12 ,. .ft-:^^- :>*■ ^-r;:|SR 12 24 36 48 m 72 84 96 108 S^: 120 132. 144 156 168 180 192 204 216 '^S 11 >•■'/; v-? rt;<' --14 ' ' * MENTAL ADDITION. v.. • Seventeenth Exercise.- {+) 14 and 14 154 and 14 294 and 1 are 28 ' c 14 are i68 " 14 are 308 " 1 " 42 ' c 14 " 182 " 14 " 322 " 1 " 56 ' t 14 " 196 " 14 " 336 " 1 u 70 c i 14 a 210 " 14 « 350 " 1 a 84 c c 14 a 224 " 14 " 364 " 1 " 98 ■' i 14 " 238 "^ 14 " 378 '^ 1 u 112 ' c 14 " 252 " 14 " 392 " 1 " 126 * : 14 " 266 " 14 " 406 " 1 "^'140 ' t 44 « 280 " 14 " 420 " 1 " 154 " 294 „ ; " 434 Eiffhteenth Exercise. 31 30 29 28 27 26 25 24 23 2S + 11 12 13 14 15 16 17 18 19 2( Are 42 42 42 42 42 42 42 42 42 45 15 14 13 12 11 10 9 8 7 + 35 36 37 38 39 40 41 42 43 Are 50 50 50 50 50 50 50 50 50 5( 5 4 3 2 1 + 45 46 47 48 49 - Aie50 50 50 -50 50 13 + 13 13 26 39 52 65 78 91 104* 130 143 156 169 182 195 208 221 11' 23 140 1^ 15 150 16 20 200 4 25 •-^15 294 ancl 1 J 308 « li 322 " 1 336 C( 1 350 a 1 364 a 1 378 a 1 392 (( 1 406 C( 1 420 (( \ 434 42 + 18 60 + 17 77 + 16 93 + 15 108 + 14 122 + 13 MENTAL ADDITIX)N. Nineteenth Exercise. + 11 . +15 +19 4 15 + 17 70 - +22 92 + 14 106 + 23 , 51 + 9 60 + 19 . 79 ' + 14 93 + 13 106 + 17 41 + 23 64 + 28 92 + 32 149 + 21 17 + 17 34 + 17. 51 + 17 + 17 "85 + 17 102 + 17 ft ■Kit. 24 23 25 18 19 2( 42 42 42 8 42 7 43 44 50 50 5( ^■»*v 1 104 ir 8 221 231 135 + 12 147 + 11 129 + 23 152 + 48 123 + 1? 1C9 + 19 170 + 33 203 + 27 119 + 17 H36 + 17 • '•■■■i ,:5 158 200 158 230 ' ¥'j:'^ 10^' •■ Twentieth Exercise. 14 + 14 14 28 42 56 70 . 84 98 112 126 140 154 168 182 196 210 224 15+15 238 252 15 30 45 60 75 90 1 05 120 135 150 165 180 195 210 225 240 20 + 20 255 270 20 40 60 80 100 120 140 160 180 ^ 200 220 240 260 280 300 320 340 360 ,k-r w MENTAL ADDITION. TO ADO DOLLARS AND GENTS. Rule. — ^Add together the dollars and cents as ii simple numbers, and point off, mentally, the tw( last figures of the sum for cents. ? v ' ^ ': Thuis, m .25 + $0.75 = $2.00. EXERCISES. 20 cents + 30 cents + 40 cents + 50 cents- 22 cents + 33 cents + 44 cents + 55 cents = 18ceUts+ 27 cents H- 36 cents + 45 cents = 81 cents + 72 cents + 63 cents + 54 cents = 1.4( 1.5^ 1.2( 2.7( 100 cents + 200 cents + 300 cents + 400 cents -$10.0( 500 cents + 600 cents + 700 cents + 800 cents = 826.0( 111 cents + 222 cents + 333 cents + 444 cents=$ll.li 555 cents + 666 cents + 777 cents + 888-cents= $28.81 Add together $1.10 + $ 2.20 + $3.30 = $6.60. Find the sum of $20.20, $30.30, $40.40 * $90.90. Find the amount of $25.25, $75.75, $0.50 = $101.50. Add together $166.66 and $222.44 == $389.10. Find the sum of $0.99, $0.27, $0.18-: $1.44. Add together $1.11 + $2.22 + $3.33*= $6.66. Add together $20.01 +$18.02 + $14.09 = $52.12. Find the amount of $14.08, $15.10, $20 00 =$49.1 8. Men lown ^ss is jssene It <.' It it u it it It It It it It tt It tt It tt tt tt tt tt tt tt tt tt . tt tt tt tt « (( <( << tt MENTAL SUBTRACTION. Mental Subtraction consists in finding, mentally; [ow much one number exceeds another. The ex^ 3SS is called the remainder or difference. Thus, 9 ^ssened by 5 is equal to 4. SUBTRACTION table: ■^- ' "■■• ■ (-) '^ "^ ■ ^ Remainc T T T- T" TT TT T T TTTT \ •« i from 2 " II II II II II II II II II II II II II li Take.. 1 2 A- 3 3 4 4 5 5 6 6 7 7 8 9 10 11 12 13 14 (i 8 9 10 11 12 13 14 15 it 3 *' 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (1 4 " 4 5 6 i 8 9 10 11 12 13 14 15 16 17 it 5 " 5 6 7 8 9 10 11 12 13 14 15 16 17 18 It it 6 " '6 7 8 10 11 12 13 14 15 16 17 18 19 It tt 7 " 7 8 9 10 11 12 13 14 15 16 17 18 19 20 It tt 8 " 8 9 10 11 12 13 14 15 16 17 18 19 20 21 tt tt tt tt 9 " 10 " 9 10 11 12 13 14 15 16 17 18 19 20 21 22 10 11 12 13 14 15 16 17 18 19 20^ ^1 22 23 tt It 11 " 11 12 13 14 15 16 17 18 19 20 21 22 23 24 tt it 12 « 12 13 14 15 16 17 18 19 20 21 22 23 24 25 it tt 13 " 13 14 15 16 17 18 19 20 21 22 23 24 25 26 .tt tt tt tt 14 " 15 " 14 15 15 IG 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 26 27 25 26 27 28 a 16 " 16 17 18 19 20 21 00 23 24 25 26 27 28 29 ti it 17 " 17 18 19 20 21 22 23 24 25 26 27 28 29 30 a 18 " 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ■4 rt: , t . —IB— .;^':^1^?' J£JB:|fTAL Sy^TRACTIpf ..^^ First Exerdse, 'f ^f fS - : ■:„;s;■;■^3,__,^^:v^■i.J^?c From,,.,. 2 3 4 5 a 7 8 9 10 11 15 Take.^i^;...»l 2 3 4 5 6 T a ^ m 11 I ti « .y. '^fv. ■ ■ ■ ^emadnder....! 1 li 1 ir^^l 111 FromS:S«.3 4 5 6 7 8 9 10 11 12 W 1^6...... .1 2 3 4 5 6 7 8 9 10 11 Remainder... .2 2 2 2 2 2 2 2 2 2 From..M 4 5 6 7 8 9 10 11 12 13 H Take..... 1 2 3 4 5 3 7 8 9 10 Ij — — Mi^ ■■■ I IM .11 ^i^M*— i— — ^— .Mil— ^1— — ^— W^M— ^M>— 1 Remau^der/...3 3 3 3 3-^3 3 3 3 3 l^^^l^plfe^t 'Second Exercise."'''-%-:;.P'"-'' From .;..5 6 7 8 9 10 11 12 13 1| T^e, 1 2 3 4 5 6 7 8 9 11 0:&:'-^'^'::K:''r:.y — —. \ — , : Jlemainder 4 4 4 4 4 4 4 4 4 From........ 6 7 8 9 10 11 12 13 14 1| - Take 1 2 3 4 5 6 7 8 9 ll -mhv ■■ '■ . ^ Remainder 5 5 5 5 5 5 5 5 "5 From........ 7 8 9 10 11 12 13 14 15 \\ . Take.:... ...... ...1 * 3 4 5 6 7 8 9 11 Remaiiiaer......6 4 6 6 6 6 6 6 6 ^From..... ...8 9 10 1112 13 14 15 16 ll ^Take 1 23456 7 8 9 11 ■m. ■ ^"^ ■ ;:;-.:-/p5. .. ^ — Remainder......?. !(: Z .%"! 7 7 7 7 '^*'y^A >>....... 1 .. ■?•; .'■" ^^H '% I ;J^^*% ■ it^^!^!^ 1 ' k '■Wft' vs;'^-^- ■ ^H ^X: Hr 10 11 19 ^ m if^ 1 f i /*!r' 1ft ^ iijgii^XL stjSTRXtrW<, :,4",'2»^ TMrd ExeWiSfe. :'^^r.;^- M <;f:- 9 10 11 12- 13 II 15 16 2 3 A 5- 6 8 17 18 9 10 2 ^=2 ! 12 9 13 1 10 1 iTake lem. From Take JRem. iFrom Take Rem. 10 10 10 10 10 10 10- 10 10 10 8 8 8 8 8 8 8 8 8 8 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 9 9 9 9 9 9 9 9 9 9 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 3 3 12 13 ll 8 9 1 Poiirth ixfeiE. ■sfe fi.''j,'^'\:>}^i 4 4 13 8 14 9 5 •5 14 8 15 9 6 6 15 8 16 9 • 1 feom 20 21 22 23 §1 2§ 26 27 Take l9 20 21 22 23 24 25 26 Rem. From ITake Rem. From Take Rem. From Take Rem. %■ fS^f^";'. ;!^ 28 f9 27 28 i 1 1 1 , 1 y\ 1 1 1 1 21 22 23 ^ IB 2t 27 28 29 §0 19 20 21 22 23 24 25 26 27 2^ 2 2 2 2 2 2 2 2 2 2 n 23 24 25 26 27 28 29 30 31 19 20 ,21 22 23 ,24 25 26 27 28 3 3 3 3 3 1 3 3 3 3 3 23 24 25 26 tl 28 29 30 31 ^ 19 20 21 22 h 24 25 26 27 28 4 444 4 44444 '^Jj; , ■.;-.(; 'T't'tM^Uh^i^^ '•- '■^•. W'-s '# h :■( : ■M. :i-^':: i \- i From! Take Rem. From Take Rem. From Take Rem. From Take Rem. From Take Rem. From Take Rem. From Take Rem. — 2a— M E*N TAIi^'SUBTRAG TTO N..} ^ Fifth Exercise, . : H ^ . . ^' 24 25 26 27 28 29 30 19 20-21 22 23 24 25 1:i :' 5 5 5 5 5 5 5 25 26 27 28 29 30 31 3j 19 20 n .22 23 24 25 21 6^ 6 6 6 6 6 6 { 26 27 28 29 30 31 32 3i 19 20 21 22 23 24 25 21 .7 7 7 .7,7- .7 " ■ ii . Sixth Exercise. 27 28 29 30 31 32 19 20 21 22 23 24 33 25 3^ 2« 8; 8 .8 8 8 8 8 i 28 29 30 31 32 33 34 3J 19 20 21 22 23 24 25 2( 9 9 9 9 9 9 9 ( V 20 30 40 50 60 70 80 9( 12 14 16 18 20 22 24 26 8 16 24 32 40 48 56 64 21 31 41 51 61 71 81 91 12 13 14 15 16 17 18 19 ► 9 18 27 36 45 54 63 72 ■■■,,-^ '^> I.N..) l-i 30 25 3| 2 5 5 ( 50 31 3i >4 25 21 6 6 • 1 11 32 3; >4 25 1 33 3^ 25 2( 8 8 8 J 34 I 25 35 2C ) 9 9 ) 80 : 24 26 56 64 81 18 91 19 63 72 ^ 21 - MENTAL SUBTRACTION. ; ; Seventh Exercise. v^ - (-) ;.i' ■,t-t iFrom 11 12 13 14 15 16 17 18 19 20 Take 9999999999 Rem. 2 3 4 5 6 7 8 9 10 11 From Take Rem. 12 8 13 8 14 8 15 8 10 8 17 8 18 8 19 8 20 8 21 8 4 5 6 r 8 9 10 11 12 13 From Take 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 Rem. From Take Rem. From Take Rem. From Take Rem. From Take Rem. 14 15 16 17 18 19 20 21 22 23 11 M ■M 6 7 8 9 10 11 12 13 14 15 :a Eighth Kxercise • „ it 14 6 15 6 16 6 17 18 6 6 19 6 20 6 21 6 22 6 23 i 6 • ••/; 8 9 10 11 12 13 14 15 16 17 ,4 15 5 16 5 17 5 18 19 5 5. 20 5 21 5 22 5 23 5 24 ■5 :,| 10 11 12 13 14 15 16 17 18 19 16 4 17 4 18 4 19 20 4.4 21 4 22 4 23 4 24 4 25 ■ m 4 -y:^ 12 13 14 15 16 17 18 19 20 21 17 3 18 3 19 3 20 21 3 3 22 3 23 3 24 3 25 3 20. ■ i+ 3 't- i'l ^cr From Take ,...;■.■•: —22— ".;■ ■ ■ I .MENTAL SUBTRACTION. M -Ninth Exercise. 241 + 15 Rem. .- ' From Take ,, Rem. From Take \l Rem. 17 18 19 20 21 22 23 24 25 2| — ' 8 9 10 11 12 13 14 15 16 11 39 1-12 9999999 91 — 17 18 19 20 21 22 23 24 25 2 27 8 9 10 11 12 13 14 15 l| + ^* 10 10 10 10-10 10 10 10 10 11 17 18 19 20 21 22 23 24 25 % 6 7 8 9 10 11 12 13 14 41 41 1-18 23 + 27 50 -36 14 + 42' 12 12 12 12 12 12 12 12 12 12| ^ 50 50 50 50 50 50 50 50 50 5o|— 24 16 17 18 19 20 21 22 23 24 25L 32 Rem. 34 33 32 31 . 30 .29 28 27 26 25| + 19 From Take Rem. From Take 11 11 11 11 11 11 11 11 11 11 ■ ' ' Tenth Exercise; - ■ .^- 17 5 18 19 20 21 22 6 7 8 9 10 23 24 11 ,12 2'S' '2C 13 14 From Take 100 33 105 44 110 55 120 66 125 77 130 88 135 99 51 —27 Rem. 67 61 From 101 .202 Take 25 35 55 303 45 54 48 42 404 505 606 55 66 77 36 1 f07 88 24 7071 +12 Rem. 76 167 258 349 439 529 619 3e •» '.. .. iX, , ,• .yvf -r,?* ■f ■■■>■•>«,,■ V » i '^. ON. ;■• "—23— '■ , ■ ■ MENTAL ADDITION AND SUBrRACXiON. ^ J 24 25 si t 15 16 1! 24 + 15 1 9 9 1 '■ '24 14 25 15 i 10 10 1( 24 25 2i 13 14 4i 11 n 1 -.. ) V 24 .12 25 13 2G 14 12 12 12 50 23 50 24 50 25 rtwf /-V y-» 27 + 14 41 I-IB, 23 N + 27 27 26 25 130 135 88 99 42 3G 606 707 77 88 529 619 14 + 42' 56 —24 32 + 19 24 + 12 36 54 . + 33 39 87 —12 —19 68 + 31 99 —33 66 + 25 50 • 91 —36 —11 80 + 19 99 —17 82 + 34 51 116 —27 —18 98 + 12 110 Exercises. 88 + 32 120 —77 43 + 82 125- —75 50 + 66 116 —19 97 + 17 114 —18 96 + 33 129 —19 110 + 12 122 60 + 17 77 —43 34 + 12 46 —13 33 + 21 54 —25 29 + 9 38 —14 24 + 47 71 —19 52 + 12 64 24 + 15 89 25 + 28 si —16 37 + 18 55 —18 37 + 32 m —19 50 + 33 m —7 76 + 12 74 + 9 83 —11 72 + 27 99 —18 81 + 13 94 —17 77 + 11 88 -22 ■ 66 + 16 82 —27 55 + 12 67 '■' i^ !':»■ (-■: f"[ Vr n t -ym- : _24-- MENTAL SUBTRACTION. * T To subtract dollars and cents. Ment ly, the Rule. — Subtract as in simple numbers, and pointBof titnel off, mentally, the two last figures of the remainderwiw^^iPH for cents. (the pro] f^Thus, $2.00 — 60.25 = $1.75. ';; . Exercises. -»•; . ^ ■ ■ :■ $100— $99.00 = $0.91. $20.20— $9.09 = $11.11. $120— $19.75 = $100.25. $13.25— $3.50 = $9.75. \ I 1 1.- ADDITION AND SUBTRACTION. Exercises, Gents 1 + 2 Gents 10 + 11 Gents 19 + 20 = 3-" 3 = 21 " 12 = 39 " 21 u 6 " 4 " 33 " 13 " 60 " 22 " 10 " 5 a 46 a 14 " 82 " 23 " 15 " 6 " GO ^' 15 " 105 " 24 cc 21 a 7 " 75 " 16 " 129 " 25 " 28 " 8 a 91 a 17 " 154 " 26 " 36 " 9 " 108 " 18 " 180 " 27 " 45 ^' 126 " 207 .. 165 44 570 116 975 188 = 121 = 454 = 787 44 -f 116 + = $5.70 188 + = $9.75 = $1.65 -B-: ■*^\ MENTAL MULTIPLICATION. Mental Multiplication consists in finding, mental- y, the amount of a number, repeated any number s, and pointBof times. The number to be repeated is called the i'emainder|/)iw/r/jo//"(?anrf, the other, the multiplier, and the result, the product. Thus, 7x5 are 35 ; 35 x 3 are 105 ; etc. « MULTIPLICATION TABLE. (x) 11.11. = «9.75. 19 + 20" 39 " 21 GO " 22 82 " 23 05 " 24 29 " 25 'A " 2(i ^0 " 27 11 " '5—188 !7 1 2 3 4 8 12 16 20 24 28 5 10 15 20 25 30 35 G 12 18 24 30 36 42 7 14 21 8 9 10 11 12 2 4 6 G 9 12 15 18 16 18 20 22 24 24 27 30 33 36 4 8 28 32 36 40 44 48 5 10 35 42 46 45 50 55 60 6 12 48 54 60 66 72 84 7 8 14 16 21 49 56 63 .70 77 24 32 36 46 45 48 54 56 63 64 72 80 88 96 108 9 18 27 72 81 90 99 10 11 12 20 22 24 30 33 36 40 50 60 70 80 90 100 110 120 132 144 44 48 55 60 66 72 77 84 88 99 110 121 96 108 120 132 a , m V>7 ■■ ' ^ . •—26— . , , MENTAL MULTIPLICATION. n . , First Exercise. f'U; /M .... ' , {,X) .. . •. Twice 1 2 3 4 5 6 7 8 9 10 11 12| aro ...'...!. .2 4 G 8 10 12 14 16 18 20 22 24 3 times 1 2 3 4 5 6 7 8 9 10 11 12] are 3 6 9 12 15 18 21 24 27 30 33 361 Second Exercise. 4 times... ..1 2 3 4 5 6 7 8 9 10 11 12 are .'.4 8 12 16 20 24 28 32 36 40 44 48 5 times 1 2 3 4 5 6 7 8 9 10 11 12 are 5 10 15 20 25 30 35 40 45 50 55 60 Third Exercise. 6 times 1 2 3 4 5 7 8 9 lO 11 12 are 6 12 18 24 30 36 42 48 54 00 66 72 7 times 1 2 3 4 5 6 7 8 9 10 11 12 are 7 14 21 28 35 42 49 56 63 70 77 84 Fourth Exercise. 8 times 1 2 3 4 5 6 7 8 9 10 11 12 arc 8 16 24 32 40 48 56 64 72 80 88 96 9 times.. .1 2 3 4 5 6 7 8 9 10 11 12 are 9 18 27 36 45 54 63 72 81 90 99 103 ^ ' ,■«**. — 27 — .■*■''**• 66 72 11 12 77 84 11 12 88 96 11 12 99 103 MENTAL MULTIPLICATION. Fifth Exercise. - / ' lOtimei^l 2 3 4 5 6 7 8 9 10 11 12 are 10^ 30 40 50 60 70 80 90 100 110 120 11 times 12 3 4 5 6 7 8 9 10 11 12 are 11 22 33 44 55 66 77 88 99 110 121 132 Sixth Exercise. 12 times 12 3 4 5 6 7 8 9 10 11 12 are 12 24 36 48 60 72 84 96 108 120 132 144 13 times 2 3 4 5 6 7 8 9 10 11 12 are 26 39 52 65 78 91 104 117 130 143 156 Seventh Exercise. 14 times 2 3 4 5 6 7 8 9 10 11 12 are 28 42 56 70 84 98 112 126 140 154 168 15 times 2 3 4 5 6 7 8- 9 10 11 12 are 30 45 60 75 90 105 120 135 150 165 180 Eighth Exercise. 16 times 2 3 4 5 6 7 8 9 10 11 12 are 32^8 64 80 96 112 128 144 160 176 192 17 times 2^456 8 9 10 11 12 are 34 51 68 85 102 119 136 153 170 187 204 ' t f '•^^i"^;!!?;;*^}:? 'iCBNTAL multiplication. •';■/•:' :*!" J WmS:i'>^M Ninth Exercise. :;;v,,t,.;::\:r^^:-;J, ■.•^;';Vli!'- ^, ^^.^Si^iiv 18 times 2 3 4 5 6 7 8 9 10 11 12i are 36 54 72 90 108 126 144 162 180 l^a 216' 19 times 2 3 4 5 6 a^*^ t> 10 11 12 are 38 57 76 95 114 133 152 171 190 209 228 Tenth Exercisei*^-.^:;K-t''"'^' Twice 9 or 3 times 6 or 6 times 3 are 18. u io " 4 " 5 '' 5 » 4 "20. « 15 " 5 " 6 " 6 " 5 " 30. « 16 " 4 '' 8 " 8 " 4 " 32. '■^n)^] Eleventh |]xereiseV '% 2x12^ 3x 8 4x 6 6x 4 8x 3 12x 2 3x12-^ 4x 9 :54. 6x6 9x 4 12x 3 18x 2 -%4xl8^ '^^"6x12 I }'=36. 8x 9 j. = 72. 9x 8 12 X 6 18 X 4 :s„,.'^'--Ji-A^ Twelfth ExereiseV 2x12:== 24. 3xl2=3e. 4x12=48. 5x12-60. 6 X 12= 72. 7x12 = 84. IV ^W??^ ' 12 + 12 = 24. 12 + 12 + 12 = 36. '^-'-S-.^^3'h- 12 + 12 + 12 + 12=48. . -fe»i^:- 12 + 12 + 12 + 12 + 12= 60. -^W'-.^^ 12+12 + 12 + 12 + 12 + 12=72. -^ 12 + 12 + 12 + 12 + 12 + 12 + 12 = 84. :-r(.^^: :^'mv- \:A'^i 20tim( s.»>. are 21 tim^ are 22 time are 23timd are ■^1 24 time are-g 25timi are ^ 1.- multi .,,«Wjfc -'^ V -' * w » > 10 11 12| 10 198 216 10 11 12 10 209 228 'e 18. :44l.w.: ' 20.. 30. 32. .^ = 72. V'"^' . i* ' ^-'4*^- *f 72. '-^ 12 = 84. ,-, :xx^=^^ . ., ;;; :;-•■• w^v ■ '^':-'--'"-'- ' ■ ',•5'- ■■^''w'v-:,-'.. ■ :^:J;v' MENTAL MULTIPLICATION. ' \|5> ;H "'" ^^ ^___ V''' -;■"'*".■ '(^"^t '' '.■"-■./ ■ Thirteenth Exercise. vV-i&-Wm^ (x) ' "' -■■'r--v-;r^f-v-;;^'' 20tiines2 3 4 5 6 7 8 9 10 11 12 are 40 60 80 100 120 140 160 180 200 220 240 21times2 3 4 5 & 7 8 9 10 11 12 are 42 63 84 105 126 147 168 189 210 231 252 Fourteenth Exercise. 22times2 3 4 5 6 7 8 9 10 11 12 are 44 66 88 110 132 154 176 198 220 242 264 23times2 3 4 5 6 7 8 9 10 11 12 are 46 69 92 115 138 161 784^207 230 253 276 \^ Fifteenth Exercise. 24times2 3 4 5 6 7 8 9 10 11 12 are 48 72 96 120 144 163 192 216 240 264 288 25times2 3 4 5 6 7 8 9 10 11 12 are 50 75100 125 150 175 200 225 250 275 300 %iilii^ Sixteenth Exercise. 9 + l-_2x4 = 32 8 + 2—3x5 = 35 7 + 3—4x6 = 36 6 + 4—5x7=35 5 + 5->_6x8=32 10 + 5—6x4-36 12 + 3—7x5 = 40 11+4—8x6 = 42 ,9 + 6—5x7=70 8 + 7— 4x8=88 1.— To multiply by 10. 100, 1000, &c. Rule.-^Annex, mentally, as many ciphers to the multii/licand as the multiplier contains ciphers, ,wii "''/i;?-:^' •i . in , l-.ii W .- M — 30— ^ MENTAL MULTIPLICATION. 2.— To multiply by 20, 30, 40, 50, 60, 70, 80 an J '^^ by 90. I J^^' ■.1.;-; "'■i^ -u. - .-^"^; „ . pOff) Rule. — ^Anhex, mentally, to the multiplicand a cip pher and multiply by 2 for 20 ; by 3 for 30 ; by for 40 ; by 5 for 50 ; by 6 for 60 ; by 7 for 70 ; by 81 | for 80 and by 9 for 90. 2. 3. — To multiply by 200, 300, 400, 500^ 600, 700,| 800 and by 900. Rule.— /Vnnex, mentally, to the multiplicand two I ciphers and multiply by 2 for 200 ; by 3 for 300 ; ' by 4 for 400 ; by 5 for 500 ; by 6 for 600 ; by 7 for| 700 ; by 8 for 800 and by 9 for 900. 1. Multiply 22 by 10.— by 100.- by 1000. 2. Multiply -33 by 20.— by 30. — by 40. — by 50. _ by 60. — by 70. — by 80. — by 90. 3. Multiply 44 by 200. — by 300. — by 400. — by 506. — by 600. — by 700. — by 800— by 900. 1. Multiply 55 by 10.— by 100.— by 1 000. 2. Multiply 66 by 20.— by 30— by 40.— by ^0.— by 60.— by 70.— by 80.— by 90. 3. Multiply 77 by 200. -by 300.— by 400.— by 500. —by 600.— by 700.— by 800.- by 900. MEN-yAL MULTIPLICATION. To multiply dollars and cents. Rule. — ^Multiply as in simple numbers, and poin |off, mentally, tne two right hand figures for cents. ■"'■- ^'fy': Exercises. ' '" ^ ■' " ■■"'■^^v i" ■■iili^i t^ ^ V- *.- » ''-r 1. What cost 6 lbs. of sugar, at 12 cents ^r lb ? 6x12 = $0.72. 2. What cost 8 lbs. of butter, at 20 cents per i!) ? ' 8x20 -=$1.60. V f 3 What cost 12 lbs. of tea, at 40 cents per lb ? .J :_,.... 12 X 4^ ■'its '■* * - 4. What cost 20 lbs. of cheese, at 25 cents per lb ? , 20x25»$5.00. i . /• 1. 'What cost 100 pencils, at 2 cents e'kch? .... „, 100x2 = $2.00. ^^ ; 2. What cost 200 oranges, at 3 cents ^ach ? v 200x3 = $6.00. „. .: 3. What cost 300 slates, at 5 cents eia6hf ] * 300x5 = $'i5.00. 4. What cost 20 doz. of apples, at 20 cents per doz.? 20x20=14.00. .. , ., , 1. What cost 20 yards of cloth, at 20 cents per yd. ? 20x20 = $4.00. 2. What cost 100 lbs.' of sugar, at 10 cents per lb ? 100xiO=»$10.00. 3. What cost 90 lbs. of tea, at 90 cents per lb ? 90x90 = $81 .00. 4. What cost 400 lbs. of cheese, at 60 cents per lb ? 400x60=$24a00. «| .. > *■■■• > .1,1 r Rule. — Reduce dollars to cents by taking away, mentally, the decimal points, and divide as m simple [numbers. The quotient v^rill be a simple num^r. :■ Eighth Exercise. C t. I $10.20-7-4 = 82.55. $12.12^-12 = ^1.01. % 3.00-f-4 = $0.75.— $ 4.20-r- 7=$0.60. 8 9 m f Ninth Exercise. ^^^ (Mi SCELLA.NEOUS QUESTIONS.) 1. In 100,000 certs, how many dollars? 2. In 10,000 farthings, how many fivepences? 3. In 24,000 cents, how many dollars? 4. In 24^00 shillings, how many nounds ? 5.' In 55,555 cents, how many dollars ? > 6. How many dollars are there in 2480 cents? 7. How many pounds are there in 1000 dollars ? 8. How many fourpences are there in 1000 pence? 9. How many cents are there in 10000 mills? y^* 10. How many pence are there in 4848 farthings? SM: iV .' \m\ W MENTAL DIVISION, Tenth Exercise. ■ .-. ■/ , V ? 2 into 3 9 11 13 15 17 times 1 + 12 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7+1 8 + 1 3 into 4 5 7 8 10 11 13 14 times 1 + 1 1+2 2 + 1 2 + 2 3 + 1 3 + 2 4 + 1 4 + 2 4 into 5 8 7 9 10 11 13 14 times l.+ l 1 + 2 1 + 3 2 + 1 2 + 2 2 + 3 3 + 1 3 + 2 Eleventh Exercise. > , > 5 into 6 7 8 9 11 12 13 14 t^Jh . I - m ^Ml- -T - - ■ - IIBI 11 ^1 ■ _l I 111 times 1 + 1 1 + 2 1 + 3 1 + 4 2 + 1 2 + 2 2 + 3 2 + 4 6 into 7 8 9 10 . 11 12 13 14 times 1+11 + 2 1 + 3 1 + 4 1 + 5 2 2 + 12 + 2 7 into 8 9 10 11 12 13 14 15 ■•":■:'*■■:■ , i , , , , , ■ . _— ____i___.— . times 1 + 11 + 2 1 + 3 1 + 4 1 + 5 1 + 6 2 2+1 / ; \^ Twelfth Exercise. 8 into 9 10 11 12 13 14 15 16 times 1 + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 2 9 into 9 10 11 12 13 14 15 1.6' times 1 1.+ 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 10 into 10 15 20 25 30 35 40 45 times IJ 2 2i 3i ^ [ENTi 4-1 8 G + 5 7 + 8 5 + 9- 3 + 10-1 7 + 5- 8 + 9- 9 + 7- 3 + 14- 7 + 10- 9 + 5- + 12- 8 + 10- 5 + 16- 9 + 18- G + 15- 8 + 5- ■■1..;,' V V-'; •■■',T ". ■ % ■■ ' - ■ '.y 15 17 7 + 1 8 + 1 13 14 4 + 1 4 + 2 13 14 3 + 1 3 + 2 14 2+3 2 + 4 3 14 2 + 1 2 + 2 15 2+1 16 + 7 2 IG- + 6 1 + 7 ) 45 — 37 — lENTAL ADDITION, SUBTRACTION, - JLTIPLICATION AND DIVISION. •^ .;*■/' -^r'^ Exercises. -. ■,,. .. ^ |4^ 8— Ix 3-7-11= 3 0+ 5— 2x 4-+ 6= 6 7+ 8— 3x 5-=-10= 6 5^. 9— 4x 6-+12- 5 13 + 10— 5x 7-^ 8- 7 7+ 5_ 6x 8-^12= 4 |8+ 9— 7x 9-5-10= 9 9+ 7_ 8xl0-f-20= 4 3 + 14_-. 9x12- 7 + 10-. 5x 9 |9+ 5-_ 8x10 10+12— 11 X C- -24= 4 6 = 18 6 = 10 - 3 = 22 8 + 10- 5 + 16- 9 + 18- G + 15- ■6x12 • 3x 2 • 7x 3 ■11 X 12- 24: 6 6: -10 = 6 6 iO 12 8+ 5- 12+14- 13 + 11- 10 + 12- 7x12 6x 5- 6x 3- 8x 6- 8= 9 ■10 = 10 ■ 2 = 27 •12= 7 I 2+12- 7+ 8- 5+17- 7+12- 9x 6- 4x12- 2x 8- 7 X 12- ■15= 6 - 6 = 22 ■16=10 - 4 = 36 10+ 9— 7xl2-r 6 = 24 10+ 9— 7x 8-f-16= 6 14+ 8— lOx 5-f-10= 6 7+ 9— 6x10-^25= 4 11 + 12— 3x 6-^12=10 12 + 13— 5x 5-f-10 = 10 8 + 14— ,2 X 8-^-16 = 10 9+ 9— 6x 5-r- 6 = 10 8+ 7- 10+ 5- 17+ 7- 16+ 6- 3x 8.+ 12= 8 3x12^ 6 = 24 8x 4-f- 8= 8 2x20-4-10 = 40 8+ 8— 6x20-+ 25= 8 9+ 7__ 8x 8-4-16= 4 10+ 6— Ix 3-- 5= 9 11+ 5— ax 10-+ 5 = 26 5- 12 + 6+ 9- 13 + 13- 12+ 9- 8x10-+ 2 = 45 3x7-+. 3=- 28 6x 5-i- 4 = 25 Ix 6-^12=^10 7+ 9— 4x 5-- 3 = 20 8+ 5— 7x 6^12= 3 14 + 13— 7x 3-r-10= 6 18 + 17— 17 x 5---10-r: 9 I V ■ IV ■'■;.■ ^': w ► ( "- - . * ■ ■;»•> 1C. .\ I MENTAL ARITHMETIC. !: ■' ■;■« i :i -; ■J-' SECOND FABT. (1) i ":l^'' TABLE8 OP MONEY, A\ EIGHTS, MEASURES, Ac. M'- :|i •>- - r? ■< 2 farthings 2 half-t)fence 2 six-pences 2 yorK-shillings 2 shillings 2 dollars 2 pounds 2 pints 2 quarts 2 gallons 2 pecks 2 strikes 2 bushels 2 hogsheads 2 pipes... r.T...... 2 barrels 2 cloves 2 stones 2 days 2 weeks 2 months make 1 1 ", 1 25 40 10 8 1 f 48 15 60 half-penny] penny. shilling, s. cents. cents. shillings. dollars. quart. gallon. peck. strike. bushel. coom. pipe. tun. puncheon. stone. tod. hours. days. days. 1 Note. — It is indispensably necessary that the pupil should bo thoroughly acquainted with the prececding tables before advancing? further. •' ^ - ^; * I "?^^ -^ »^ * ' ' '■ > - . ^-i , — 30 — - MENTAL ARITHMETIC. II - Id scruples make 1 dram. 3 quarters of a yard " 1 Flemish ell. 3 barley-corns " 1 inch. . . i 3 feeti " 1 yard. ' .| Smiles " 1 league. 3 barrels " 1 butt. 3 bushels " 1 sack of coalfi. >• 1 3 feet, 3J inches (eng; m.) " 1 metre. |4 farthings mak6 1 penny. :''.'' ;, 4 pence.. * " 1 groat. 7.11 •• 14 nails " 1 quarter of a yai'dL l4 quarters ** 1 yard. U quarts " 1 gallon. ; '^. "* 14 hogsheads " 1 tun. '''^';^^ ,. |4 weeks " 1 month. • ' '•; '; |4 roods " 1 acre of land. ' * ■%'• , itf • ■ ■ *■:.■.:-■ '■a . ■"■•;, •'■'■■' ' . ' /, ■ '/'i ; > • ' |5 cents...... make 3 pence. 7 gallons " 28 quarts. 7 dollars " 35 sliillings. ' 7 shillings " 84 pence. s* 7 dozen " 84 articles. 7pounds£ " 28 doUars. :' • VII ' 8 drams make 1 ounce. 8 ounces " 1 half-pound. 8 furlongs " 1 mile (5280 feet.) 8 gallons " 1 firkin of soap. 64 lhi\ 8 farthings " 2 pence (3 J cents.) 8 dollars " 2 pounds. 8 shillings " 96 pence. 8 dozen " 96 articles. 1. Add five successively to 40. — 100. to 120. '' 2. Count from 25 backwards to 1.- - — flrom 100. -to 50. to 80.— tol —from 50. from 75.| i - - ■'• ■ ■: • : '■■ ■ •* — 41— ' ■ '■' V- ' MENTAL ARITHMETIC. Vlil ' ■ 9 feet make 1 square yard. 9 inches " 1 span or palm hour. ■ 9 gallons " 1 urkin. . v J 9 pence "^ 15 cents. \ 9 leagues " 2"^ miles. \' j 9 barley corns " 3 inches. ^ , ^ ivr/-' 9 scruples. " 3 drams. . r ";;^*^ 9 dozen " 108 articles. ^ ^ "lOmills make *1 cent. ' :• ^^ "10 cents " 1 dime. (6 pence.) 10 dimes " 1 dollar $ : /? 10 dollars " 1 eagle. ./.>-:.' "^ ' "lOeagles " 100 dollars. "^ '^^ ; 1 10 square chains " 1 acre. - - * >'; 10 gallons of Paris ... " 1 Canadian busheL^ " lOleagues *<,. 30miles. ■ - -'■V.'f'-,'' ■• ■'- ■:-■■'.' ■ ' '■ : ■me'-". '' '" ' . I ■ .' ■■ ■ ''/%■■.•-;;>. i I :«'¥t-r'- -,-- . ■ ■ -ifv-'i H'^ - ' * ■ ' » ' ,-'■■'' - . '^ ^■ '■■/■ ' feet.) 112 pence make 1 shilling. *; ; i > oap. 64 lbs.1 1 2 ounces " 1 lb. Troy. ' ; : v^'^' ^ J : J^, ents.) 1 12 lines " ^ ^^^^'^ i^ 12 inches m?w- " 1 foot. ' ''^^,:^'i^^^;.^i 12 articles ...lyUis*. " 1 dozen. *^^ 't T i,; 12 signs ,...^Z-^ " 1 circle. . - ^j^'-; ■ ^^.W-; 12 months " 1 year. ■' ;!^^!;fe X OA ,-12 French bushels... " 1 pipe oflime^T^t^ . . •■ » fpjjg (jgjj|. pjgQQ jg Qjjjg jjjgij jjj diameter, and 100 weigh one tb. Avoirdupois. (Canadian money.; \'''''-.jr-;:^';^^^-^f;'-.i I ' I I'. li! — 4? — XI 14 pounds, lbs make, 1 stone. 14 grainSi, french m., " 1 scruple. 1 4 farthings " 3 J pence. 14 pence " 56 farthingfi. 1 4 shillings " 1 68 pence. 1 4 dollars. " 70 shillingB. 14 pounds.... " 66 dollars* 14 leagues. .^,..M........ " 42inile& XII 15 cents , make 9 pence. 1 5 pence " 25 cents. 1 5 shillings " 3 dQllars. 15 miles... " 5 leagues. 15 feet " 180 inches. 1 5 minutes " i. of an hour. 15 days " Jofamontl]^^ 15 dozen, " 180 axtiqles;. xin 1 6 drams make 1 ounce. 16 ounces " 1 pound, fib. 16 nails " 1 yard. 16 yards " 48 feet 16 leagues " 48 miles. 16 farthings " 4 pence. 16dollars " 4 pounds. 16 pounds " 64 dollars. 1. Count threes to 144 and backwards.— — Count tens 200 and backwards. 2. Toll, mQ one-tentti part of 1000. of 2000. of' of 4000. MBNTAL ARITHMETIC. XIV 18 feet .tnake 1 perch. 18 gallons " 1 kilderkin. 18 pence " 30 cents. \Sframs " 3 dollars. 18 shillings " 216 pence. 18 feet " 216 inches. 18 years " 216 months. 18 dozen ...*.... " 216 articles. XV 20 cents. .make 1 shilling. 20 shillings " " 1 pound. £. (240 d) 20 penny weights ' ^ 1 oimce. 20 hundredweight... " 1 ton. 20 articles " 1 score. 20 quires of paper. " 1 ream. 20 leagues " 60 miles. ^ 20doz " 240 articles. XVI 21 shillings ster... make 1 guinea. 21 chaldrons " 1 score of coals 21 miles ''^ 7 leagues. 21 feet " 7 yards. 21 days " 3 weeks. 21 gallons " i barrel of salmon. 21 dozen " 252 articles. 21 years " the age of majority. 1 . 20+ 13—1 Jrrhow many ? 1 5+ IT— 7==how many ? 20-1- 36=how many? 2. "W^hat is the cube of 3, added to 5 score ? What is one- fourth and tree-fourths of a pound?— ^-of a sovereign? — 44 -- MENTAL ARITHMETIC. XVII 24 grains Troy make 24 sheets of paper 24 hours 24 farthings 24 pence 24 dollars ^4 ax vicies ••••••••••••••• 24 roods... 1 penny weight. . 1 quire. 1 day. 6 pence (10 cents.) 40 cents. 6 pounds. 2 dozen. 6 acres. i XVIII 25 cents...' ......<.. make 25 shillings " 25 dollars " 25 pounds 25 years 25 dozen " 25 feet " 25 leagues (4 (( 15 pence. 5 dollars. 125 shillings. 100 dollars. J of a century. 300 articles. 300 inches. 75 miles. XIX 27 cubic feet make 27 pounds 27 dollars 27 shillings 27 pence 27 inches 27 miles 27 quarters 1 cubic yard. 108 dollars. 135 shillings. 324 pence. 108 farthings. 12 nails. 9 leagues. 9 Flemish ell. 1. 4xl2+6x6=how many? 4x9-f6x8r=how many? 7x7 — 'i=ihow many ? 2. How many lbs. of meat are there in 10 stones? in 12 stones ? in 14 stones ? , ^w many? — in 12 » — 45-: MENTAL ARITHME'taC. • - XX 28 pounds, lbs make 1 quarter. 28 dollars " 7 pounds. 28 pounds " 112 dollars. 28 leagues " 84 miles. 28 acres " 112 roods. 28 gallons " 112 quarts. 28 bushels " 112pecks. 28 tens " 280. XXI 30 shillings .make 1 moidore. 30 degrees " 1 sign. 30 seconds '-'• J minute. 30 minutes " Jhour. - 30 dollars " 3 eagles. 30 miles '-'• 10 leagues. 30 leagues " 90 miles. 30 days .• " the months of April, June, September and November. XXII 36 gallons make 1 barrel. 36 bushels, canad.m.. " 1 lead of coals. 30 inches : " 1 yard. 36 articles.. " 3 dozen. 30 sacks " 3 lasts. 36 quarts " 9 gallons. 36 square feet....... " 4 square yards. 36 miles " 12 leagues. 1. 8x8+4x16= how many ?—-- 20x3+ 15x4+2 = how many ? 2. How many days in the months of May, June and July, added together ? - i4- S^ii Wr m. II. I -I I«- — 46 — I* MENTAL ARITHMETIC. XXIII 40 perches . . ; make 1 furlong. 40 rods or jjoles " 1 rood. 40 square perches '' 1 square rood. 40 feefc of round tim.. " i ton or load. 40 articles " 2 score. 40shillmgs " 2 pounds. 40 dollars " . 4 eagles. 40 leagues " 120miles. . XXIV 42 gallons.! make 1 tierce. 42 cubic feet '' 1 ton of shipping. 42 gallons « 1 barrel of salmon. 42 shillings '' .2 guineas. 42 days " G weeks. 42 quarters '' 7FIomishelL ■ 42 ounces " 2| lbs. 42 drams-. " 2| oz. , XXV 48 farthings make I shilling, s. 48 pence " 80 cents. 48 dollars " 12 pounds. 48 ounces Troy " 4 lbs. Troy. 48 lines '< 4 inches. 48 inches " 4 feet. 48 articles ...; '^ 4 dozen. 48 leagues " 144 miles. 1. 10x10+10— 40 x2+7=how many? 12x4+2--10x'i •~5=how many ? 2. How many two-pences §re thera in a dollar? how many groats ? 50 shil 50 feet 50 cen 50 yea 50 leag 50 yar( 50 pou 50 tens 56 poui 1 6 poui 56 poui 56 dolli 56 poui| 56 lurh 56 leag 56 doze 60 fram 60 seco 60 min 60 mih 60 grai 60 poui 60 pen 60 arti 1. Ho !^30? — 2. In in 480 y od. d. [)ping. jalmon. *• .■ - \ _^ . ^ .. ' ■ ■ > -I. / . — 47 — J4BNTAL ARITHMESTia XXVI 50 shillings * make 1 eagle. 50 feet of newn tim.. " 1 ton or load. 50 cents ,. " ^ of a dollar. 50 yearg " J of a century. 50 leagues " 150 miles. 50 yards " 150 feet. 50 pounds " 200 dollars. . 50 tens " 500. XXVIl 56 pounds, lbs make 1 firkin of butter. ^6 pounds, fibs " „ J hundred- weight 56 pounds, lbs " 1 truss of old hay. 50 dollars *^ 14 pounds. 56 pounds " 224 dollars., 56 furlongs " 7 miles. 56 leagues '' 168 miles. 56 dozen " 672 articles. XXVIII &0 francs make 1 eagle. 60 seconds '-' 1 minute. 60 minutes " 1 hour. 60 miles " 1 degree. 60 grains ''• 1 dram. 60 pounds, lbs " 1 truss of new hay. 60 pence " 1 dollar. 60 articles " 5 dozen. ill M:- }-2--.10xi how 1. How many pence in $10? in $20? in $25?- — in 5^30 ? in $50 ? 2. In 120 pence, how many dollars? in 240 pence?— in 480 peueo ? in 960 p^nce ? W m w >l — 48— s MENTAL ARITHMETIC. XXIX 63 gallons. make 1 hogshead. : ^ 63 days..... ", 9 weeks. t 63 miles " 21 leagues 63 dozen " 756 articles. 64 pounds, lbs " 1 firkin of soap. 64 dollars " 16 pounds. 64 drams " 4 ounces. ; 64 ounces '' 4 pounds, lbs. XXX 66 pencfe ..: make 1 French dollar. 66 feet " 11 fathoms. 66 miles " 22 leagues." ■ : . 66 yards '' 108 feet. ^ 72 farthings " 30 cents, (18 pence.) 72 pence '• 6 shillings, 72 dollars " 18 pounds. 72 pounds '' 288 dollars. XXXI 80 strikes make 1 wey. 80 furlongs '' 10 miles. 80 poles " 2 furlongs. 80 cents " 4 shillings. 84 quarts *' J tierce. 84 pence " 7 shillings. J 84 articles '' 7 dozen. 84 inches " " , 7 feet. 1. In 144 pence, how many shillings? in 240 pence, how many dollars ? 2. In 80 lbs, how lbs? in 640 lbs ?- many scores ?— — in 1280 lbs? -in 160 lbs ? in 320 • —49-- ^ MENTAL ARITHMETIC. XXXII ■ , 1 88 farthings make 22 pence. 88 pence " ei.46f. .:* ; 88 dollars " 440 shillings. 88 furlongs " 11 miles. 00 miles " - 30 leagues. 00 gallons " 9 ankers. . .. 00 tens " 900. •■: 'OO hundreds " 9000. ^ XXXIII 1 00 francs.... . ! . . . .^. . i .'. . . .make 1 portugaise. V. ■ 06 pence " 8 shillings. . inches " . 8 feet. ^^ 06 articles " 8 dozen. ^ . .• 00 miles '' 33 leagues. , ^ /r 09 tens " 990. 99 hundreds " 9900. 09 dozen " 1 188 articles. XXXIV 100 lbs. new weight..make 1 hundred-weight, sh. 100 feet " 1 square of flooring. 100 centimes " 1 franc. , ;. iOO cents '* 1 dollar. '^; 100 years " 1 century. : . . lOOslHllings " 5 pounds. 100 dollars -^ 25 pounds. 100 grains " 5 scruples. 1 . How many dozens in 30 ? in 36 ? in 42 ?- — in 48 ? ii^ 54 ? in 60 ? ^ . . ^ ^ 2. How many dozens in 66 ? in 69 ? in 72 ? m 76 ? in 80 ? ^"in 84 ?- in 90 ? - 50 - . " ; MENTAJ^ ARITHMETIC. XXXV 108 lbs. avoirdupois, make 100 Ifes. French weight 108 lines '* 9 inches. 108 inches " 9 feet. 108ounces " 9 lbs Troy. 110 dollars... " 550 shillings. 110 pounds " 440 dollars. 110 leagues *' 330 miles. 110 yards '' 330 feet. ^ XXXVI 112 lbs......». *....make 1 barrel of raisii^s. 112 lbs. avoirdupois '' '1 hund., weight lonf,. 112 Ibs.french weight '^ 120 lbs. 15J ounc. eng. w. 112 dollars " 28 pounds. 120 articles " 1 great hundred. 120 articles " 10 dozen. s 120 pence '* 10 shillings. 120 farthings " J dollar. XXXVII • 132 articles make 11 dozen. 132 lines " 11 inches. 132 inches " 11 feet. 132 ounces " 11 fts.Troy. 144 articles '" 1 gross. 144 pints. " 1 runlet. 144 square inches " 1 square foot. " 144 inches '* , 12 feet. ^ 1 . How many scores in 40 ?— — in 80 ?- -in 200 ? in 400 ? -in 100? in 120? 2. Add up in your memory twice 40 and 4 times 64+ Ti times 12. h weight raisius. 3ight lonf,. mc.eng.w. idred. It. -in 120? • — 51 — MENTAL ARITHMETIC. XXXVIII 126 gallons make 1 pipe. 196 fts. of flour " 1 barrel. 200 Us. of pork " 1 barrel. 240 pence " 1 pound J^, 252 gallons " 1 tun. 256 lbs. of soap " 1 barrel. 360 degrees " 1 circle of the zodiac. 365 days " 1 common year. 366 days (52 w. 2 days.) " 1 leap year. 640 acres " 1 square mile. ,^ XXXIX _. • 1000 cents make $10. 1000 pence " $ 16.66 J. . ■■''''■' 1000 shillings " £50. 1000 dollars " £250. 1728 cubic inches " 1 cubic foot. 5280 feet,eug. measu. " 1 mile. 6720 feet, Irisli meas. " 1 mile. 8000 dollars.. " £2000. XL '■.■■■ ' ' ' ' 100 bushels, Canadian measure, make 108 English bushels, 7 gallons, 2 quarts and i pint. lOO feet, French measure, make 106 feet, 9 inches and 7J lines, English measure. 1. How many tens in 200? in 220? in 440? in 500? in 660? 2. Add up in your memory 10x20+6x9+8x8. 9x9+7 X7+8X8. ill 111 '.>'■■ I J ' mr, life- '' w i --52 — MENTAL ARITHMETIC. MISCELLANEOUS QUESTIONS. i. Charles paid 5 cents for a top, and 4 cents for a cord ; how many cents did he give ? 2. James bought G apples at 3 cents each, and 3 cakes at 2 cents ; what did tlie whole cost ? 3. John is 8 years old, Peter is 4 years older ; what is the sum of their ages ? 4. Peter had 44 nuts and he gave 12 to James, 12 to Jane ; how many had he left ? 5. Mary is 13 years old and Emma 7 • what is the difference in their ages ? 6. Joseph had 12 years old in 1868, in what yeai was he born ? 7 What number added to 144 will make 1728 ? 8. William bought 5 oranges at 5 cents each, 5 apples at 4 cents, and 5 cakes at 3 cents j how many cents did he give ? 9. Harry had 96 marbles, and he gave 24 to James and 24 to Frank ; hcvw many had he left ? 10. What number added to 20 will give 30? 36? 48 ? 50 ?-. — 60 ? 66? — 72 ? — 100 ? 11. Francis paid $20 for a cow, twice as much for a horse, 810 for 2 calves, and 5 sheep at $6 a head; what did the whole cost ? 12. Lewis bought a farm S1234, and sold it again to Reynold so as to gain $567; what did he sell the farm for ? 13. What are 4 times 4 and the half of 16 ? F!li — 53 — MENTAL ARITHMETIC. 14. Edward has twice as many peaches as Michael, and Michael has E times 5 ; how many have they both? 15. Margaret paid 25 cents for thread, 25 cents for needles, 36 cents for ribbon, and 14 cents for pins; what did she pay for all ? 16. If John earn $2 a day, how much will he earn in 72 days ? 17. Name the figures of the sum of eleven thou- sand, eleven hundred and eleven. * 18. How many pounds in 20 pounds, 20 shillings and 20 pence ? 19. Add together 30 pounds, 30 shillings and 30 pence. 20. Subtract 18 pounds, 18 shillings and 18 pence, from 24 pounds, 24 shillings and 24 pence. 21. What are 9 times 9 and the half of 9 ? 10 times 10 and the half of 10 ? 22. What number represents the one-third and a half of 100? 23. Multiply 20 pounds, ~0 shillings and 20 pence by 20. 24. Reduce 10 pounds, 10 shillings and 10 pence to pence. 25. Divide 30 pounds, 30 shillings and 30 pence by 4. -\% • _ . -^ - 26. How many months in 25 years? in 50 years? in 100 years? 27. How many thousands in 40 thousand, 40 hun^ dred and 40 ?— in 25 thousand, 25 hundred and 25 ? m M fi — 54 — MENTAL ARITHMETIC. 28. How many cents in $20? in $40? in $50? in 8100? 29. How many dozens in 48? in 80?- — in 72? in 84? in 96? in 108? in 144? in 1728? 30. Add together 20 thousand, 20 hundred and 20 ; 10 thousand, 10 hundred and 10. 31. Add together 20 pounds, 20 dollars, 20 shill- ings, 20 pence and 20 cents. 32. Divide 144 cents among 6 children ; 1 728 cents among 1 2 poor men. 33. What is the fourth part of 120? of 132? — l-ofl44? of 1728? 34. How many yards in 27 yards and 27 feet? in 30 yards and 30 feet ? 35. Leda paid 5 cents for 3 apples ; what will 9 apples cost at the same rate ? 36. Mary hought 6 yards of muslin at 20 cents a yard, and 12 yards o.f satin at 50 cents a yard; what is the amount of her purehase ? 37. Frank had 99 sheep, and sold 1 third of them ; how many had he left ? 38. How many oranges at 3 cents, can you huy for 90 cents? 39. How many apples at 2 cents, can you buy for 1 dollar? - 40. With all the figures (12 3 4 5 6 7 8 9 0), form one hundred. Answer 80 + 19 + f + tt«10P* . - 41. 46. H leagues 47. Hi old?— w 48. N( months '. 49. H( in 4 eagl 50. H( 2000 shil 51. At —at 1 J c 52. M^ « ner age 1 53. He five grof 54. He reanis?- — 65 — MENTAL ARITHMETIC. 41. What is the number of the stroked of the ham- mer of a clock in a da^l 42. Find the value of 10 cents + 15 cents + 20 cents + 25 cents + 30 cents + 35 cents. . 43. Count sevens to 140 and backwards. — Coimt threes to 99 and backwards. 44. How many seconds a boy lived, who is 2 days old ? — who is 4 days old ? — ^who is 6 days old ?- I who is 10 days old? 45. How many leagues in 144 miles ? — in 333 Imiles?— in 720 miles? 46. How many miles in 48 leagues? — in 111 I leagues ? — in 240 leagues ? 47. How many days a boy lived, who is 5 years old? — who is 10 years old? — ^whois 15 years old? 48. Ned is 5 years old and Billy 10, hov/ many I months have they both ? 49. How many cents in 1 eagle ? — in 2 eagles ? — I in 4 eagles ? — in 1 eagles ? 50. How many pounds in 1000 shillings? — in 1 2000 shillings ?— in 3000 shillings ? 51. At 2 cents each, what is the cost of 25 articles? I —at 1 J cent each, what is the cost of 2 doz. oranges ? 52. My mother is born in 1816, can you tell me Iner age? 53. How many doz. buttons make two gross ?— I live gross? — six gross? 54. How many quires of paper are there in 10 I reanis ? — in 20 reams ? '•Hi •::?- ,;'! iii' — 56 — This table serves to find any number whatever thought of by another person, for example, the age which one person seeks for another. The person who has thought of the number, or whose age is sought, should indicate the different columns in which that number is marked. The addition of the numbers which are found at the head of each of these columns gives the number thought of, or the ago sought for. Thus, a person nineteen years old, whose ago is sought, will indicate that tho number is to be found in the 1st, 2nd, and 5th, columns and the addition of the numbers 1, 2, and 10, at the head of these columns, will give 19, tho ago sought for. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 A5 47 49 51 53 55 57 59 61 63 4 8 16 3 5 9 17 6 6 10 18 7 7 11 19 10 12 12 20 11 13 13 21 14 14 14 22 15 15 15 23 18 20 24 24 19 21 25 25 22 22 20 26 23 23 27 27 26 28 28 28 27 29 29 29 30 30 30 30 31 31 31 31 34 30 40 48 35 37 41 49 38 38 42 50 39 39 43 51 ■ 42 44 44 52 43 45 45 53 46 46 46 54 47 47 47 55 50 52 56 56 51 53 57, 57 54 54 58 58 55 55 59 59 58 60 60 60 59 61 61 61 62 62 62 62 63 63 63 63 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 5J 54 55 56 57 58 59 60 61 62 63 loo cents ["he coinj to cent |;ents piec pne cent j t cents = !5 cents d.= l^l 6s. 8d -^57 MENTAL ARITHMETIC. - THIRD PART. Commerce and Trade. I- Canadian decimal money. Old Canadian currency. JOO cents make 1 dollar $. ["he coins are a 5 cents piece, 10 cents piece, and a 20 |;ents piece of silver, and a Dne cent piece of copper. 4 farthings make 1 penny, d. 12 pence 5 shillings 20 shillings 4 dollars ,1 24 s. 4 d. 1 shilling*, s. 1 dollar. $. 1 pound. £. 1 pound. 1 pound ster. Aliquot parts of a dollar. cents = l/25, 5 cents = l/20, 10 = 1;10, 20 cents=l;5, 5 cents = 1/4, 50 cents =1;2, 75 cents = 3/4. Aliquot parts of a penny. 1/4 = 1/4,1/2=1/2, 3/4-3/4. Aliquot parts of a shilling. . 1(1.= 1/12, 1 l/2d. = 1/8, 2d.= l/6, 3d. = l/4, 4d.=:l/3, 6d. 1/2, 8d. = 2/3, 9d..-=3/4. Aliquot parts of a pound. |s. = l/20, = 2s. = l/10, 3s. 4d.-l/6, 4s. = 1/5, 5s. = 1/4 6s. 8d. = l/3, 10s. = l/2, 13s. 4d. = 2/3, 15s, = 3/4. fiS .iv.l ■I if:: m — 58 — \ MENTAL ARITHMETIC. No. 1. — ^To find the value of any given quantity,! No.I when the price of 1 unit is given. land it Rule. — Multiply the price of 1 unit by Ihe quan^ R^^ tity. Exercises. i i 11 articles ) at 2 cents each =$0.22 12 (( at 3 cents " = 0.36 13 u at 4 cents " = 0.52 U u at 5 cents ** = 0.;0 15 u at 6 cents " = 0.90 16 u at 7 cents " ^ 1.12 17 a at 8 cents " = 1.36 18 (( at 9 cents " = 1.62 19 (( at 10 cents " = 1.90 20 a at 11 cents " = 2.20 &c., &e. -^ 1. If 1 lb. of butter cost 20 cents, v^hat will be thj cost of 144 lbs. ? Analysis. — If 1 ft. cost 20 cents, 144 lbs. will cosfl 144 times 20 cents = $28.80. 2. If 1 barrel of flour cost $5.50, what will be iH cost of 100 barrels? Analysis.— If 1 barrel cost $5.50, 100 barrels will| cost 100 times v 5.50 = $550.00. 3. If 1 yard of cloth cost $2.10, what will be thii cost of 3^ yards ? Analysis. — If 1 yard cost $2.10, 3J- yards willcosli 3J times $2.10 = $7.35. 4. If 1 lb. of tea cost 50 cents, what will be the| cost of 8^ lbs ? Analysis. — If 1 lb. cost 50 cent's, 8J lbs. wiU cpst times 50 cents =$4.25. ^fW' — 50 — < iiSNTAL ARITHMETIC. ^en quantity,! No.2.— To find the price of 1 unit when a quantity and its price are given, hy the quanj Rule. — Divide the price by the quantity. Exercises. 11 articles cost 60.22, 12 13 14 15 16 17 18 19 20 u u a a u u u u 0.36, 0.52, 0.70, 0.90, 1.12, 1.36, 1.62, 1.90, 2.20, 22 36 52 70 90 1.12 1.36 1.62 1.90 2.20 11 12 --13 14 15 16 -f-17 -7-18 -^19 -^20 = 60.02 - 0.03 == 0.04 = 0.05 = 0.06 = 0.07 = 0.08 = 0.09 = 0.10 = 0.11 &c., &c. 1 . If 1 44 !bs. of butter cost $28.80, what will be the cost of 1 K). ? Analysis— If 144 ibs. cost $28.80, 1 lb. will cost •di of $28.80=20 cents. 2. If 100 barrels of flour cost $550.00, what will be the cost of 1 barrel ? Analysis — ^If 100 barrels cost $550.00, 1 barrel will cost Tiir of $550.00 = $5.50. 3. If ^ yards of cloth cost $7.35, what will be the cost of 1 yard ? Analysis — If 3Jyards cost $7.35, 1 yard will -cost ? of $7.35 = $2.10. 4. If 8J lbs. of tea cost $4.25, what will be the cost of 1 ft. ? - Analysis. — If 8J lbs. cost $4.25, I lb. will cost -jV of $4.25 (tV of $4.25 = $0,25 x 2 = 50 cent:-.) / ^v 1 ■m 'A if -I ^1 l\ ■mm ml mm J - 60 - MENTAL ARITHMETIt!. No. 3. — ^To find the quantity when the price of quantity and the price of a unit of that quantity ai given. Rule. — Divide tlte rrice of the quantity by thj price of unity. - Exercises. Apples at 2 cents each, ho"vr many for 22 cents? 22-r 2= 111 " at 3cents " " '' " 36 cents? 36-^3=11 4 cents Pears at at at 5 cents Oranges at 6 cents " at 7 cents Cocoa n. dt 8 cents " at 9 cents Books at 10 cents " at 1 1 cents it t( (< (( it it it (( u it it (( it a tt t! it it it it it it it 52 cents? 52^ 4=ri; 70 cents? 70-^ 5=1^ 90 cents? 90-7- 6=15| 112 cents? 112-:- 7=10! 136 cents? 136-f- 8=1]| 162 cents? 162-^ 9=11 " 190 cents? 190-^10=191 " 220 cents? 220-^11=201 (< (I it a tt &c., &c. 1. If 1 Ib.of butter cost 20 cents, how many lbs. cai be purchased for $28.80? Analysis. — If 1 lb. cost 20 cents, for $28.80 we cai fet as many lbs. as 20 cents is contained times ii 28.80 ; $28.80-J-20 = 1 44 lbs. ' 2. If 1 barrel of flour cost $5.50, how many barrels can we get for $550.00 ? Analysis. — If 1 barrel cost $5.50, for $550.00 we can get as many barrels as $5.50 is contained times in $550.00 ; $550.00-r-$5.50 = 100 barrels. 3. If 1 yard of cloth cost $2.10, how many yards can be purchased for $7.35 ? $7.35-4-$2.10 = 3J- yards. 4. If 1 lb. of tea cost 50 cents, how many lbs. can be purchased for $4.25 ? $4.25^-50 = 8ilbP. le price of quantity ar itity by th 22- 3& 52 70. 90- 112 ;? 136 ;? 162 ;? 190-MO: 5? 220 ? ? ? ? ? ? 112-:- 2=-. 3=12 4=ri; 6= 7=16 8=11 9=18 1=19 11=20 lany lbs. can 8.80 we eai ed times h Tany barrels $550.00 we ined times lany yards Qylbs. can 61 MENTAL ARITHMETIC. No. 4. — To find the value of 12 articles (1 dozen), the price of 1 m pence or in cents being given. Rule. — Reckon every penny in the price 1 shill- ing, and every farthing 3 pence, because the value of 12 articles'at 1 penny each is 12 pence or 1 shill* iiig. If it be cents, multipW 12 by the cents. Exercises. 12 articles at 12 " at 12 " 12 12 12 12 12 12 12 12 12 12 u u u u a cc a a cc d. each=£0 3 - 6 = 009 = 010 1 1 2 2 3 4 6 9 6 6 7 6 12 oranges 12 lemons 12 oranges 12 lemons 12 knives 12 books &c., at at at at at kc. 2 cents each; 3 cents " 4 cents 5 cents 6'Pents cc (I cc at 10 cents cc .24 0.36 0.48 0.60 0.72 1.20 &c,, &c. 11 m M " 'V '?; ;i!^ 1!^* 1 \ 62 — W i ■! MENTAL ARITHMETIC. No. 5. — ^Toiindthe value of several doxonevtliei ^l price of one dozen beii^g given. i wlfj Rule. — Multiply the price of one dozen by the I liiJ number of dozens. I as mi Exercises. 2 doz. apples 3 .^ 6 8 10 20 24 25 a u lemons u •' li oranges a at at at •:t at at at at at 3d. per dozen. ^ 4d. 15d. 3s. 5s. 63. 7s. 6d. 8s. 4d. 9s. &c., u u u it u u u &C. u i-. (C u u £- G f 3 7 iO .11 5 18 2 10 5 5 doz. articles at 5 cents per doz. = $0.25 0.70 0.99 2.20 2.64 4.50 7 9 11 12 15 u u a u (C cc at 10 cents at 11 cents at 20 cents at 22 cents at 30 cents &c. a u (C u U &C., 1 What is the value of 12 articles at 8d. each ?— at8|d.?— at 9d.?— at O^d.?— at lOd.?— at lOJd.?- atlld.? 2. What is the value of 1 2 articles at 7 cents each ? — at 8 cents? — at 9 cents? — at 11 cents? — at 12 cents ? — at 20 cents? •* 3. What is the price of 24 articles at 5d. each ?— of 36 at Od. ?~of 48 at 4d. ?-of 60 at 3d. ?— of 72 at 2d.? 1. \^ per ya] 2. ¥ per yai 3. \^ per ya] 6. \^ per yaj 7. y\ cents p 8. W cents p — cs — MENTAL ARITHMETIC. N"/. 6.^— To find the value of a number of articles, •whpw iheve are a few over or under the doz. iiuie.— Calculate for a dozen, and add or subtract as may be required. Exercises. 14 articles at 4d. eaqh^. £04 8 14 at 5d. " = 5 10 14 • at 6d. " = 7 25> at 4d. " =s 8 4 m at 9d. " = 19 6 37 at 15d. " = 2 6 3 *73^ at 20d. " = 6 1 8 74' at 20d. " = 6 3 4 724 at 5d. " = 15 1 8 843 at 7d. *' = 24 11 9 966 at 6d. " = 24- 3 1081 at 8d. " = 36 8 - \ &c., &c. - 1. What is the price of 25 yards of cotton at 5d. per yard ? 2. What is the value of 37 yards of cambric at 9d. per yard ? 3. What is the value of 38 yards of muslin at lOd. per yard ? 6. What will be the cost of 13 yards of cloth at 4s. per yard ?— at 5s. 6d. ? — at 6s. 4d. ? 7. What will be the cost of 25 lbs. of sugar at 5 cents per lb. ? — at 6 cents ? — at 7 cents ? 8. What will be the cost of 37 lbs, of tea at 20 cents per lb. ?— at 30 cents ?-— at 50 cents ? " '1 ' 't lit' * m •it /t — 64 — MENTAL ARITHMETIC. No. 7. — To find the value of one article, the price per dozen in shillings and pence, and tne price in dollars and cents being given. Rule. — Reckon one penny for every shilling in the price. If it be dollars and cents, divide the price by 12. Exercises. doz. cost 3d.= id. " " 6d.= |d. " " ls.Od. = l d. " « " 5s. Od. = 5 d. " " 4s.3d. = 4id. " " 2s.6d. = 2|d. " " 6s.0d.=^6 d. &c., 1 doz. cost 7s. Od. = 7 d. 1 " " 7s.6d.= 7Jd. 1 " " 8s. Od. = 8 d. 9s. 6d. = 9Jd. 10s.0d.= 10 d. 20s.0d. = 1s.8 d. 24s. 6d. = 3s. OJd. &c. 12 12 12 12 12 12 articles cost S0.36, 36-r-12 = 12 " " $0.48, 48-j-12 = $0.6', 66-^12 = eO.72, 72-4-12 = $0.88, 88-^12 = $0.96, 96-f-12 = $1.44, 144-5-12 = $0.03 0.04 0.05J 0.06 0.07J 0.08 0.12 &c., &c. 1. What cost 1 article at 6s. 6d. per doz. ? — at 10s. 3d. ?— at 12s. 6d. ? 2. What cost 1 article at $4.00 per doz. ?— at $6.00 ? —at $6.60 ? 3. What costl article at 9s. 6d. per doz.?-.-at lis.? — at 13s. ? — at 15s. ? — 65 — 1 MENTAL ARITHMETIC. No. 8. — ^To find the value of one dozen articles in dollars and cents, the price of one article being given in half-pence {sous). Rule. — Add a cypher to 'lie given price, and point off the two last figures for cents. •Vll.,.:3 '*• Exercises. 12 articles at 8 half-pence each Lx:$0.80 12 '* at 10 a u = 1.00 12 ^ at 11 u a = 1.10 12 " at 12 u - u = 1.20 12 '<• at 13 u a = 1.30 12 " at 14 a u = 1.40 12 » at 15 u u = 1.50 12 " at 20 &c., u &C. (( = 2.00 No. 9. — ^To find the value of several dozens, the price of one being given in half-pence. Rule.— Find the value of one dozen by the last rule and multiply by the given number of dozens. Exercises. 2 doz. at 8 half-pence each, will cost $1.60 3 " at 12 " " '' " 3.60 4 " at 11 " " " " 4.40 5 " at 10 " " " " 5.00 &c. &c. 'I!- i|vi fi M -66 — MENTAL ARITHMETIC. No. 10.— To find the value of one article, the price of one dozen being given in dollars and cents, or only in cents. Rule. — Reject from the given price the point and the last figure. The remainder will be th9 a.QSwei in half-pence. Exercises. 1 doz. cost $0.80, one article will cost 8 half-pence. a u u u u 2.10, 2.25, 3.50, 4.40, 6.60, u u u u u u cc u u u u u u u u 21 22* 35^ 44 66 (( u &c.. &c. No. 11. — ^To find the value of one article, the price of several dozens being given in dollars and cents. Rule. — Reject from the given price the point and the last figure, as in the last rule, and divide by 2 for 2 dozen ; by 3 for 3 dozen ; &c. Exercises. 2 doz. cost $6.50, each article will cost 32J half-pence 3 " 4 " u u 6 4C a u u 9.90, 8.80, 5.50, 6.60, u cc cc cc cc cc cc cc cc cc cc cc 33 22 11 11 (4 (( 4( kc. &c. — 67 — MENTAL ARITHMETIC. No. 12. — ^To find the value of one gross, the price of one article in pence or in cents being given. Rule. — Reckon the pence in the price of one ar- ticle as shillings, and the number of pence in these shillings will be the price of one gross in shillings. Because taking the pence in the price of one article as shillings is the same as mutiplying by 12, and taking these shillings as pence again is the same as multiplying by 12 another time, and 12x12 = 1 44 = 1 gross. If it be cents, reckon 144 cents fbr every cent in the price. ExerciseB. 1 gross at 4d. each = 48s. 1 "• at 5d. " = 00s. 1 " at 6d. " = 72s. 1 " at 7d. " = 84s. &c., 1 gross at 2Jd. each = 306. 1 " at3|d. " =39s. 1 " at3|d. " =428. 1 " at4id. " =54s. &c. 144 articles at 2 cents = $2.88 cents. 144 " at 3 cents = 4.32 cents. 144 " at 4 cents = 5.76 cents. 144 " at 5 cents = 7.20 cents. &c., &c. iV 'I :|.' 1. If 1 lb. of butter cost 10 cents, what will be the cost of 144 lbs. ? 2. If 1 yard of cambric cost 6d., what will be the cost of 144 yards? 3. If 1 lb. of sugar cost 4id., what will be the cost of 144 lbs. ? I ) — 68 — MENTAL ARITHMETIC. No. 13. — To findtho value of two or more gross, the price of one article in pence being given. Rule. — Reckon, as in the preceding rule, the pence in the price of one article as shillings and multiply them by the number of grosses. Exercises. 2 gross at 4d. each = 12 x 4 x2= 96s. 3 " at 6d. " =12 X 6 x 3 = 216s. 4 5 u u at 9d. at lOJd. a &C., = 12x 9 x4 = 432s. = 12xl0ix5 = 615s. &c No. 14. — To flud the value of one article, the price per gross in shillings being given. Rule. —Reckon the shillings in the price per gross as pence and divide them by 12. Because taking the shillings as pence and dividing them by 12, is the same as dividing twice by 12, or 144. Exercises. 1 gross at 30s. = 2Jd. 1 " at39s. = 3|d. 1 " at96s. = 8 d. 1 " at99s- = 8Jd. &c. 1 gross at 100s..- 8Jd. 1 " atll4s.= ^d. 1 " at 120s. = 10 d. 1 " at 144s. = 12 d. &c. ore gross, en. rule, the lings and — 69 — MENTAL ARITHMETIC. No. 15. — ^To find the value per score, the price of one article in shillings and pence being given. Rule. — Reckon a pound for every shilling and Is. 8d. for every penny in the price ; thus, there being 20 cvvt. in a ton, the price of one ton at Vs. 6d. per cwt. is £7 10s. ' i I ! I 96s. M6s. i32s, )15s. the price rice per Because them by >r 144. 3..-= 8Jd. 3. = 10 d. 3. = 12 d. 20 ♦* 20 ." 20 " Excrcises- at 4s. Od per lb. at 5s. 3d. " " doz. a 20ft)s. 20 " 20 doz. at 5s. 6d. " at 8s. 3d. " at 9s. Od. " at 14s. Id. " 20 sc. at 17s. 6d. " 20. " at 19s. 9d. " &c., u sc. u = £4 Os. Od. = 5 5s. Od. = 5 10s. Od. = 8 5s. Od. = 9 Os. Od. = 14 Is. 8d. = 47 10s. Od. = 19 15s. Od. &c. No. 16. — To find the value per score, the price of one article in cents being given. Rule. — ^Reckon one shilling for every cent in tho price. Exercises. . 20 lbs. of sugar at 5 cents per lb = 5s. 20 20 20 20 20 a u u a a a a u a a u u a at 6 cents " at 7 cents " at 10 cents " at 12 cents " at 20 cents " u a u u = 6s. = 7s. = 10s. =:12S. = 20s. &c., &c. ^ !. I t' t 1 f** . : — 70 — MENTAL ARITHMETIC. No. 1 7. — ^To find the value of one article at a certain rate per score. Rule. — Reckon one shilling for every pound in the price. Exercises. 20 ft)s. cost £ 4 Os. Od., 1 lb. will cost 4s. Od. 4s. 6d. 7s. Gd. 8s. 9d- 9s. Od. 17s. 6d. 19s. 9d. 20s. Id. 20 " " 20 doz. " 20 " " 20 cwt. " 20 " " 20 sc. " 20 " *' u 4 10s. Od., 7 10s. Od., Idoz. 8 15s. Od., " 9 Os. Od., 1 cwt. 17 10s. Od., ^' 19 15s. Od., sc. 20 Is. 8d., a u a u u C( (C a u a u u a u . &C., &C. No. 18. — ^To find the value of one article, the price per score being given in shillings. Rule. — Reckon one cent for every shilling in the price. Exercises. 20 20 20 u 20 lbs. cost 20s. = 20 cents. 20 '' " 19s. = 19 cents. 18s. = 18 cents. 17s. = 17 cents. ifis. = 16 cents. &c.. 20 lbs. cost 15s. =15 cts- 20 " " 12s.6d. = 12Jcts. 10s. =10 cts. 5s. = 5 ctS' 2s.6d-= 2icts. 20 20 20 a a a. u u a &C. 1. If I scruple cost 9 shillings, what will be the cost of 1 grain? 2. If 1 ream of paper cost 10 shillings, what will bo the cos* of I quire? 71 — at a certain y pound in 4s. Od. 4s. 6d. 7s. Gd. 8s. 9d- 9s. Od. 1 7s. 6d. 19s. 9d. 20s. Id. , the price ig in the = 15 cts- = 1 ^ cts- = 10 cts- = 5 cts. = 2 J cts. >f 1 grain? the cos< MENTAL ARITHMETIC. No. 19. — ^To find the value of a number of scores, the price of one article in shillings and pence being given. R^je. — After having operated as in rule the 15th., multiply by the number of scores. Exercises. 2 s(!ore at 4s. Od. per lb., 4 x 2 = £ 8 ' Os. Od, 3 " at 5s. 3d. " " 5Jx3= 15 15s. Od. 4 6 u at 5s. 6d. at 10s. Od. (( cc u a &C., 5J X 4 = 22 Os. Od. 10 x6= 60 Os. Od. &c. No. 20. — ^To find the value of a number of scores, the price of t)ne article in cents being given. Rule. — After having operated as in rule 16th, mul- tiply by the number of scores. Exercises. 2 score at 4 cents per ib., 4x2- 8 shillings. 3 " at 5 cents " " 5x3-15 " 4 " at 6 cents " " 6x4 = 24 « &c., &c. No. 21. — ^To find the value of one article when the price of two or more scores is given. Rule. — Divide the given price by the number of scores, and afterwards reckon one shilling for every pound, and one cent for every shilling in the price. •■ii'ji m m ■^m ' J — 72-- MENTAL AUITIIMETIG. Exercises. 2 score cost £8 Os. 0fl.-^2= 4s. Od. 3 " " 15 15s. 0cl.-^3= 5s. 3cl. 4 " " 22 Os. 0(1.-^4= 5s. 6d. 6 " • " 60 Os. 0d.-^6 = 10s. Od. &c., &c. No. 22. — ^To find the value of 100 articles, the price of one in pence being given (1 hundred weight short.) Rule. — For every farthing in the price, take as many pence and twice as many shillings. Thus, 100 pencils at 2d. each cost IGs. 8d., being the num- ber of farthings taking for pence and twice for shilUngs. 2d. x4 = 8x2 = 16s. + 8d. Exercises. 100 Sbs. of sugar at SJd. = 14 f. x 2 + 14d. = 29s. 2d. lOOlbs. of 100 lbs. of 100 lbs. of 100 lbs. of 100 lbs. of u u at 4jd. = 19 f. X 2 (- 19d. = 39s. 7d. at 5 d. = 20 f. X 2 + 20d. = 41s. 8d. at 5Jd. = 21 f. X 2 + 21 d. = 43s. 9d. at 3fd. = 15 f. X 2 + 15d. = 3Is. 3d. at 4 d. = 16f. x2 + 16d. = 33s. 4d. &.C., &c.- 1. If 1 lb. of beef cost /lid., what will be the cost of 100 lbs? 2. If i lb. of butter cost 7^ J., what will be the cost of 100 lbs. ? 3. If 1 yard of cambric cost 8d.. what will bo tho cost of lot yards ? ). Od. 3d. 6d. Od. rdcles, the red weight price, take gs. Tlius, ? the nuin- twice for = 29s. 2d. = 39s. 7d. 41s. 8d. 43s. 9d. 31s. 3d. 33s. 4d. Jf 100 lbs? ost of 100 tho cost of ^73 — MENTAL ARITHMETIC. No. 23.— To find the value of 100 articles, the price of one in cents being given. Rule. — Reckon one dollar for every cent in the price. Exercises. 100 100 100 100 100 100 lbs. at 2 c. each = $2. a u u at 3 c. at 4 c. at 5 c. at 6 c. at 7 c. cc cc cc cc cc 3. 4. 5. 6. 7. &.C., 1 00 lbs. at 2 J c. each = $2.25 100 " at3Jc. " = 3.50 100 " at4ic. " = 1 too " at5Jc. too '' atOic. 100 " at7f c. &c. cc cc cc cc 75 = 5.25 = 6.50 = 7.75 No. 24. — To find the value of 1 00 articles, the price of one in shillings and pence being given. Rule. — For each shilling reckon £5, for 6 pence £2 10s., for 3 pence £1 5s. and 8s. 4d. for one penny. Thus, lOOlbs. at 3s. lOJd. £5 x3 = £15 6 3 pence cc = 2 10s. = 1 5s. 1 penny cc 8s. 4s. 4d. 2d. £19 7s. 6d. Ans. Exercises. 100 yards at 7s. per yard = £35 Os. Od. 100 '' at 8s. " " = 40 Os. Od. 100 " at 8s. Id. " " = 40 8s. 4d. &€., &C. k hi .'li 'i Mil I 1:; I'® — 74 — MENTAL ARITHMETIC. No. 25.— To find the value of 200, 300, 400,500,&c., the price of one article in pence or in cents being given. Rule. — Find the value of 100 and multiply by 9 for 200, by 3 for 300, by 4 for 400, by 5 for 500, &c. 200 apples Exercises. atl d eacli= 8s. 4d.x2= 16s. 8d 200 '' - at lid. 300 pears at 2 d. 300 " at2Jd. 400 oranges at 3 d. 400 " at 4 d. 500 cocoa-nuts at 5 d. 500 " at 6 d. a a u (.(. u u a &.C., = 12s. 6d.x2:- 25s. Od = 16s. 8d.x3= 50s. Od -20s. 10d.x3= 62s. 6d = 25s. 0d.x4 = 10us. Od = 33s. 4d.x4 = 133s. 4d = 41s. 8d. X 5 r 208s. 4d -50s. Od. X 5 = 250s. Od &c. 100 apples 200 " 300 " 400 '' 500 " 600 " at 1 cent each-$ 1.00 at 2 cents at 3 cents at_4 cents at 5 cents at 6 cents cc C( a (.(. C( = 4.00 = 9.00 = 16.00 = 25.00 = 36.00 &c.. &c. 1. What cost 200 ooooa-nuls at 5 conts a piece ? 2. What cost 400 lbs. of sugar at 10 cents per lb.? 3. What cost 1000 lbs. of beef at 2jU. per lb. ? of 1| poii in Tl cost — 75 — MENTAL ARITHMETIC. 0,500,&c., Its being ply by ? ' 500, &c. = 16s. 8d r. 25s. Od = 50s. Od = 62s. 6d = 10us. Od pl33s. 4d '208s. 4d 250s. Od No. 26. — To find the value of one article, the price of 100 in shillings and pence being given. Rule.— Reduce the shillings and pence to pence, point off the two last figures, you have the answer in pence. Thus, 100 lbs of sugar cost 37s. 6d., each ft. will cost 4Jd. ^^ 37s. 6d. X 12 = 4,50 = 4 J pence. Exercises. 100 lbs. cost 45s. lOd., each lb. will cost 5Jd. 100 " '' 91s. 8d., " " " ' " 11 d. 100 " " 104s. 2d., " " " " 12Jd. 100 " " 110s. 5d., " . " " '* 13|d. 5^c., &c. No. 27. — ^To find the value of one article, the price of 1 00 being given in dollars and cents. Rule. — Reckon the dollars in the given price as cents, and the cents as hundredths of cents. Thus, 100 yards of tape cost $4.50, eaqh yard will oost 4-i cents. ($4.50 = $0.04^.) Exercises, 100 yards cost $ 6.75 = $0.06} per varl 100 "• '' 8.00= 0.08 " " " 100 " " 24.50= 0.24J " " &tc., &c. W ■ — 78 — MENTAL ARITHMETIC. No. 32. — To find the value of one article, the price of 240 in pounds being given. Rule. — Reckon one penny for each pound in the price. Exercises. No.; lars an Rule price. V.'l u imv 240 lbs. cost 240 " 240 '' 240 " 240 " 240 " ^5= 5d. 10=:10d. 15 = 15d. 20 = 20d. 25 = 25d. 30 = 30d. &c.. 240 lbs. cost £ 5 10s. = 5Jd. 240 240 240 240 240 10 10s. = 10id, 15 10s. = 15id. 20 10s. = 20|d. 25 10s. = 25id. 30 10s. = 30id &c. No. 33. — To find the value in pence of one article, the price of 240 being given in dollars and cents. Rule. — Reckon one farthing foi' every dollar in the given price. Exercises. "'^. 240 lbs. cost $18.00 = 18 farthings = 4^d. per lb, 240 " 240 '' 240 " 240 " 240 " a u u 13.00 = 13 20.00 = 20 23.00 = 23 24.00 = 24 32.00 = 32 &c.. u u •/ = 3id. = 5 d. = 5id. -e d. = 8 d. if, kc. 240 lbs. 240 " 240 " 240 '• No. 3l cle, the Rule. in the g 120 12C 12C 120 120 120 — 79 — MENTAL ARITHMETIC. the price d in the No. 34. — ^To find the value of 240 articles in dol- lars and cents, the price of one being given in pence. Rule.— Reckon 4 dollars for 1 penny in the given price. Exercises. ;!fl 3.= 5Jd. 5.= 10|d. 5. = 15id. ;. = 20|d. J. = 25id. J. = 30|d 240 lbs. at 1 d. each=$4.00 ) article, cents. ollar in er lb. u (C 240 " at 11 d. 240 " at IJ d. 240 '• at 2 d. " = 6.00 " = 7.00 = 8.00 << 240 lbs. at 2i d. each=$l0.00 240 " at 23 d. " = 11.00 240 " at 3 d. " = 12.00 240 " at 3J d. " = 14.00 No. 35. — ^To find the value in pence of one arti- cle, the price of 120 being given in dollars and cents. Rule. — Reckon one half-penny for every dollar in the given price. Exercises. 120 lbs. cost 8 2.50=^ 2J= IJ d. per lb. 120 120 120 120 120 a 4.00= 4 = 2 d. " " 16.00 = 16 = 8 d. " " 16.50 = 16i= 8id. " " 20.00 = 20 =10 d. " " 24.00 = 24 =12 a. " " &c, &c ■1 " iK; U:. I. W^ i*"^'^ — 80— • MENT VL ARITHMETIC. No. 36.— To find the value of 120 articles vi Jol- lars and cents, the price of one being given in pence. Rule. — Reckon one dollar for every half-penny in the given price. Exercises. 120 articles at 1 J d. each = $ 2.50 = 4.00 = 16.50 = 20.00 = 40.00 = 41.00 120 120 120« 120 120 a a at 2 d. at SJd. at 10 d. at 20 d. at 20J d. &c., &c. a u (C u No. 37.— To Bad the value in pence of one article, the price of 60 being given in dollars and cents. Rule. — Reckon one penny for every dollar in the given price. Exercises. , 60 doz. cost $ 1.50= IJ d. per doz. 60 60 po 60 60 u &C., 4.25= 4Jd. 3.50= ^d. 5.75= 5|d. 11.00 = 11 d. 21. 50 = 21 J d. &c. a (C u u No. 3 and oer Rule, given p No. 3 of 25 01 Rule by 4 fo 25 25 50 50 m — 81 — MENTAL ARITHMETIC. les ia dol- I ^o. 38.— To iind the value of 60 articles in dollars nin pence, land cents, the price of one being given in pence. lalf-penny I Rule. — ^Reckon one dollar for every penny in the .50 .00 .50 .00 .00 .00 »ne article, I cents. dollar in oz. (C C( given price 1 Exercises, GO articles at 1 d. each = $ 1.00 60 " at lid. •' = 1.50 60 " at 2 d. " = 2.00 60 " at 2id. " = 2.25 60 ". at 3id. '' = 3.50 60 . " at lOf d. " = 10.75 60 " at 20 d. " = 20.00 60 " at 25J d. " = 25.25 &C., &.C. No. 39. — ^To find the value of one article, the price of 25 or 50 being given in dollars and cents. Rule. — Consider the dollars as cents and multiply by 4 for 25, and by 2 for 50. Exercises. 25 K)s. cost $ 8.00. 8 x 4 = $0.32 per lb. 25 " " 10.50. lOJx 4=- 0.42 " " 50 " " 8.00. 8x2= 0.16 " " 50 " " 10.50. 10Jx2= 021 " " &c., &c. f] Jill '', I IMAGE EVALUATION TEST TARGET (MT-3) % 1.0 I.I 1.25 ii|l£ 12.5 50 "^" !■■■ 1^ 12.2 US |56 us ^ 2.0 1.8 U IIIIII.6 P /i VI ^;. ^j c?5^''.^V > '/ Si.. /A Photographic Sdences Corporation 33 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4S03 r i> — 82 — \v \\ MBNTJkL ARPTHMETIG. , No. .40.>-^To find the value of miy nuHiber of ai ticlt^, the price of one hemg given in dollars an( cents. tkl6s Rul Rule.^Multiply the number of articles by ih and given price in dollars and cents, or miiltij^y th artiill given price by the number of articles, and point o£v8st; mentally, the two last figures for cents. T]}ua , 20 lbs. of rioe at 4 oentB p^r lb (20x 4>«90.8O). Sel pagedX. : ' 240^ 3ja; 364: 1 25 lik at .10 cents eaedi, 25xl0=$2i50 26 '* at. 12 cents ** 56x15= 3.12 27 " at .11 cents « 27x11= 2.d7 30 " at.08cent3 « 30x(^= 2.40 32x05= l.«0 32 ^* at. 05 cents « 00 " at .03 cents " 100x03= 3.00 • 10 yards at $1.20 each, 11 ^ at 2.10 « 1.20x10=112,00 2.10x11= 23.10 12 " at 3.Sa « 33xt2^ 39.98 12 « at 2.12 ** 2.15x12= 25.44 10 " at 4.50 " 4.50x10=45.00 12 " at 5.05 " 5.05x12= 60.60 ike, &CC. No. tides Ru3 lijags Thus, 120* 1. What l»tb6 Valae of 12 'artielat ai^6 cents each I-*- — at 7 cents ?-«-— at 10 cents ? at 11 ^^?-— -.at 12 cents? at 2i cents? 2. What cost 20 yards of cloth at $2.00 per yard ? at $3.00? at $2.10 r at $».W ? at.f^^iOO? at $6.00 ? 6( 10( 20( 30( umber of ai dolkprs am MBNVMi ARI'mMBTIQ. Nb; 44.— To find the vakie 6f any number of ar- Mes wlit^ the* price of ^cme is given in pence. Rule.^ — CSonsider the number of articles as pence, icles by Ihf andimiiillii^y by the ;peneo in the price. Thus, 96 artiiiles'ai'Sdi eachy cost 24»., became 96'pence are md point o£i86t5 aa§\B x 3 m%^. ;ents. Tius •0.80). Sdt Ez^cises. ■-$tso = 3.42 = 2.d7 = 2.40 ^ l.«0 3.00 112.00 23.10 39.96 25.44 45.00 60.60 126ia^ticles^t4i4*>126Ti-12»=10s.6d.x4|^r, 47s. 3d 24a: "^ at m, 240-*-12 = 20s. m x ^« 170a. Od. 318- ** ^t 4 4^ 31B^12,^ 268, 6d. x 4 « 106s. Od. 364; <^ s(t 3Jd> 3^^12^ 30b. j|pL^^?5 10W» 2d. • &C., &ci- ';■ i« ach ?— — at Jcentt? iit$3.001 6.00? Nq. 42r^*rvTjQ.9nd 1^ value-of sq[^y number of ar- ticles '^heiathe pnce of o^e is given in shilling^. Rule.~~Gonsider the number of articles as shil- linfsnofl.atfatiply by; the shUliugs in the pace. Thus, 120i^x>f (teaiat^ per/JIb. mai^ £12, because Ex^rQise^. 6afts.at 6s. ei^h, 60^20 = ^ 3x 6»£18. m " at lOs. ^* 100-f-20= 5x10^ l»a 200 « at 5s. ^** 200-1-20= IjQx 5« 50. 300 " at '4s. " 300-^-20= 15x 4x 60. &c., &c. ijii m iiv' H i: ■!■■' ill"!;! i I •' I *■■ I, Pi' mv MENTAL arithmetic; ■^^ifeif-f-^.^^. No. 43:— To find the value of any number of a tides, the price of one being given at 1 Jd., at 2d., a 3d., at 4d. and at 6d. Rule. — Consider the given price as aliquot part of one shilling, and divide by 8 for 1 Jd., by 6 for 2d for 5d. No. tides, at7Jd. Rul( of one by 4 for *. 1., by 3 for 4d., and by 2 for 6d., you hav the anawer in shillings. ;i : ■ Exercises. ■if ^v*w 32 ya^s at 1 Jd. each, 8 in 32 = £0 4s. Od. 44 36 63 72 u u u u at 2 d. at S d. at 4 d. at 6 d. U U U 6 in 44 = 4 in 36 = 3 in 63 = 2 in 72 =^ Q 7s. 4d. 9s. Od. 1 Is. Od. 1 16s. Od. **,- •.'v- '..,... &c. y 4 t \ X 15d. 60 ji 70 75 80 90 No. 44. — ^To find the value of any number of ar tides, the price of being given at 2Jd., at 3d., a 5d., and at 7Jd. Rule. — Co i!4der the given price as aliquot parti of 15d., and divide by 6 for 2Jd., by 5 for 3d., by for 5d., aiid by 2 for 7Jd., you have the answer ii JT.."^ ^ 15penc8s. o ar Exercises. •.f'WM No. article lOd,, 2 Rul of ad( 25 fts. at 2Jd., each, 6 in 25= 4 (15d.) + 2id. 31 " at 3 d., " 5 in 31= 6 — +3 d. 42 " at 5 d., " 3 in 42 = 14 — CO " at 7id., " 2 in 80 = 30 — , &c., , &c. . m. imber'of a |d., at 2d., a liquot part , by 6 for 2d )d., you hav ) ^ 4s. Od. 1 7s. 4d. ) 9s. Od. - Is. Od. 16s. Od. r^M^ 85 — MENTAL ARITHMETIC. II No. 45. — ^To find the value of any number of a^ tides, when the price of one is given at 2Jdj at 5d., at 7Ja., at lOd., and at 15d* Rule. — Consider the given price as aliquot parts of one half-dollar, and divide by 12 for xjd., ny 6 for 5d., by 4 for 7Jd., by 3 for lOd., and by 2 for , 15d. .■■^rfm^:}^^^z. ^: ■-'■ I J^M'-f-^0^^ Exercises. 60 yards at 2M. each, 12 in 60= 5 half-crowns. 70 " at 5 d. " 6 in 70 = 11 — +20 d. 75 " at 7id. " 4 in 75 = 18 — + 22M. 80 " at lOd. " 3 in 80 = 26 — ^ 20 d. 90 . ^ at 15d. " . 2 in 90 = 45 — &c.,^ :it::,.yJ , &c mber of ar Jd., at 3d., a iliquot parti ?or 3d., by ; e answer ii )d.) + 2Jd. - +3 d. '■f '■■'' '■¥: '¥Sk*ff''< >.:^'*-'ij. ?^%,'- ■rr-' •-'••^■a;;'1*i/'»;:''; No. 46.-^To find the value of any number of articles, when tiie price of one is given at 7Jd., at lOd., at 15d., and at 20d. Rule. — Copsider the given price as aliquot parts of a dollar, and divide by 8 for 7Jd., by 6 for lOd., by 4 for 15d., and by 3 for 20 ; the anwer will be in dollars. : Exercises* 40 doz. at 7Jd. each, 8 in 40 » 5 dollars. fe60 " at 10 d. " ,6 in 60-10 " 80 " at 15 d. " ,4in80«20 " 4>;JC|..f^ at20d. " ,3in90«30 " 11 I Ii!'; 'I IS llil Ii !ifn \\ MEirr^AIIITHMBTIG. No. 47«r^Toflnd the value of any ntimber of ar- tidoH^ the price of one heing given at 2|d. an4 5d» Rule. — Consider the given price as aliqtiot p£u^ of a franci The answwr will be in flratOt. (2id. - i fr. and 5d. « i fr.) Exercises. V.'*. 40 yards at 2Jd. each, 40-f-4 « 10 /^'an^x. 64 "-^'^2|d. " 64^4 = 16 «» 80 « ^ &t5 d. « 80h-2«40 « 90, " X^ 5 d. " 90-4-2=^45 *^ :-^ ■'.:>: rj. -^';v| No. 48. — ^To find the value of any number of ar- ticles, when the price of one is given in ceniimei. Rule. — Multiply the number of articles by the price in centimes^ point off the two last figuiesr you have the answer in francs and cenHmfiz, ■ '. " V- ' .' ,,■"^^ +. ■- ' ■■■-■'.-,■-- 36tbs. at 6 '■->■'■■ ■-• ■ • % centimes each, 36 X 6«: 2 frs. 16c. 40 " at 8 « ' 40 X 8« 3 u 20c. 25 '^ at 10 « 25;x 10« 2 u 50c. 31 ** at 14 /"■ \ r. f. , 31 X 11 « 3 (C 41c. 50 " at 12 (( ' « 50x 12 « 6 (( 00c. 100 ''^ at 25 :.p^ " K. tOOx 25s! 25 ti 00c. &c., &c. -■■'.-.■Tfs.f'ii V.%P^' 32,5-f 24( 36( 32( 48( 33: 1. ^ at 2. \ at 4(1. 3. \' doz. ?- 4.^ doz. ?- at 50 c umber of ar- ali(|tiot plurts ;>';. francs. ■>?i umber of ar- I ceniimes, ctes bf tbe I figures 2 frs. 16c. 3 " 20c. 2 " 50c. '3 " 41c. 6 " 00c. J5 .^ 00c. J^T"'-'-^' —87— ^r; .>{;;,.^' .^.H%- ■ MENTAL ARITHMETIC, -r-i;'^!.. ., No. 49. — ^To find the value of any number of ar- ticles, when the price of one is given at 2d., 3d., 4d., 6d., and 8d. Rule. — Gut off the units of the given num- ber .of articles, and divide by 12 for 2d. ; by 8 for 3d. ; by 6 for 4d. ; by 4 fo^ 6d. ; and by 3 for 8d. ; but if there be remainders, double the first remainder, and, as before, divide it for shillings ; if there J3e a second, multiply it by 12, and divide it for pence as in the foregoing rules. • • ;• .Ai Thus, 325 articles at 4d. each. * " ' - 32,5 -i- 6= £5 + 25x2 = 50-^6 =8s. + 2x 12=24-^6 = 4d. = £5 8s. 4d. - Exercises. Ur> 240 yards at 2d. each. 366 " at 3d. '' at 4d. at6d. at8d. 326 480 333 u 24,0- 36,6 32,6 48,0 33,3 " =33.3^ &c.. &c. ■12=:£ 2 Os. Od. 8= 4 lis. 6d. 6= 5 8s. 8d. 4= 12 Os. Od. 3= 11 2s. Od. 1. What is the value of 126 yards of cotton at 2d. per yard ? at 3d. ? at 4'd. ? at 6d. ? at 8d. ? 2. What eost 360 lbs. of beef at 2d. per lb. ? at '3d. ?— at 4d. ?■ ^t 6d. ? ^at 8d. ? c^^.,^v ,. 3. What is the value of 480 doz. of apples at 5 cents per doz. ?— at 6 cents ?^— at 7 cents ? at 8 cents ? 4. What is the value of 600 doz. of pears at 20 cents per doz. ? — rat 25 cents ? at 30 cents ? — -at 40 cents ?-^— at 50 cents ? 'M ill ffi w it* ■ ^ mil M' — 88 — MENTAL ARITHMETIC. No. 50. — ^To find the value of any number of ar- ticles, the price of one being given in an even number of shillings. Rule. — Multiply the units of the number of shillings in the price for the answer in the shillings, and the remainder by half the price for the pounds. ' .' ". ■' >^;~ '"' 1 Exercises. -■ > ~ m:>^ 200 yar^s at 2s. per yard. 20,0 X 1=. £ 20 Os. Od. 224 at 4s. 22,4 X 2 = 44 16s. Od. 335 at 6s. 33,5 X 3 = 100 10s. Od. 420 at 8s. 42,0 X 4 = 168 Os. Od. 212 at 10s. 21,2 X 5 = 106 Os. Od. 420 u , at 12s. 42,0 X 6 = 252 Os. Od. "'4- f: 11 &c. J &C. ' » .1 - .- "u No. 51.—- Toflnd the value of a hundred- weight (112fts.) the price per lb. being given. Rule. — Take 9 times as many shillings, and 4 times as many pence, as there are pence in the price per Tb. ; because 9s. 4d. = 112d. c^.jj .^, ' Exercises. ' ." "^-^: 1 cwt. at 2d. per lb. 112^12 x 2 = £0 18s. 8d. 1 " at 3d. " " 112^12x3= 1 8s. Od. 1 « at4d. " " 112-4-12x4= 1 17s. 4d. 1 " at6d. " " il2H-12x6= 2 16s. Od. &c., &c. 1. What is the value of 1 cwt. of sugar at 5d. per lb. ? at7d.? at7id.? 2. What is the value of 144 yards of cotton at 2s. per yard t m — at4s.? at 6s.? at 88.? ^. ^ :-.fe- limber of ar- in an even number of he shillings, the pounds. ■•••■ ;.- '^ 20 Os. Od. 44 16s. Od. 100 10s. Od. 168 Os. Od. 106 Os. Od. 252 Os. Od. red-weight ngs, and 4 nee in the 18s. 8d. 8s. Od. 17s. 4d. 16s. Od. per lb. ? is. per yard ? -^ 89 — MENTAL ARITHMETIC. -.«'*'. No. 52. — ^To find the value of ia pound (Sb.), the price per cwt. being given. in shillings. -^^ \ Rule. — Multiply the shillings, by 3 and divide by 7 for the price of one pound in farthings ; because taking the shillings as farthings is the same as dividing- by 48 and dividing by 48 and by 7, and multiplying by 3, is the same as dividing by 112. Exercises. ■t.i?'. '=«^,'.; :ft. 1 lb. at 9s. per cwt. 9 x 3h-7 1 " at '•es. " " iO X 3-J-7 1 " at .Is. " " 11 X 3-4-7 1 " at 70s. " " 70 X 3-f-7 ! }d. and + .Id. « + Id. « + 7id. ' - &c. &c. -. ■* . No. 53.— -To find the value of a ton, the price per] ft), being given. ' Rule. — Reckon one pound for every shilling in the price of a ton, and add 6f 8d. lor every 4d. Thus, 1 cwt. = 112,lbs. at Id. = 9s. 4ci. x 20 = £9 6s. 8d. 1 ton at 2d. 1 " at 3d. 1 " at4d. 1 " at5d. 1 " at6d. •-. Exercises. per lb. = 18s. 8d. per " " = 28s. Od. « " " = 37s. 4d. « " " =: 46s. 8d. " " " = 56s. Od. " &c., &c. cwl « a .=:£1813&4dJ = 28 Os.Od. = 37 6s. 8d. = 4613s.4d. = 56 Os. Od.- 1 1 1. 2. What will be the value of a ton, at 7d. What will be the value of a ton, at 8d. pe;* lb. ? per lb. ? \ i ^i / m : i -SO- MENTAL ARITHMETIC. No. 54. — ^To find the Vcalue of an ounce, the price per lb. being given. Rule. — If it be an ounce avoirdupois, take the shillings as farthings and multiply by 3 ; if it be an ounce Troy, multiply by 4. Because^ taking the shillings as farthings is equal to dividing by 48 instead of 16 ; therefore we multiply by 3, for 16 X 3 = 48 ; and in the case of Troy-weignt we mul- tiply by 4, for 1 2 x 4 = 48. V Exercises. ^ 1 ft. Avoird. cost 3s. one oz. will cost 3f. x 3 = 21-d. 1 1 1 1 1 u L U U U O- > !' U it u u u u u u u C( 6s. 9s. 10s. 12s. 20s. &c., a u u u cc a cc cc cc cc cc :c cc cc it &C cc cc cc cc cc 6f. x3 = 4id 9f. x3 = 6M lOf. x3 = 7|d 12f. x3 = 9 d 20f. x3r-15d 1 ft. Troy cost Is. one oz. will cost If. x 4 = Id. 1" " " 2s. " " " " 2f.x4^2d. 1 " " " 3s. " " " " 3f. X 4 = 3d. I cc cc cc 4g, cc cc cc cc 4f. x4 = 4d. 1« " " 5s. " " " " 5f. x4 = 5d. &c., &c. Otherwise, reckon every shilling in the price one penny. 1ft. Troy «ost 10s. the value of 1 oz. is lOd. ^ 1 " cc cc lis. cc cc 1 " lid. 1 " (C cc 12s. ct cc 1 " I2d. 1 " cc cc 14s. cc cc 1 « 14d. 1 « cc cc 15s. cc cc 1 " 15d. 4< &c., &c. ■•i. , the price take the 3 ; if it be se^ taking ividing by by 3, for it we mul- '. x3 = 2Jd. :x3 = 4|(i . x3 = 6M . x3 = 7|d . x3 = 9 d . x3r-15d x4 = ld. x4^2d. x4 = 3d. x4 = 4d. x4 = 5d. the price is lOd. ' lid. ' I2d. 14d. ' 15d. ^ r- : ■ ■ ■ : .1 n : ■ '■" ■«.'''»-' ■,-v;..i. — 91 — MENTAL ARITHMETIC. No. 65.— To find the value of a pound (!b), the price per oz. being given. Rule. — If it be a pound avoirdupois, divide the farthings in the price per ounce by 3, for the an- swer in shilling ; if it be a pound Troy, divide by 4. Because, taking the farthings as shillings is multi< plying by 48 ; 48-r-3 c 16 o:?. avoirdupois; 48-r-4 = 12 oz. Troy. : ; ■ ■■'■••■. •"•■■'%. Exercises. 1 lb. Avoird. at 2d. per oz. 2 x 4f.-f-3 = 2s. 8d. 1 " " at 3d. " " 3 X 4f.-5-3 = 4s. Od. 1 " " . at 4d. " " 4x4f.-r-3^5s. 4d. 1 " " at 5d. " " 5 X 4f.-i-3 = 6s. 8d. 1 « " at 6d. " " 6 X 4f.-f-3 = 8s. Od. &c., &c. / lb. a u u u Troy u u u at 2id. per oz. 2J x 4f. -i-4 = 2s. 6d. at 6|d. '' " 6* X 4f.^4 = 6s. 6d. " 6| X 4f.-^4 = 6s. 9d. " 7i X 4f.-f-4 = 7s. 6d. 8 x4f.-f-4 = 8s. Od. &c. a u u Otherwise, reckon every penny a shilling. lib. 1 « 1 " 1 " 1" Troy u u at 7Jd. per oz. = 7s, 6d. at 9Jd. " " = 9s. 6d. at lOfd. " " = 10s. 3d. at llfd. " " -^ lis. 9d. at 12 d. « " « 12s. Od. SfC, &c. /n ■ i I ¥■ j ifi MENTAL ARITHMETIC. No. 56. — ^To find tho value of one article, the price of 5 being given in dollars and cents. >> Rule. — Double the given price and reject the units of the product, and the remainder will be the answer in dollars and cents, or in cents only. ^ , ' Exercises. .,f. 5 yards cost $4.50. 45,0 x !2 = 60.90 4.75. 47,5x2- 0.95 3.25. 32,5x2= 0.65 1.10. 11,0x2 = ' 0.22 10.20. 102,0x2= 2.04 21.50. 215,0x2= 4.30 24.00. 240,0x2^ 4.80 &c., &c. 5 '' 6 « 5 M « 5 " 5 " 6 « liiv ■>■■<, No. 57. — ^To find the value of one article, the price of 10 being given in dollars and cents. , Rule. — Reject the last figure of the cents and alsc the point in the given price, and you have thfl answer in cents. . .^, I '-,- 'T- '■■■ ■.i''-W^: Exercises. 10 fts. cost 10 " " 10 " ."' 10 " " 10 10 10 u u u u u 1.10, each lb. will cost $0.11 1.20, " " " " 0.12 4.50, " " " " 0.45 3.25, •" '^ " " 0.32} 25.00 17.30; 18.00, &c.. (( u a a u &C. u u u u 2.60 1.73 180 20 q 20 20 20 20. 20 20 1. quire 2. yard^ icle, the price id reject the cr will bo the is only. $0.90 :^' 0.95 0.65 yim:^ • 0.22 --0:^0:^ 2.04 4.30 : 4.80 tide, the price cents and also jrou have th< cost $0.11 " 0.12 a 0.45 0.32} 2.60 1.73 1.80 — 93— .; ;; , MENTAL ARITHMETIC. No. 58. — ^To find the value of one article, the price of 20 Leing given in dollars and cents. Rule. — Reject the point and the uniis, and divi de by 2 for the price. ' See page 70. , / Exercises. ' ;^^ ; 20 yards cost $4.40. 44 h-2 20 20 20 20 20 20 u (I (( u 2.10. 21 -T-2« 3.50. 35 -f2=r 3.G5. 36} -^ 2 = 6.20. 62 -4-2 = 8.40. 84 .4-2 = 10.50. 105 -2 = .22 per yard. 0.10}" 0.17} " 0.1 8| " 0.31 '' 0.42 " 0.52} " u 20 cwt. 20 '' 20 " 20 " 20 " 20 " 20 " • 20 quires 20 " 20 " 20 " 20 " 20 " 20 JL- cost$ 17.30. 19.75. 15.00. 33.15. 99.50. u a (I u u u 173 -i-2 = 197}-j-2 = 331} -J- 2 = 995 -v-2 = 121.00. 1210-4-2 = 200.00. 2000 -4-2- $0.86} 0.981 150-^-2= 0.75 1.651 4.97} 6.05 10.00 per cwt. u u u u u u li u u u u of paper cost $ 3.20. 324- 5.00. 50 -f- *6.00. 60-4- 10.20: 102-T- 5.50. 55-r- 4.00. 40 -f- 20.00. 200 -^ &c. (C u u u 2 = $0.1 6 p. quire 2= 0.25 2= 0.30 2= 0.51 2= 0.27} 2= 0.20 2= 1.00 u (I u u u u &c., 1. If 20 quires of paper cost $4.00, what will be the costpor quire? 2. If 20 yards of cloth cost $50.00, what will be the costpor yarcT? ■ 'iK*-:* ^ ,.N»,'; I :■% ■/».- A — 94 -A MENTAL ARITHMETIC. No. 59.— To find the value of one article, the price of 30, 40, 50, 60, 70, 80 and 90 articles b jing given in dollars and cents. Rule. — Reject the point and the units, and divide by 3 for 30 ; by 4 for 40 : by 5 for 50 : by for 60 ; by 7 for 70 ; by 8 for 80 ; by 9 for 90. Thus, 30 yards cost$5l.00 (510- 3 = $1.70 per yard). Exercises. 30 yards cost $ 5.50. 55 -^ 3 = $0.1 8^ per yard. 30." " 7.25. 72^-3= 0.2 if " " 4.75. 474^3= O.lo^ 9.00. 90 -f- 3= 0.30 30.00. 300 -f-3= 1.00 99.90. 099 -3= 3.33 30 30 30 30 a a u u u Li. U H u u a a a u &C., &C. 40 lbs. cost $14.00. 140-f-4 = 40 40 40 40 40 40 a u u u u u u u u u .35 7.00. 70-f-4--= 0.1 7J 12.50. 125--4= 0.31i 4.40. 44--4= O.il 1.10. li-v-4= 0.021 72.40. 724--4= 1.81 80.00. 800-f-4= 2.00 per lb. a u li a u u u u &C., &C. 50doz. cost $ 6.00. 60-j-5 = $0.12 per doz . 50 " " 6.50. 65-f-5= 0.13 '' " ' ^4 60 " " 7.00. 70-f-5= 0.14 i 50 " " 48.00. 480-^-5= 0.96 50 " " 66.50. 665-v-5= 1.33 •50 " " 75.50. 7^-v-5=. 1.51 (( u (( u C( u (C a 50 (( (( 80.00. 800-f-5= 1.60 " ** &c. &c. - w. ' -'.V, ^/ ticle, the price bjiiig giveu in le units, and for 50; by for 90. Thus, r yard). !J per yard. , I u u U U per ib. h " '' ^ a a u u u u u u u u per doz. iV.-.^ i^"J — 95— . MfiNTAL ARITHMETIC. Exercises. 60 ft>s. cost $ 50.40. 504 -f- 6 . $0.84 per fh. 60 " 60 " 60 " 60 " €0 " a u u 48.60. 486 -T- 6= 0.81 36.00. 360 -f- 6-- 0.60 86.50. 805 -T- 6= 1.44^ 100.00. 1000-6= 1.66f 486.66. 4866 -T- 6= 8.11 &c., &.C. u u u 70 yards cost 70 '' " 70 " " 70 " " 70 " " 70 " 8.40. 84--7 = $ 0.12 per yard 9.10. 91-^7= 0.13 " " 63.70. 637-^7= .0.91 " " 88.90. 889-^7= 1.27 " " 77.70. 777-f-7= 1.11 " " '* 777.70. 7777-^7= 11.11 " " he. &c. *r- i 80 doz. cost $ 88.80. 888^ -J- 8 = $1.11 per doz. 1.23 " *• 1.88J- " " 1.85 J- " " 1.20| " " 1.63tV" " 80 98.40. 984 : 8 80 1 50.50. 1505 ^8 80 148.20. 1482 -v-8 80 96.70. 967 4^8 80 130.75. &c., 1307J : 8 90 90 90 90 190 *i ■fM '(4 (I a a 40.50. 405 -^9 = 20.25. 202^-^9^ 90 lbs. cost $81.00. 810 -f-9--^$0.90 0.45 0.22J 0.10 0.12 0.15 27.00. 270 -4-9 = 0.30 per lb. 9.00. 90 10.80. 108 13.50. 135 -9- 9 = 9:^ a a u u u u u ^ ^C, \ ^c, ^^',yMf^^::<^'ly — 96 — MENTAL ARITHMETIC. No. 60.-^To find the value of 2 or more doz., the price of one article being given in pence. Rule. — Consider the given price as shillings, and multiply by 2 for 2 doz. ; by 3 for 3 doz. ; by 4 for 4 doz. ; &c., and you have the answer in shillings. See page "65. Exercises. 2 doz. art. at 2d. each X 2= 4s 9doz.arLat 9 d.eachx 9= 8ls 3 ' at 3d. X3= 9s 10 " at to d. XlO=lOOs 4 ' at4d. X4=lGs 11 " at 11 d. Xlt=12ls 5 ' at5d. ^ ii X5=25s 12 "" at 12 d. Xl2=l44s 6 ' atCd. xn=3Gs 12 " at lh\. X 12= 90s 7 ' at7d. X7— 49s 12 " at 8^d. Xl2— I02s 8 '■ atSd. X8=64s 12 " at 9id. X 12— 1 14s &C., &C. • . No. 61. — ^To find the value in dollars and cents of 2 or more doz., the price of one article being given in peace. Rule. — Reckon every penny in the price 20 cents, and multiply as above. Exercises. ' * 2 doz. articles at 2d. each. 20 x 2 x 2 = S0.80 3 " 4 " 5 " 6 " 7 " a a u u at 3d. at 4d. at 5d. at 6d. at 7d. &.C., u a 20x3x3 = 20x4x4 = 20x5x5 = 20x6x6- 20x7x7- 1.80 3.20 5.00 7.20 9.80 &c. 1. If an apple cost IJd., what will be the cost of 6 doz.? 2. If a pear cost 2id., what will be the cost of 12 doz. ? >■. 5 - •■-» , -■ * tnoredoz.j the ;e. shillings, and z. ; by 4 for 4 shillings. See d.eachx 9= 8ls d. d. d. d. d. d. <( XlO=lOOs xn=i2is Xl2=l44s X 12= 90s Xl?=l02s Xl2=ll4s s and cents of [e being given price 20 cents, 2 = 80.80 3 = 1.80 4 = 3.20 5 = 5.00 6- 7.20 7- 9.80 )st of 6 doz. ? of 12 doz, ? -; i ■' -97 — MENTAL ARITHMETIC. No. 62. — Given the yearly rent of a house in £*8., to find that per month. Rule.— Divide the £'s., by 3 and you have the ansvi^er in dollars. Exercises. A house rent of £18 per annum, 18-^-3 = $6.00 20-^3-^ 6.66f 25-j-3= 8.33J 60-r-3 = 20.00 80-f-3 =.26.66f 90-f-3 = 30.00 u u u u u u u u u u u u i. a u u u u 20 (( 25 (C 60 '.(. 80 u 90 a &c.. &( No. 63. — To find the percentage or assessment, when it is given in half-pence per pound, or in cents per dollar. Rule. — Reckon one shilling and one half-penny for each hundred dollars. If it be cents, multiply by the cents and divide by 100. £ 62 10s. = $ 250 at p. = £0 2s. 7Jd. 75 = 300 atl d.= 6s. 3 d. 150 = 600 atl d.= 12s. 6 d. 300 - 1200 atljd.- 1 17s. 6 d. &c., &c. ^ 300.00 at 1 600.00 at 2 1200.00 at 3 2400.00 at 4 2500.00 at 5 3000.00 at 6 3600-00 at 7 4000.00 at 8 &c., cent =$ 3.00 cents = 12.00 cents = 36.00 cents = 96.00 cents = 125.00 cents ^180.00 cents = 252.00 cents = 320.00 &c. ''*(i» '^c^ — OS- MENTAL ARITHMETIC. )■'•«■ ' No. 64. — ^To find what any number of pence per day will amount to in a year. ftule. — Add together as many pounds,half-pounds, and live-pences, as there are pence per day. Thus, 4 pence per day, is 4 pounds 4 half-pounds, and 4 flve-pences, per year ; that is £6 Is. 8d. Because £>\ = 240d., 10s. = 120d. + 5d. = 365. Orj take 365 as pence, that is £1 10s. 5d„ and multiply this by the number of pence per day. Exercises. 365 days at ld.=£l " " at 2(i.= 3 " " at 3d.= 4 " " at 4d.= 6 " " at 5d.= 7 103. 5d. Os.lOd. lis. 3d. li. 8d. 12s. Id. &C., 365 days at 6d.=$ 9 2s. 6d, *' " at 12d.= 18 5s. Od- " « at 15d.= 22 16s. 3d " " at 24d.= 36 10s. Od " " at30d.= 45 12s.' 6d* &C. If it be cents instead of pence,multiply 365 days by the cents and point off the two last figures. Exercises. 365 days at .01 " " at .02 " " at .03 " " at .04 "• " at .05 \ 3.65 7.30 10.95 14.60 18.25 &c.. 365 days at .10 = $ 36.50 " '^ at .20= 73.00 " " at .25= 91.25 " " at .40= 146.00 " " at .50= 182.50 &c. 1. If a man smoke 3 sGgars a day, at IJd. each, for how much will he smoke in a year? 2. If a man drink 4 glasses of wine a day, how much will he drink in a year, and how many »ents would il cost at 4 eents a glass ? 3. If a man drink a pint of milk a day, how many gallons Will ho drink in a year, and how much would it Q05t at Is, pcrgftUon? "^ c. ber of pence per * nds,half-pounds, per day. Thus, f-poimds, and 4 8d. Because £>\ £1 10s. 5d„ and ice per day. 6d.=$ 9 2s. 6d 12d.= 18 5s. Od* 15d.= 22 16s. 3d 24d.= 36 lOs. Od' 30d.= 45 12s.' 6d' iply 365 days by gures. at .10 = at .20 = at .25 = at .40 = at .50 = $ 36.50 73.00 91.25 146.00 182,50 d. each, for how how much will )uld il cost at 4 )w many gallons luld it Qost at Is, — 99-^ MENTAL ARITHMETIC. No. 65. — ^To find what any number of pence or cents per day will amount to in a year, omitting Sundays, (313 days). Rule. — Add together as many pounds, dollars, shillings and pence, as there are pence per day. Thus, 3 pence per day, is 3 pounds, 3 dollars, 3 shillings and 3 pence, per year of 313 days: that is £3 IBs. 3d.— Because £l-240d., 1 dollar =60d., 1 shilling = 12d. and 1 penny = 313. Or multiply £1 6s. Id. by the number of pence per day. If it be cents, multiply 313 by the cents. Exercises. 313 days at ld.=£ i 6s. Id. " at 2d.= 2 12s. 2d. " at 3d.= " at 6d.= " at 7d.= tt (< « 3 18s. 3d. 7 16s. 6d. 9 2s. 7d. at 13d.= 16 19s'. Id! at 14d.= 18 5s. 2d. at20d.= 26 Is. 8d. 313 days at .01=$ 3.13 at .02= 6.26 at .03= 9.39 <( ti (t at .04= (( at at (( 05= 06= at .07= at .20= 12.52 15.65 18.78 21.91 62.60 ,&C, &c. 1. If Emma earn 7id. a day, how much will she earn in a year, omitting Sundays? * 2. IfLeda earn lOd. a day, how much will she earn in 313 days ? 3. If Francis spend 9Jd. a day, how much will he spend in 313 days? 4. If Lewis gave to the poor 4Jd. a day, how much will h» gave in a year, omitting Sundays ? 5. If Ned gave to his sister Mary 3d. a day, how much will he gave her in 313 days ? 6. If Nicholas earn 25 cents a day, how much will he mx^ ii|3t3day3? . .* \ * : i i — too — MENTAL ARITHMETIC. • V No. 66. — ^To find what any number of pence or cents per day, will amount to in 300 days. Rule. — Add together as many pounds and dollars as there are pence per day ; or 5 dollars for every penny per day. If it be cents, reckon 3 dollars for every cent. Exercises. 300 days at 1 d.=£l at 2 d.= 2 at 3 d.= 3 at 4 d.= 5 at 5*d.= 6 at 6 d.= 7 at7id.= 9 it It 4d.= i8d.= )Ocl.= )0d.= rOd=: 50d.= 1 60.00 120.00 240.00 250.00 300.00 350.00 400.00 .05- $ 15. .06 = 18. .20 = 60. .4(1 = 120. am in 300 days? 11 she spend in i^ill he earn in 1 will he spend ill he earn in ;h will he spend vill she earn in will he spend ■■■/:i''.f ''r' '':■■ ',t^^ ''-sw:'. ■%>«: • t . ■ ■ct:;' — 101 — MENTAL ARITHMETIC. No. 67. — ^Tp find what any number of shillings per week will amount to in a year. Rule. — Take two and a half as many pounds and twice as many shillings, as there are shillings per week. Thus, 6s. per week is £15 12s. ; for twice as many pounds is £12, and half as many pounds is £3, and twice as many shillings is 12g. and £12 + £3 + 12s. = £15 12s. Exercises. ^ 52 weeks (a year) at •2s. per week = £ 5 4s. Od. (( u u u u a (C u u 11 Sit 4s. (C s: 10 8s. Od. at 6s. (( =z= 15 12s. Od. at 7s. t; s; 18 4s. Od. at 8s. • u ■M 20 16s. Od. at 10s. u = 26 Os. Od. &c., • &c. '. No. 68. — To find what any number of pence pei week will amount to in a year. ^ Rule. — ^Take 4 times as many shillings and pence as there are pence per week,and if there be farthings in the rate, add Is. Id. for every farthing. If it be cents, multiply 52 by the cents. Exercises. 52 weeks at 6d. per week = 26 shillings. «' " at7d. " " =30 " «' " at8d. " " =34 " '' " at9d. '• " =39 " and4d. and8d. &c.. &c. ''>y' 1. If Edward earn lOd. per week, how much will he earn in a year? 2. If James spend 40d. per week, how much will ho spend in a year? ;.iv Wfi.^'> \- ^^r r-:'^ -102- MENTAL ARITHMETIC. * No.69. — ^To find the interest or discount upon any given sum at 5 per cent, per annum. Rule. — Reckon one ishilling for every pound, and 3 pence for every 5 shillings. . ^ Exercises, £12 10s. Od. at 5 o/o per annum = £0 128. 6d. 15 5s. Od. at ss 15s. 3d. 18 10s. Od. at s^ 18s. 6d. 25 15s. Od. at SI 1 5s. 9d. 68 Os. Od. at S; 3 8s. Od. 70 5s. Od. at &c., &e. 3 10s. 3d. No. 70. — To find the interest on any given sum foi any number of montLs at 5 per cent, per annum. Rule. — ^I'ake the pounds as pence, and multiply them by the number of months, for the ans- wer in pence. Thus, £4 at 5 o/o for 2 months, 4x2 = 8d. Exercises. 1 7 Os. Od. at 5 o;o p. a. for 3 months. 9 10s. Od. at " *' " 3 " 60 Os. Od. at " " " 7 " 72 Os. Od. at " " " 9 144 15s. Od. at " " " 9 « ? X3= 9JX3! 21 d 28id 60 x7= 420 d 72 x9=: 648 d 144£x9=:1302Jd &«., &e. 1. What is the interest on £48, for 3 months, at b^j„ per annum ? mw . '2. What is the interest on £54 10s., for 5 months, at 5«;, per annum? N 3. What is the interest on jgiOO, for 7 months, ftt 5 '^^ j)§i ttanumf I cl Dnany d, and 6d. . 3d. . 6d. . 9d. . Od. . 3d. sum f 01 num. ultiply ans* s,4x2 21 d 28)d 420 d 648 d :13025d |5o2o per at 5«>2, 1> p«l ..••■ y^ — 103 — / ■ ■ --r MENTAL ARITHMETIC. • No. 71. — ^To find the interest on any sum at 5 per cent, per annum for any number of days. Rule.— Multiply the days hy J of the sum, and reject the units for the answer in pence. Exercises. £21 at 6 0/0 for 6 days. 21-J-3 = 7 x 6 = 4,2 = 4 d. 24 at " " 7 " 24-^3= 8x 7= 5 6= 5id. 60 at " " 8 " 60-5-3 = 20 X 8 = 16,0 = 16 d. 90 at " "20 " 90-7-3 = 30x20 = 60,0 = 60 d. &c., &c. No. 72.— To find the interest on any sum at 6 pei cent, for months. Rule.— Multiply the pounds by the months; cut off the units of the product, and the remainder will be the interest iu shillings. The units cut off ar« tenths of a shilling. When the sum is in dollars, and the interest is to be found for two months, divide by 100. See page 109. ^ Exercises. £ 7 at 6 0/0 for 3 months. 7x3= 2,1 = 2s. Id. 30 at " " 5 " 30x 5= 15,0= 15s. Od. 60 at " "10 '* 60x10= 60,0= 60s. Od. 100xl2 = 120,0 = 120s. Od. 100 at " "12 " $140 at 6 o;o for 2 months =$1.40 420 at " " 2 " ^ 4.20 • The interest on$140lbronemonth will J3e$i.40^2=$0.70 • for 3 months, $1,40+0.70=$2.10 ; for4 months, $1.40x2=$2.80, &c. p, ■• 1;" ',-i *ft-^ ^. ■.,, — 104— 4;;.;':' MENTAL arithmetic' ;(i No. 73.— To find the interest on any given sum in dollars and cents for a year at any rate. Rule.— Multiply the sum by the rate, and cut off She decimal figures; ^^ m. ... i' Exercises. $ 50.50 at 6 o;o 25.25 at 6 " 60.40 at 7 " 84.50' at 7 " 125.50 at 8 '' ,275.25 at 8 '■' 320.00 at 9 " 444.20 at 9 '' ^555.55 at 10 " 777.77 at 10 " 50.50 X 6 = $ 3.03 • 25.25 X 6= 1.51,50 60.40 X .7= 4.22,80 84.50 X 7= 5.91,50 125.50 X 8= 10.04 275.25 X 8= 22.02 320.00 X 9= 28.80 444.20 X 9= 39.97,80 555.55x10= 55.55,50 777.77x10= 77.77,70 '•■" &c. ' . '\ ' -t ■.yf^flkf ■•7^ 'i^ ■if-f-' Per annum. W $1.00 at 1 per cent, is 1.00 at 2 per oent. is 1.00 at 3 per cent, is 1.00 at 4 per cent, is 1.00 at 5 per cent, is 1.00 at 6 per cent, is 1.00 at 7 per cent, is 1.00 at 8 per cent, is 1.00 at 9 per cent, is 1.00 at 10 per cent, is 1.00 at 11 per cent, is .11 1.00 at 12 per cent, is .12 1.00 at 13 per cent, is .13 &c., &c. .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 ^ >■*. i^*^; .♦■J'- v. ■S-.<;- di ad V -* the ]•■:■> Tl jand No., * f^ancsA anniun add a answej ^ccordj ■?* $800 Z $3000 ? ;; — on 31 £666?. 'm.>^:^. a '~'':55^'' — 105- 1 ^ ,. MENTAL ARITHMETIC. No. 74. — ^To find the interest of any given sum in francs, or in dollars, or in pounds at 5 per cent, per annum. Rule. — When the sum is in francs or in dollars, add a cipher and take the half after having cut off the two last figures, and you have the answer in francs or in dollars, according to the case. Thus, 125 francs at 5o/o 12,50-5-2= &frs. 25 c. 125 dollars at 5o/o 12,50-r-2==$6.25 When the sum is in pounds, cut off the units '' /ind take the half of the sum for tne answer. Thus, £125 at 5o/o 12,5-f-2 = £ 6 5s. ^- 722 at 5o?o "72,2-^2= 36 2s. &c., &c. ^■■i- ..'■' 1-^^^:' ■■■"■■ "'' No, 75. — ^To find the interest on any given sum in • francs J or in dollars, or in pounds at 10 per cent, per annum. Rule. — ^When the sum is in francs or in dollars, add a cipher and cut off the two last figures for the answer in francs and centimes, or in dollars and cents, according to the case. ■\. '■^ f >. -: - Thus, 1236 /)\incs at 10o;o= /V'5.123.60 V V 1236 dollars at 10o?o= $123.60 1. What is the interest on $700 at 5 % per annum?— —on $800? on $1000? on $1,200? on $2500? on $3000 ? 2. What is the interest on 200 francs at 5»/o per annum ? on 300 frs. ? on 400 frs. ? on 500 frs. f on 600 frs. ? on 800 frs. ? — -on [000 frs. ? 3. What is the interest on £355 at b% per annum ? — ^on £666.? on 3333 frs. lO'f, ? on$3333 at lO^o, — M06 — MENTAL ARITHMETIC. When the sum is in pounds, double iho units for shillings, and the interest is thus found. Thus, £ 4044 at 10o/o£.404 Ss. i\^ »-H 5555 at 555 lOs. 6666 at 666 128. 7777 at 777 14s. 8888 at 888 16s. 9999 at 099 i8s. 10000 at 1000 '.i. »: f'i;f-. J: J tl I til 1 in v«.f w 1 iO'J No. 76. — ^To find the interest on any sum at 4, 5, 6, 7, 8, 9 and 10 per cent, per annum for days. Rule. — Multiply the sum by the number of days anddividnby . . •f ^ 3650. for the interest at tOO|0 1 ; 4055.6 " at 9 ' '\'''\ .4562.5 " at 8 ■ -■ '^if*- 5214.3 " at 7 ■ !■ ^* 6083. " at 6 ; ,,* 7300. " at 5 4 .. '';, :-'>-'**'fj^'" When we consider, as we do it in the Banks of France, Ihe months of ti)e year of 30 days, we wiU divide the product by -; 3600 for the interest at lOo/o ■'.''V' .' . 4000 (( u (( at 9 4500 u u cc at 8 5143 u u u at 7,.v,^;:,; ^6000 u u (C at 63..!-^^' *: 7200 a ii cc at 5'-'"^' 8000 u u cc at 4J 9000 u n cc at 4 ,: i.VTr ;■• ,-"; ;■*■ ■ /".:e!'i-..-.- •\rV^:i;^:B^5;:# >?'■ 4,5,6, o£ day« — 107- MENTAL ARITHMETIC. No. 77. — To find the interest on any given sum in dollars for any niimbor of days, at 6o;o per annum. Rule. — Multiply the given number of dollars by the number of aays, then, cut off from the product the units, divide by 6, and you have the interest in cents. > ^ v t-. Exercises. $250 for 10 days = 250,0-f-6 = $0.41 J 455 " 20 " = 910,0h-6=: 1.51| 500 " 27 " =1350,0-f-6« 2.25 650 ". 33 " .-.2145,0-*-6-. 3.57J &c.. &c. Banlift o( •we "Wi** No. 78. — ^To find the interest on any given sum> in dollars for 6 days or a multiple of 6, at 6o;o per annum. 'V .:'^.u:.,n v.>)-. Rule.— In pointing off the units of tl\e giver sum, you have the interest in cents for 6 days, then, multiply , by 2 for 12 days ; by 3 for 18 days ; &c., but, when the number of days is less than 6, or exceeds 6 or a multiple of 6, subtract or add the aliquot parts of 6 as it will be required. Exercises. ^ > $250 for 6 days 1 » $0.25 455 " 6 (( # = 0.45* 250 " 12 u x2 = 0.50 455 " 18 u xa = 1.36* .= 0.37| 850 " 9 u +i HO '< 17 u &c., X 3 (-*of &cr 25)= 0.70i ji :: -108 MENTAL ARITHMETIC. No. 79. — ^To find the interest on any given sum in dollars for any number of days at 7 o;o^ 8 o/o, 9 o/o per annum. Rule. — Reject from the principal the units, mul- tiply by the number of days divided by 6, and add to the product ^ of itself, when the interest is at 7 o^o ; add J if it be at 8 o/o, and add J if it be at 9 o/c ; for the answer in cents. Instead of dividing the number of days by 6, we sometimes divide the principal by 6, after ha^ ^ng before cut off the units. I Exercises. u in 1 pe 1 prj 1 mi 1 iim $240 for 240 " 240 " 24« " $420 for 420 " 420 420 a it $840 for 840 " 840 " 840 " Interest 24 days. 24 30 " 24 36 " 24 42 " 24 Interest 24 days. 42 30 " 42 36 ^' 42 42 '• 42 Interest 24 days. 84 30 " 84 36 " 84 42 " 84 at 7o/o. x4= 96+J = $1.12 x5_120 + i= 1-40 x6 = 144 + i=; 1.68 x7 = 168 + i- 1.96 at 8o/o. X 4 = 168 + J = $2.24 x5 = 210 + J= 2.80 X 6 = 252 + J= 3.36 X 7 = 2944 J= 3.92 at 9 o/o- x4 = 336 + i=-$5.04 x5 = 420 + i= 6.30 x6 = 504 + i= 7.56 X 7^588 + 1=^ 8.82 Interest at 7 »/o. $240 for 5 days. 24,(H-6=4 x 5=20+l26=$0.23j. Interest at 3 o/o- $420 for 7 days. 42,0-f6=7 x 7=494-i=$0.65i. Interest at 9 "/o- $840 for 8 days. 84,0-f6-=14 x 8=112+i=$1.68. 9% . No. ^n doJl per anr Rult cipal c« \1>. ad pt be at] klOM|V mmm ■«> >:w: sum , 9 <>?o mul- idadd 6, we .12 L.40 1.68 .96 2.80 3.36 3.92 )5.04 6.30 7.56 8.82 — 109- : •^*'<;-- . ^-^ .. • ■ ■ • ;^V ^ MENTAL ARITHMETIC, "No. 80. — ^To find the interest on any given sum in dollars for 1 month at 6>, 7o/o, So/o and at 9o/o per annum. Rule. — When the interest is at 6>, divide the principal by 2 and call the quotient cents for the interest of 1 month ; if it be at 7o;o, add to the quo- tient i of itself ; if it be at So^o, add J, and if it be af 9o/o, add J. . Exercises. $240 for 1 m. at 6o;o. 240-4-2 240 " 1 ra. at lojo. 240—2 = 120 + 4 = 240 " 1 m. at 8o;o. 240-^-2 = 120 + 4 = 240 " 1 m. at 9o/o. 240^2 = 120 + 1 = SI. 20 1.40 1.60 1.80 &c., &c. No. Sl.—To find the interest on any given sum in dollars for 2 months at 6o;o, 7o;o, 8o/o and at 9> per annum. Rule.— -Wh-en the interest is at Go/o, call the prin- cipal cents for the interest of 2 months ; if it be at 7o;o, add 4 to itself ; if it be at 8o/o, add J, and if lit be at 9^7 add J. Exercises. $366 for 2 m. at 6o/o 366 3S6 366 u u a 2 m. at 7'J/o + ^ 2 m. at 8o?o + 1 2 m. at 9> + 1 $3.6j6 4.27 4.88 5.49 &c., &c. I - *4 "*^; "''■ :v'i': . -.i >^ •-'.rt, ' ■ »< :■ •i«*'> — 110-^ . MENTAL ARITHMETIC. ;>., ;*■;,(' :i^-^';. No. 82. — ^To find the interest on any given sum in dollars for any number of months at Go^oj 7o;o, 8o;o and at 90/0 per annum. ' v r Rule. — When the interest is at 6o;o, mukiply tfee' principal by the number of months divided by 2, for the interest in cents ; if it be at 7o;o, add to the Erincipal J of itself ; if it be at 80/0, add i, and if it e at ^o/oj add J, then multiply the sum by the months divided by 2. , Exercises. $240 for 3 m. at 60/0. 240 xlj 240 " 4 m. at 60/0. 240x2 = $ 3.60 = 4.80 $240 for 6 m. at 7o;o. 240 + i x 3 = $ 8.40 240 " 8 m. at 70^0. 240 + |x 4= 1^20 $240 for 8 m. at 80/0. 240 + J x '4 = $12.80 240 '' 14 m. at8o?p. 240 + ix 7= 22.40 $240 for 16 m. at 9o/o. 240 " 20 m. at 90/0. 240 + J X 8 = $28.80 240 + 1 X 10= 36.00 &c 1. What is the interest on $555 for 3 years and 9 months at| 3 yearsxl2+9=45^2=22i. 555x22J=$124.87j. 2. What is the interest on $666 for 6 years and 6 months at| 7>? 61 years X 12=784-2=39 666+^=777 X39=$303.03, To No in do years, Ru forth the h rules 6mon -»«-«4 •'•■'*!'■■ far sft stun [ply tl^e d to tke ind if it by the 3.60 . 4.«0 ' i 8.40 n.2o 1 H ^12.80 22.40 « |$28.80 36.00 |9 months at I 6 months at] — Ill — MENTAL ARITHMETIC. ^tum$:mm^:zc TABLE ■■■Ml^ #r. To find tlie interest on any given sum in dollars at 6 <^p per annum, for any number of years, -fffa months and days, f^ '! Months. Tears. 16 Months. Days. Prinoipat. 200 = 8 . , » 1 100 = 8 - 4 ■■: ^^0-^'^- ;l/: 'M?ll -J- 50 = 4 2 M *' =' 1 25 = 2 1 Q.?4i J/ ss' ' i 20 = 1 8 ' - iV 12i= 1 15 = iV 10 =: 10 = uV 6f = 6 20 - w 5 = 5 .. ^ = Vff ^^ 2 15 = w No. 83.— To find the interest on any giv6n tuim in dollars at»6 o;o per annum, for any number of years, monthc and days. Rule. — Take the aliquot parts of the given sum for the interest of the years and the months, and for the interest of the days, do as in the preceding rules ; thus, what is the interest on $358, for 2 years? 6 months and 6 days ? -r^ 0ji 25* months = J of $358 = $44.75 ||,.^, M.^:^ -^ of 358 = 8.95 fiidays «.■ ' :^f^:^?-my 35,8:- /:\^^ \ ■■'■■■^■^M,^4-fmm^ Answer $54.05^ '^:.Z'.:r ■ l "ff^^^' '^•■^M^f'^^-^t^P^-^- il i ifeS** ■te!-f ■■: mm •'■ :•' ? r MiTfikETIC: '£wm-'i]$iQ '^k^i'^r^. t- /.:-|^ No. 84. — ^To find the value of one or more penny, weights, the price of ^. grain (XTfy^yfmMiMM^m being given. .. - ' ^; ; n^^':'\-':\¥'--x^ Rule.— Reckon 28. for every pisnny in the price, and multiply i)y the number of penny-weights. ' •■*?'Cl-'.->-N»rflV*(*.!**»r' ■i i dwt at ? d. per gr. = ?s. x 2' = £0 4$. 6d. . 2 ".at 3d. " "=2s.x3 x2= 12s. Od. I 3 " atSJd. " "=:2s.x3ix3= 1 Is^Od.. i: M:^!W''M^^^^ &c.,%:/ &ci- ■^)i-'-^.^^«"-f'l. J U: t M> No. 85. — To find the value of a grain (Troy weight,) the price of a penny-weight in shillings being given. Rule. — For every shilling in the price reckon ■ one halfpenny. ^.^ ,.|^, ^^.^ ;,;,,, :.^^ ;---''-'>:>*:^'5;' ;'■■■ ." Exercises. n'-iW-fr'Of^: ,ev^?v*^^'- Isfl; •^M- -Hy' .. to.-:^ 1 grain at 4s. per dwt. =4 half-pence = 2 d. " " " " «3 d. «3id. " at 6s. " " =6 u # " at 7s. " u 7 ^ J' :immri- tlLl Ls 1. At 2id. per ^rftin, hCiw much for 4 penny-weights ?- for 8 ponny- weights ? — -for 12 penhy-weights ? 2. 1 dwt. at 5s;, what cost 1 grain of gold? at 6s.?- ftt 7s. ? at 9s. ?- at 10s. ? at Us. ?- — -at 12s. ? 3. At 4d. per grain, how much for 2 penny-weights ? foi 6 penny-weights? fo^8 p«niiy-weights ? for 10 penny] weights ? for 12 penay-weights ? for 14 penny-weights j ■^fV>' f 3. At at{ 4. At — at^ V wer- •»-*h'Wt«r»?'CT«*'^ " ' •r-T'W.. ■iviMHI il.iHljllWUIIiW.miff :',>^ >V' ■ /■■■'Jt, penny- a pence e price, rhts. ^10 » :'.r 4s. 6d. 29. Od. Is. Od. - ■ ;»;'!■ 5 dn (TroV shiUings 5e reckon ^' '. , ~ ■ >*._■■• -^ .■■^' 2 d. 3 d; 3id. reighis?- '-i :K *■ ■ t ':-'.',V', iV-j"''-" ;-;■■?" >»>{, ■■:: ''^z^B-0(,-^i^ "MteNTAL ARITHMETIC. ::^:,.. ..,.,,,.. ir No. 86.— To find tne value of an ounce, the price I of a grain (Troy height,) in pence being giv^n. Rule.— Reckon £2 or $8. tat every penny m th§ price; or double the pence of the price gives tne price of an ounce in pounds. _.|jir'^f:^,--fV:'. . Exercises. ■?\i:^ ;■• ■:>*. sr. ■T. 1 dz. at IJd. IVIES' gr. =$8x if J$i2. 1 " at 2 d. J^. " = 8x2 =16. '«i>i..! 2,,„".M2ji.vS= ^.m %^jxjii5 m. 1^ ' i'pxiJf' * ■■'■; 4'i^^V"|^J ' 'I^ No. 87. — To find the value of a grain (Troy weight,)the price of an ounce in dollars neing given. Rule.— For every $8. in the price reckon one penny. -.'::'„,,..., . .. •--■.-- ■ - :' ^' - Exercised, ^v ■■■■ ,■'.'» ••»}' 1 i <■- „ 1 grain at $12. peroz. = lJd. 1 " at 16. " " =2 d* ^" : ^--« at 24. " " =.3 d. i;t^.:."-^ #-" at 32. " • "■=:4d.f^'%5^W^^ "^'^c, fc. Ei rhts? -^0^ jr 10 i)enny [ny-weigWs 1. At 2id. per grain, what cost an otiilce of gold ? at 2%d ? — at 3d.? at 3 id.? 1. At $20. per oz., whiai cost a grain of gold?— ^at $22. ? — at $24. ? at $28. ? 3. At 4d. per grain, what cost an Ounce of gold ? — —at 4jd. ? _at 5d. ? at 5id ? at 6d. ? at 7d ? at 7jd. ? 4. At $21 per 6z., what cost a grain of gold?— at $23 ? _«at $25 ? at $26 ? at $27 ? at $29 ? [I < T M ■ .-,-*..- •:?fi5wrj-fii;. — 114 — "•• /"i5/-v^ MENTAL ARITUMETIG. ■•::';«-;■ No. si.— To find the value of a pound/ t&e price ■of a grain (Troy weight,) in pence Being given. Rule.-— Reckon £24 for every penny in thQ^price j or multiply the farthings of the given price by 6. ■ Exercises, -i^m^^m' , • !!'■■ *.,<\i. 1 lb. at lid. per gr. = £24 x IJ =£36 Os. Od. 1 " at 2 d. " " = 24 X 2 = 48 Os. Od. " 2 " at 2 d. " " = 24 x2x2 ^ M Os. Od; 1 tt»^at3 d. pergr. = 12f.x6«:£72 Os. Od.b ;1^ 1" atSM. " "=13f.x6= 78 Os. Od.B 1 « atSJd. " " =14f.x6= 84 Os. Od.¥ ■'*".'■-■ '■•5"" &c. No. 89.— To find the value of a grain (Troy weight,) the price of 1 lb. in pounds being given. Mim-^h Rule. — For every £24 reckon one penny ^ i«, ;-' 'ii • Exercises. ■■riSl 1 grain at £72 per lb. £72h-24 = 3 d. 1 :" at 78 " " 78-^24 = 3Jd. ^ ^; at 84,.« « 84-?-24 = 3|d. X. At 2}d. per grain, what cost a pound of gold? at2jd.? --at4d.? ,_v-i.fV.;. ■ 2. If 1 lb. of gold cost £60, what cost 1 grain?— -—^grains? -8 grains? 3. At 3d. per grain, what cost a pound of gold t— rat 4Jd. ? I 5d.? '•J- V t- fr^- '<:• 't^'V 'x-':i. ■ 4. If a pound of gold eost £48, what cost I grain?— -21 grains ? 3 grains ? 4 grains ? , - . , „ ^... •*•'. -.J^ ,•■>.. :^*L1ir.rgHw a «"|i i «w « » i «w.. ' tlW*^- '' v '■r- le price laprice ; Os. Od. Os. Od. Os. Od; Jod. . Od. i. Od. ..&,■'.,'■■ ^!:^,^ ■' t .X; i P rt:' s .yweigl^Lt,) ^y -' d. "i? 4 grains? .at4Jd.? [grain?— —5 .-''^'"^ — H5 — ^ii«,: TjO,,, ;'^t/ MENTAL ABITHMETIG. lif^: Wffi— To find the value of an ounce (aVoirdu- pois,) tha price of a dram in pence being given. Rule.--Reckoa Is. 4d. for every penny in the price. Exercises. %^p.-: 1 oz. at 2 d. per dr. = 18. 4d. x2 3- e£0 2s. 8d. 1 " at4 d. " " =l8. 4d.x4 -^r = 5s. 4d. 2 " atSJd. " " =l8. 4d. x8Jx2= 1 2s. 8d. &c. '■'■;-x, ]W'- ::■ ■^h '?^^ .;? ; "' ■ s ••:-i: '." .•" > •'V ' ■''■.:: ;^' No. 91. — ^To find the value of a dram (avoirdupois,} the price of an ounce in shillings being given. Rule.-— I)ivi(|e the price hy 16, for the answer in .pence.. M.:'^y^0^:'i- ''\if/-;-i'-^::'^^^ Exercises. ^^■m-iiism' 1 dr. at 2s. 8d. per oz. 2s. 8d.-!-16=:2 d. ^ 1 " at 5s. 4d. " " 5s. 4d.-4-16 = 4 d.-*^ .1" at lis. 4d. " « lis. 4d.-f-16 = 8Jd,-^ I ,^*- -;: &C., &C. >:';:v-'«---'-^' «<■.'; '>'.« '■' . f'i'J: _^y..>.;^.j-, *^ i - No. 92. — ^Toflnd the value of 1 ib. (avoii-dupois,) the price of a dram in pence being given. 8, ; Rule.— Reckon £1 Is. 4d. for every penny in the price.^.: •^,;^ ,.,.; ■ ..-:.,.^:-^v- v:,.v;'^-^'- ■ -i'.-; ■'■■:;W;|p;^B#^ Exercises. 1 lb. at 2 d. per dr. £1 Is. 4d. x 2 = £2 2s. 8d. 1 " at 3 d. " " 1 Is. 4d. x3 = 3 4s. Od. I"at3id. " " •! ls.4d.x3J= 3 148.8d. 1 f f, '■'-■■< ■ ■• >:• •«• ::f — 116 — ,-J •'•.■ J No. 93.— To find the value ol a drem (^yoirdu- pols,) the price of 1 lb. being given. :^> Rul'.— Beckon one penny for every 2l8. 4d. ^m the price for the answer in pence' ^^ , , :,.;, -Exercises. -■■- 7; '::^^^^^^^^^^^^ - liJ^'^f (ll dr. at £2 2$. 8d. per lb.= 2 d. e ,26 f = tj: "' .4 " at 3 4s. Od. " " =3 d. s - r 'M$- T" ^t^^.eos. Od. « "=5|d.;xi;;:i:;:^ ; .-#• ^c^ ■•icfe^ ■■I'. ■ ■: ' f *•■ »■■ .0 i ; No. ^4.— To find the value of a hogshead, the price of a quart in pence being given. A hogshead «»63 gallons. jji ■■^.i^.bV'^.^ viAli-V'jv^v'^:',*.- -■/;;;;.. Rule. — For each penny in the price of a quart count £1 Is. ., 1, ».;.,. vi ^ ■■ ^:.----'\-y-:' sr^::-"v Exercises. ''. ,„ "" • "^^ ■: .;j;^ 1 hhd.at * 4 d. per quart = £1 Is. x 4 = £ 4 4s. Od, 1 " at 4id. " '^ = lls.x 4J= 4 14s.6d. 1 " at 10 d. " " = lls.xlO = 1010s.0d. &c., &c. a inl ? ft, rv ■ 'Jl! V No. 96.— To 'find the value of a quart, the price per hhd. being given. Rule.— Reckon 1 penny for every 21 shillings ia the price. Jlxerdses. IV 1 quart at £ 4 4s. Od. per hhd. = 4 d. i '^■:wii " at 4 14s. 6d. " " = 4Jd. ; iv] " at 10 10s. Od. " " r=10d. f ,.,i,tL.»..l:.'> &to. &c. !;.;#*•&-■ N gall( R pric( 1 1 1 ■^A-: >, '<< ■'Ma: \:, f- . ■'» ,■'' '^^s .- ;■.. f., Is: 4^ in I. :>-;.^'.,,^\- I -.•,..5' ■ '^ V mammn'. >..i^>Vv jshead, the V hogstead of a quar^ 4 4s. Od, 414s.6d. 1010s.0d, the price Ihilliri^ia 4 d. ) 4id. ; d. f 4,^, "f ,.<,v;. :^ iifi > * •■■;».' No. 96. — To find the value of a pipe of wine, the price per quart in pence being given. A pipe = 126 gallons. Rule. — Count £2 28. for every penny in the price. v_ Exercises. -i 1 pipe at lOd. per quart=£2 2s. x 10 = £21 Os. 1 *^ atl2d. " "' = 2 28.x 12=. 25 4s. 1 *' atlSd^ " '' » 2 2s.xl5» 31 10s. &C., &6^ No. 97. — To find the value of a quart, the price of a pipe being given.''^^-^'^^'^'^t^=^>^^'^- ^^^^^ Rule. — Reckon one penny for every 42 shillings in the price. .,^,.,.H^ ,. ^,.: . .c,v. ,:■>: fkf. ■ Exercisfes. ^ -^'- '^^^^ -^-^l^M:'; ^ ■ 1 quart at £21 Os. Od. per pipe = lOd. rpfir / 1 " at 25 4s. Od. " " -12d. ^ r. ■ i'^ " at 31 10s. Od. " " =15d. : i ,;■•< &c., &c. ••f No. 98. — To find the value of a tun, the price pei gallon in pence being given. A tun - 252 gallons Rule. — Multiply £1 Is. by the pence in the given price. -: '■ w -■;:",.■'• V* - ^ '•-•■» •//>- ■ :,<-': ■ J V •• 1 tun at 30d. per gallon = £1 Is. x 30== £31 10s. 1 " at40d. " " = lis. x40= 42 Os. 1 " at44d. " " = Us. x44- 46 48. u * r 1 u ".Jif:- a^. I |5 1- '»f MENTAL ARITHMETIC. ■'^:>V' -. ■. .. -f^ No. 99. — To find the value of a quart, the price P of a tun being given. Rule. — Reckon 1 penny for every 21 shillings in M the price. \ i . Exercises. i;' 1 quartat£31 iOs. Od. pertun«30d. " V? I .«;;;: si " at 42 Os. Od. " " =40d. j i '*. at 46 4s Od. " " ^44d. &c., &c i c I i !■-■ No. 100. — ^To find the value of a tierce or 42 gal- lons ; of a puncheon or 84 gallons, the price per gallon in pence being given. Rule. — For etrU penny in the price of a gallon count 3s. 6d. for the t^alue of a tie:ce, and 7s. for the value of a puncheon, .m ":n' i : ^ : ^ ; Exercises. 1 tierce at 15d. per gal. 1 " atl8d. " " 1 " at24d. " " 3s. 6d.xl5 = 52s. 6d. :3s. Cd.xl8r=63s. Od. 3s. 6d. X 24 = 84s. Od. 1 puncheon at 1 5d. per gal. 7s. x 1 5 = £5 5s. Od. 1 " atl8d. '' " 7s.xl8= 6 6s. Od. 1 n « at 24d. " " 7s. x 24 = 8 8s. Od. &c, &c 1. At £30 per tun, what will be the cost of a quart ? at £32 ? at £33 ? ^at £34 ? at £35 ? ^^ r ; ' ; ^ 2. At 60s. per tierce, what will be the cost of a gallon ? at 72s. ? at 80s. ? at 90s. ? I I >'.^ tie price LUngsin — ..yT.>'M-» ■', V a. ^- i )r 42 gal- price per f a gallon s. for the 2s. 6d. 3s. Od. 4s. Od. 5s. Od. 6s. Od. 8s. Od. irt? at iallon? T;>>' "'*'ji'\- ■-I.'-' 119 — MENTAL ARITHMETia -.?■ No. 101.— To find the value of a barrel or 36 gal- Ions, the TOdce per galloif in pence being given. Rule.— -]For each penny in the price count Ss "H.f' Exercises. ..^i 1 barrel at lOd. per gal. Ss. x 10 « 30s. •f)/) 1 " atl2d. " " 38. X 12 -368. ^1 " atlSd. " " 38. X 15 ^458. "f" &C., .A ^r &C. % •<• No. 102. — ^Toflnd the value of a gallon, the price of a barrel in shillings being given. -1 > Rule. — Divide the price in shillings by 3 for the ^nswer in pence. ^"■:S':5:-'??:^^''.Exerds ,<;*< ■ •; ';,iT.v A' — — ■»•. ,, ^^ ^ ,: (,•■ ff; . , i- ■ :v-. '■'. *'? !": y- i: 1 i n»it i i . : i j:ii I I . I Mi l a n ;■■? f pork in the ■ *, . 8d. . 4d. . Od. of pork nts. in the 16. - ^ 20. )rice per reckon horoughly Bome fami- — 121 — MBNTAJi ARITHMETIC. ■..:^ No. 107 — ^To reduce pounds, shillings and pence to dollars and cents. Rule. — Reduce pounds, shillings and pence to pence, multiply by 5, then divide tne product by 3, and 'point ou the two last figures. Thus, .: ^rir £16 138. 4d.- 4000x5^3 -$66.66| No. 108. — ^To reduce dollars and cents to pounds, shillings and pence. Rule. — Multiply the dollars and cents by 3 anr^. divide the pypduct by 5. and then Ijy 12juid by 20. Thus ' ' ' -^ i-i^ir,im;-t i t 'm a\^ i <^^. e v c tr • ^ ' >. nr^ffA .* $fe6.66§x 3^5 = 4000^12 = 333s. 4d-i-20« . y £16 13s. 4d. - t V*!-. -•«'; , No. 109.— To reduce only pounds, or shillings, or pexice to dollars and cents. Rule. — ^To reduce pounds, multiply by 4 ; to reduce shillings, multiply by 20 : to, reduce pence, multiidy by 5 and divide by 3. •^<^'-'^' '■ "^ ' ^ ^ Thus, £16 X 4 = $64.00") ' r : ^^ :v 188. X 20= 3.60 [ =$67.70 ' ' "1r lm: I I it ! li ' III * 12 ¥ Si I I,' I'iii « 'iA 'i i ] — 122— V '• . ■ MENTAL ARITHMETIC. No. 111. — ^To compute interest on dollars for any number of years, months and days, at 6, 7, 8 and 9> per annum, by a single multiplication. Rule. — Reduce years and months to months, put on days in decimal of months in dividing them by 3, then multiplying this by \ principal gives inte- rest at 6 per cent, in cents. When the rate* is at 7o;o, add J ; if it be at 8o/o, add \ and if it be at 9o;o, add J, then multiply by i principal. .. Thus, interest on $1 400^ for 2 years, 3 months and 9 days, at ^^f per annum. =rm. 27.3x700 = «191.10. ; Interest on $358, for 2 years, 6 months and 6 days, at 6o/o per annum. %=m. 30.2x1 79 = $54.05,8, , v Interest on $1400, for 6 years, 6 months and 17 days, at 7 per cent, per annum. ~m. 78.6 + J = 91.7x700 = $641.90. : : Interest on $1242, for 3 years, 5 months and 20 days, at 8 per cent, per annum . . • « m. 41 .7 + J = 55.6 x 621 = $345.27,6. Interest on $1000, for 5 years,! month and 27 days, at 9 per cent, per annum. = m. 61.9 + ^ = 92.9:^ 500 = $464.50. ;. > .;; (§^Q page 111.) — 123 — i for any 7, 8 and aths, put them by ves inte- is at 70/0, |o;o, add i, onths and nd 6 days, Ls and 17 Is and 20 MENTAL ARITHMETIC. No. 112.— -To compute interest on dollars for days, by one multiplication and one division. Rule.— Multiply the amount by the number of days, then divide the product ' bv 90 when the rate is at u u u (( (C u (I 72 60 45 40 36 30 .24 20 18 a u u a u a (( lb a a a a u a <( a u a (( (( a u a a u (C u at at at at at 10 at 12 at 15 at 18 at 20 4 per cent.1 5 6 8 9 u u 4( (C (C a a 03 a O SCO ^ CtD ^03 The days in each calendar month, will be more easily remembered by committing to memory the following lines : — " Thirty days has September, ^ '' '^ ' April, June and November, * All the rest have thirty-one. Except the second month alone, T "Which has but twenty-eight in fine Till leap year gives it twenty-nine." ^ t ' d 27 days. 1 ■1^ i 1 1 I 11 I: i U- Mt' I'l ; W:'i^: — 124 — MENTAL ARITHMETia ' Miscellaneous questions. 1. What is the value of 12 articles at 2id. each ? —at 3id. ?— at 4 Jd. ?— at 5Jd. ?— at ^d, ?— at TJd. ? at ^d, ?— at 9id. ?— at 1 OJd. ? —at 1 l|d. ? ' ;: ^ . 1 . ji ill. r':y 2. At 3d. each, what is the cost pf 13 articles? — of 14 articles ?— of 15 articles ?— of 16 articles ? — of 1 8 articles ? —of 25 articles ?— of 26 articles ? 3. What is the price of 24 articles at 5d. each? — of 36 articles ?— of 48 articles ?— of 60 articles ?— of 72 ariic^s ?— of 84 articles ? f. At 4d. each, what is the price of 1 gross? — of 2 gross ? — of 3 gross ? — of 4 gross ? — of 5 gross ? — of 6 gross ? — of 7 gross ? — ^of 8 gross ? 5. If 12 yards of cotton cost 8s*, what is that per yard?— if 24 yards of cambric cost 32s., what is that per yard f— if 1 gross of knives cOst 72s., Whai is that per knife ? .„. , ■. ■ 6. What cost 20 yards of cotton af2s. a yard? — at 2s. 6d.?— at 3s.?— at 3s. 6d. ?— at 3s. 9 ?— What cost 40 yards of cloth at 10s. ?— at 15s. ?— at 16s. ?— at 1 7s. ?— at 1 8s. ?— at 19s. ? 1. Here 12 articles at 2id =2s. fid. 2. Hero 12 articles at 3d.=:3s.+3d.=:3s. 3d. 3. Here 12 articles at 5d =5s.x2=l0s. 4. Here a gross at ld.= 12s. x4=48s. 5. Here 12 yards cost 8s., 1 yard will cost 8d. 6. Here 20 yards will cost £2. pei tha -is t 8. — al at 2; 9. — at 5s. 6( 10. of 1 11 —ifl II. —at 2 at Hd 12 1 lliat pe per lb. that pe 7. Hen 8. Her( a. Hef£ 10. Her n. Her ., 12. Her n20=j;12 n eacliT .? Lcles?-- les ?— of '5.1 iies?— of OSS?— of gross? — " that per what id jfes., — 125 MENTAL AIUTILMETIG. ' 7 . If 20 yards of cotton cost £1 10s., what is thai per yard? — if 40 yards of cambric cost £4, what is that per yard ? — if GO yards of cloth cost £138, what •is the value of 1 yard ? 8. What is the value of 100 articles at IJd. each? —at Ud. ?— at If d. ?— at 2d. ?— at 2Jd. ?— at 2|d. ?— at 2|dr?— at 3d. ?— at S^d. ?— at 4d. ?— at 4p? 9. What is the value of 100 articles at 2s. eaeh? —at 2s. 6d. ?— at 3s. ?— at 3s. Gd. ? — at 4s. 4d. ? — at 5s. Gd. ?— at 6s. Gd. ?— at 8s. 9d.?— at 10s. 3d. ? - 10. If 100 Us. of sugar cost 45s., what is the value of 1 lb.?— if 100 ll)S. cost 5Gs., what is that per lb.? — if 100 lbs. cost 72s. Gd., what is that per Vb. ' 1 1. What is the value of 120 articles at 2d. each? —at 2|d. ?— at 2^d. ?— at 2|- d. ?— at 4d. ?— at A^d. ?— at ijd. ?— 4f d. ?— at Gd ?— at l^d. ?— at ?d. ? v .: ' ." , . 12 It 120 lbs. of maple-sugar cost £3, what is yard?— Ihatper lb.?— if 1201bs. cost £3. 10s., what is that f_ What per lb. ?— if 1 20 yards of cotton cost £20 5s., what is pat 16s.? — I that per yard ? " ' 7. Here 1 yard will cost 1/20 of £1 10s.=ls. 6d. 8. Hero I l/4d.=5 farthingsx2=10s +5(1. a. Here 10r&.=£5 x 2=i:iO. 10. Here 1 lb. cost l/lOO of 45s.=5 2/5d. ^ 1 1. Here 120 lbs. will cost 2-i-2=£l. 12. Here 1 ^b. will cost 1;120 of je3=6d., or i:3x2=:6d., or |l20=l2l20 of 1200 cents=10 cents. 1 m »'WV1 I'll".' .i" . .^•s*?**; I.I li ^ 11 ■ -m- m-. ■ ''■"•:.- ■ ■-^' ■•■■■■• ■ ' .. MENTAL ARITHMETIC. 13. What is the value of 240 articles at 2d. each ? —at 2M. ?— at 3d. ?--at 3Jd. ?— at 4d. ?~at 4id. ?^ at 7d. f— at 7Jd. ?-at 8d. ? —at 9d. ?— at lOd. ? i-rm 14. If 240 yards of cambric cost £2 10s.. what is that per yard? — if 240 of cotton cost £3, wnatis that per yard: — if 240 yards cost £10, what is that per yard ? 15. What is the value of 42 articles at l|d. each ? —at 2d. ?— at 3d. ?— at 4d. ?— at 6d. ?— at 2id. ?— at 5d. ?— at 7 Jd. ?— at 1 Od. ?— at 1 5d. ?— at 20d. ? 16. What is the value of 112 lbs. of sugar at 4d. per ft.?— at 4id.?— at 5d.?— at C^d.?— at 7d.?— at Jid. ?— at 8d. ?— at 8Jd. ?— at 9d. ?— at lOd. ? :,iy)0.)- 17. Iflt2fts. of sugar cost 37s. 4d., what is that per ft. ? — if 112 fts. cost 42s., what is thatperft.?^ — if 112 fts. of maple-sugar cost 46s. 8d., what is that per ft.? . , 18. What is the value of 1 ton of iron at Jd. per ft. ?— at Id. ?— at IJd. ?— at 2d. ?— If 1 ton of iSad cost £28, what is that per ft. ?— if 1 ton cosj £56, what is that per ft. ? 13. Here 240d.=:£l <2=je2. or 240=20 doz.=208.x2=409.| 14. Here 240 yards cost £2 lOs., I yard will cost 2jd. 15. Here lid.=l?8 of a shilling 42^=5s. 3d. 16. Here U2 lbs.=98. 4d.x4=37s. 4d. - :,A u 17. Here 1 lb. will cost 1*1 12 of 37s. 4d.=4d. 18. Here 112 lbs.4-12;=:i8. 4d.=X9 6s. 9-i-l=z£i 13s. 4d. 1 soa at£ ' 2( ??^^ Ifd. ajpo 21. bottle adozi 22. atlf ( will a pound, 23.1 yard ?- cost at 1 24. If get for a & 2 cake "8doz.: 19. Here 20. Here 21. Here 22. Here 23. Here 24. Here j =83 1;3 app iiiii *■**»«■- •wx^K'-ww a each? id. vliat is lis that hat per L. each ? ^d. ?— at at 4d. 7d. ?— at ir Lt is that ierlb.? — It is that t id. per of lead llSs. 4d. / ^>i'.'Wi ■''.' 'i'S'i .' ^^^T'^- '? -^'-^^i'i^W>^ ^ ^ ' ^V'V4J'-'''^i^;>HM:' 1 ^ """ ■ 9't :. ,.':: 'i*i.i27 — MENTAL AJUTHMBTia 19. What is the value of 1 hundred-weight of soap at 6Jd. per lb. ?— at 4Jd. ?--at 7Jd.?— at 2*d. ?— at 5 Jd. ?— at 7d. ?~at 3d. f— at 3id. f— at 8d. ? ' I II 20. How many sheets of pnper are there in 20 quizes, each 24 sheets ?— What will 20 pears cost at If d. each ?— what is the |, the *, the iV, Mid the i of a pound? 21. What Avill4J dozen of win*^ come to at 3s. a bottle ?— What is the price of a bottle of wine, when a dozen cost 40s. ?— 50s. ?— 60s. ?— 70s.-? ■'"■ 22. How much will 200 apples cost at U cent each ? at If cent ?— at 3 cents ?•— If 2 kites cost 4d., what will a dozen cost ?— Add together i of 10s. to 4 of a pound. ■m 23. What are 18^ yards of calico worth 2s. a yard ?— at 40 cents ?— What will iOO yards of tape cost at 1 J cent a yard?— -at IJ cent?--at 2 cents? 24. If ^ apples cost 5 cents, how many could I get for a dollar ?--for 2 dollars ?— for 5- doUars ?— If 2 cakes cost 2 Jd.. what will 2 dozen cost ?— 3 doz. ? "8 doz. ?--12 doz. ? - > ^^ II' 5®'^^^^^inersx2=52s.+2s.2d.=r54g.2(i. € 20. Here 20x24=480 sheets. 21. Here 4} c;oz.=54x3=162s. 22. Here 200x1 J=$3.00. 23. Here 18J yardsx2=37s. -.^^.''r =83* l^^Ipplw? ^^ ''°** ^^ "^""^^ ^•*^^^ ^- ""^ ^^ ««»*■ 'mmmmm. HI il I 'ilHi . 4 ■*•.»■:•''>'.■ >\: ._ '.;• \-'. — m- MJS^JTAL ARITHMETIC. - . 25. What is the price of a book, when a dozen cost ;iOs. ?— 55f ;f-%Ok ? — 70s. ? — 72s. ? — 80s. ? — 90s. ?-r96s. ?—$2.t)0 ?r-f 3.00 ?-$5.60 ?— $10.00 ? V, 5i 26. What is the price of a lb. of sugar, when 100 ft)?. C09t e7.Q0 ?--r7.50 ?— $10.00 ?--£3. ?— £3 10s ? ^^T7*5 458. M.t~£3 15s.?-$17.00?,. . 27. Add up in your memory i of 10s. and f of £4. — ^If I spend 3s.* 6d. out of 3 crdwns, what have I left?— 5f JsD^ ei.aSJ out of 13.50, wliat have I left? ^■;-*"^1o^^fJ:torl7i:^v^MPt;T'^>Mi.aft&W-^ •■■■■*■ *"^' »■•?'•■'*'■■''"'* ■■■'■«.":.■ .<•••.,',*'•" .'■■-^•',i">.' ■■'■''■'!•■.' ' 28. If I buy a cow for $20.70, and sell it for $24. 80, whai do 1 gain ? — (1 ) How much will be due to a servant for a month^s wages, at £10 a year ? — at ^£12 Iari4 10s. ?r v^p 29. What is the price of a dozen, when 80 dozen ( ^5. cost $98.40,— $100.04 ?—Teil me what 22^ yards of P^, at 3 eacj ceni 34 each -at ^^»ci:'^^ilr<^-r.i^=4/?«:?;^^^rie^^*--^\:^ij^JSf ^-sR ii:^i^'^--Pf.M*M. 30. What is the weekly expenditure of bread at brice Is. 4d. a day ?— at 23 cents? — (2) 1x4 yards of cloth that pe CO?!' $18.40, what will be the cost fit 25 yard^?-r0f|s that 50 yards?— of 100 yards? ' -^^ ''-"^ ' [. 31. Hi 25. Hpre a book wil^ cost 40d;~ -"^r^ '-"' -^ -^ I 32. He 26. Here llb:Vill cost 1»060 of $7.00=7 cents. l^^^i^W 33. He 27. Here 1/5 of i0«.^2s. ; 3/5 of X4=a48B.^2s.=508. *» 34. Ha 28. (1) Here-jei(H-3=$3.33 ifJ.- : ' - : i,.|S 35. Hei 29. There $98. 40^80=$ 1.23. ^-MS'k^i'l^i^^m^-.mm- :y<^' f 17 half. 30. (2) Here J yard will cost 1;4 of $18.40=$4.60x25=:f'iiiiga , $115.90. ^■^,4:_^-\i'+-'yir^t^^ i)\;^^:A?l^i y^i^i; t ;:-j.;H. ,u-; j36. Her "mrrr^rrt^: H--.. '"■->■ i^ /; •\:i ■:S.- MENTAL ARITHMETIC. '■^■'*''/?:'^' a dozen -80s.? — ar \vnen ndiofM. tiat have 1 what have 31. If 1 ft), of tea cost 2s. Od., what is that per oz. ? — ^if 1 ft. cost 4s., what is that per oz. ? — ^if 1 ib. cost 58., what 18 that per oz. ? 't>•■■■^t^''^-■1* '**r*'r^''*''^"T ■^#^- 32. What is the value of 1 ft. of tea at 2d. per oz. ? —at 2id. ?— at 3d. ?— at 3id. ?— at 4d. ?— at 44d. ?— at5d.f-rat5id.?--^t6d.? . ■V. 33. What is the value of 12 articles at 2 cents each ? — at 3 cents ? — at 4 cents ? — at 5 cents?-— at 6 cents?— at 7 cents? — ^at 8 cents? — at 9 cents? ■; i^AA'^ .'«;- A';i'-iv "'ijv ■:.■ ' i;-- >«/"' 4/: ^ -'i^^i^l \ it for $^^- I 34. What is the value of 12 articles at 10 cents \ be due to a leach ?— at 11 cents?— at 12 cents?— at 13 cents?— .Of '?— -at ^^^ (at 14 cents ?— at 15 cents ?— at 20 cents ? h%^^ t *^ >ar '^■iW'- ■>■■ .,'»¥; ■■••*-r^ :'" i'*- ■*■'• , ' '•--*: J ^« I 3^' What is the value of 12 articles in dollars sn 80 dozen i^^^^ ^^^^g ^^ ^^ ^^^^ y_^^ 4id. ?— at 6d. ?— at 5id. ? m Jff' ^ I— at 6d. ?— at 7Jd. ?— at 8d. ?— at 8Jd. ? v ^fi^^fa^ 3s 31. Here 2$. Od. -=2x3=6=1 id. T 32. Here 2dx4 fi.=8^3=2s. 8d. 33. Here 12x2=$0.24. Its. :'r^;|.% 134. Here 12xl0?s$l.20. •=^ ;p 35. Here 4d =8 half-pcnce, addi ig a cipher=80 cents ; 8jd. -A^^m4-S'^ \P l^al^penee, adding a cipiier=$l.70; 7jd.=15 half-pence, " *rAAVl5s=P^"^g*cipher=$l.50. T; ^(hsf*-**"?^ 36. Here 80 iQent^vlfeO 2^3 c^ts. Iif #.-?,^J^ii^^^ H "'II iliii ill ' iV > ^JTl ^ MENTAL ARITHBET^C. . ^ 37. At 12s. 6d. per yard, what cost IJ yard? — IJ yard ?— 1 J yard ?— If yard ?--lf yard ?— 2^ yards ? — 2| yards ? — 3 J yards ? — 3 J yards ? V - '•.-;-^^f' '.<^?: t^ti 38. At $2.75 per yard, what cost IJyard?-— U yard ? — IJ yard ? — If yard ? — 1| yard ? — 2 J yards ? ; — 3J yards ?— 3J yards ?— 3 J yards ? ' ft. 25 of wi '^ 39. A\ 8d. per yard,what cost 66 yards ? — 74 yards? —84 yards ?— 88 yards ?— 90 yards ?—96 yards ?— - , 100 yards?— 120 yards?— 144 yards?— 240 yards?! P®^ 40. What costl ft. at lOJd. per penny-weight ? — i . at lid.?— at I24d.?— at 13d.?— at 5 cents? — at 7| ^^^ cents ?— at 8 cents ? — at 9 cents ?— at 10 cents ? ^* ■u:t' at cent —at f 41. What cost 75 fts. at 4Jd. per lb. ?— at 5}d.? at 8 cents ? — at 1 cents ? — at 1 2 cents ? — at 1 3 cents . , —at 14 cents ?— at 15 cents ?— at 9d. ? _^ | « , ■■ ^^t^v •o ;.-!*. .-',.> ,2^ yards T -240 yards? 44. What is the area of a school 30 feet long ?nd 25 feet wide ?— of 19 ft. sq. ? — What is the lenght of a school that contains oOO sq. ft. and is 20 feet wide ?— ^^u . ,-' 'V-^^ if JKa>» :.I.'W 45. What is the value of 2484 yards of tape, af Jd. per yard ? — at ^d. ? — at f d. ? — at 1 Jd. ? — at 2 cents ? —at 4 cents ? — at 5 cents? (See aliquot parts, p. 57.) •'■r ; ..i-i.l\^-^ *"''i: ^ ■11 '* ^y-weight T--I 46, j bought 480 yards of ribbon, at 4d. per yard? icents ? — at a _at 6d. ?— at 8d. ? — at 9d. ? — at 1 cents ? — at 20 cents t \ cents ? — at 25 cents ? — at 1 s. 3d. ? — at 2s. ? — at 2s. 6d. ? •r V —at 3s. 4d. ? .(^ iky.:T'^. i^fvsi^;' m-^ /> A« k— at 54d. t--atl3 cents ^ 47 ^^at is the interest on £60 at 5 per. cent for 3 years ?— on £40 for 3 months?— on £30 for 10 days? — on £20 at 6 per cent, for 3 months ? — for 6 months ? ildbethecoa rards ? -^,^^« J 48. Find the interest on $225 at 5 per cent, for a of 8 yar^--] year?— ate per cent. ?— at 7 per cent.?— at 8 per cent. ? — at 9 per cent. ?— at 10 per cent. ? — at 12 per cent? .^mMf i,1\^' ' 't \ 43. Here $l00=t0000cent94-5=2000 lbs. 4 .ARvara ^^' Here 25x30=750 feet Li5— 4s. ,00 jf 1 ^5 jjgpg 2484=207 doz.x3drt51s. M. ^. nwpe 1 46- Here 480=40 doz. 4s.=l60s.=£8. b^^. OR? lid I 47. Here£60=60s.x3=ia0s.=£9. h lt*=''® I 48. Here count 5 cents for every dollar=$ll.25. m i !! ill I ,1-,, ■ If;--- ■ ■■ . .-*. .i^' fc. /:■•;••■. —132,— ^ Mtil*JfAL ARlfilMEflC. 1 '' '• >. JAi 4y. What is the interest on $660 at 6o;c per an- num, for 6 days ? — for 12 days ? — for 18 days ? -^ for 24 days ?— for 30 days ?— for 36 days ? — for 42 days? '.<■.■■" ---"lif-,' '•■"'^•'^" ,;-■'.' -^ ,-: ,. ij. ■**'j J 50. What ite the 'interest en ^1 200 at 7o;o per iah- num, for 2 months ? — at 8o/o per annum, for 4 months? — at 9o;o per annum, for 6 months ? — at 10 . o;o per annum, for 8 months ? ,,!>t '"r.ifl'*^ i., /»*i-v# II What is the premium of insurance tffi $880, at 8 per cent. ? — at 9 per cent. ? — at 10 per cent. ?- -at 1 1 per cent. ? — at 12 per cent. ? — at 13 per cent. ? — at 14 per cent. ? '": ;: .,rW-'f I* /... -^ (■ Uf^W^' C 52. What is the commission on $660 at 5 pei •t (*ent. ? — at 6 per cent. ?— at 7 per cent. ? — What is th( brokerage on $1400 at 3 per cent. ? — a;t 4 per cent. —at u per cent, r ., >>'\..*,kv.iiui;A«w' >. ;r' 53: What islhe interest on $1000 at 6 pefr Cent V for 4 years and 2 months? — for 2 years and ^ ■ months ? — for 20 months ? — for 10 months ? — for i months and 20 days ? See page 111. 54.* If I bought butter at 25 cents per lb. and soli it at 29 cents, what was my gain per cent.? — (*) a 12 cents per lb. and sold it at 15 cents, what wa ^ m^ gain per cent? ..^.--Her^?? " .# i 1 1 ' liii i ■W'-": ,-;(•) Here 29—25=4=4/2/ of 100=16. . V :. .§i;(*) Here 15— 12=3=3/ 12= 1/4 of 100=25. ^ '^^' Note. — The pupil should perform on his slate all the pr ceding exercises, in order to prove what he has counted mei tally. .y-:. ■:M^?'^-- 133 — MENTAL ARITHMETIC. Addition, Subtraction, Multiplication and Divi- sion Table. i-u- ift'. an tm int t-C) -what wai ft(<^%.' w 2 2 4 3 3 6 4 4 8 4 12 5 5 10 5 15 6 6 12 7 7 14 8 8 16 9 10 11 12 2 9 18 10 20 11 22 12 24 3 2 6 2 8 2 10 2 12 3 9 6 18 7 21 8 24 9 27 10 30 11 33 12 36 4 3 12 3 15 3 18 4 16 4 20 4 24 4 28 5 20 5 25 6 24 6 30 7 28 7 35 7 42 8 32 8 40 9 36 10 40 11 44 12 48 5 9 45 10 50 11 55 12 60 C 5 30 5 35 5 40 6 36 8 48 9 54 10 60 11 66 12 72 7 2 14 2 16 2 18 2 20 2 22 2 24 3 21 6 42 6 48 7 49 8 56 9 63 10 70 11 77 12 84 8 3 24 3 27 3 30 3 33 4 32 4 36 7 56 8 64 9 72 10 80 11 88 12 96 9 5 45 6 54 7 63 7 70 7 77 7 84 8 72 9 81 10 90 11 99 12 108 10 4 40 4 44 5 50 5 55 6 60 6 66 8 80 9 90 10 100 11 110 12 120 11 8 88 9 99 10 110 11 121 12 132 12 3 36 4 48 5 60 6 72 8 96 9 106 to 120 11 132 12 144 jl the prj ounted vm tea THE END. ; ' ^f^-^i'^^t^^f'. >