o 00 co O >- LIBRARY 01 THK UNIVERSITY OF CALIFORNIA. ( )K Y Received G2,c3f~ . Accession No. 7^-3 bO . Clots No. ARITHMETIC SHORT METHODS * SWEET * OF THE UNIVERSITY SWEET'S Hand Book OF SHORT METHODS Arithmetic j. s. SWEET, A. M., 'Principal of the Santa Rosa IJusiness College. Santa Ho.-a, Cal. formerly President of the Oix-^oii State Xormal School. Ashland. Or., Author of Sxveet '- Sv~u-m of Act- nal Hnsiness Practice, Element* of Geom- etrv, lousiness t"orm~. Etc. SANTA ROSA, CALIFORNIA Entered according to Act of Congress, in the yi-;ir IS!)!!. ByJ. S. SWEET, In the Office of the Librarian of Congress, at Washington, D. C. >. J PREFACE. The principal object of this little work is to place in the hands of the student, in compact form, many of the briefer methods of rapid calculations. ''Time is money," and especially so to many of our young people who are trying to obtain a business education in a brief time and with limited means. Hoping that many may profit by the suggestions here- in contained, I most respectfully dedicate this little volume to the young business people of America. Santa Rosa, Calif., 1893. J. S. SWEET. 6 XIIORT METHOD* 2. Slims Greater than 9. 54321543 56789678 6543 654 6789 789 765 76 87 789 89 89 8 9 9 9 .V. To Itetrtl fit Sight. When a student sees the figures 1 and 3 written side by side, he instantly recognizes "thirteen" or "thirty-one" ac- cording to their positions. The same facility may be ac- quired in regard to numbers in addition; thus, 4 over or under 8, may be read "twelve" as readily as the figures 1 and 2 side by side. Ten minutes practice daily for one month will accomplish the work. 4. Always add TWO or MORE figures at a time. Never be guilty of adding single figures. Name the results of the following as rapidly as possible : 246975634674-89 35323678988723 38765725475399 48797999888789 IX AltlTHMKTIC. 56854322462537 49987873878689 73776298897778 84698549739894 J. Nine added to any number is always ONE LESS in its unit's place than the number. Thus, 8 9 - 7 in its unit's place. 36 9 5 6*. Eight added to any number is TWO LESS in its unit's place than the number. Thus, 7 8 == 15, 15-8 = 23. T. To Add btf TenM. A good method is to add by 10's, carrying the EXCESS in the mind, as in the following : 8" 7 2 9 5 63 95 7 6 30 27 Here the 3 of the 13 is carried to the 7 of the 17 mak- ing three tens in all. Add in this manner the following: 3 9 6 5 9 8 8 8 8 8 7 5 5 7 9 9 9 5 9 6 4 3 4 4 5 6 4 9 8 6 8 *1IORT MKTHOIt* 8. When the Columns are Long. When there are two or more columns of consider- able length, add each column separately as instructed, and write the sum of each alone, then combine results into one number, as follows : 32476 58976 76892 39428 73548 67943 28745 "^8 37 46 43 33 378008 This method is almost indispensable in book-keeping, as an error can be located much more readily than when the separate results are not known. 9. To Add Two Columns at a Time. To add two columns at a time practice on the fol- lowing, by adding the tens' column first, and by reading the units' column, tell at a glance the number to carry : 23 36 72 49 35 44 66 27 38 79 38 44 59 71 88 64 39 89 88 26 86 49 94 87 75 89 85 94 f.\ ARITHMETIC. 9 10. Proof* of Addition. In long columns the best proof is to add them again, up or down, the opposite of your first addition. In short col- umns and several of them to add, you may prove the work by casting out the 9's as shown below. 25189654 - 4 36972105 - 6 94375517 - 5 15155815 - 4 85310652 - 3 95315175 - 352318918 - 4 Casting out the 9's of the first nnmber, we have an e.< of 4 ; of the second, 6 ; of the third, 5 ; and so on, finally casting out the 9's of these results which gives an excess of 4. Also by casting out the 9's of the sum, we have 4, we therefore conclude that the work is correct. XOTK. This is not always a sure test, the answer mi_ 3 4 5 6 7 o 10 11 12 2 4 o 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 OD 60 6 12 18 24 30 42 :>4 60 66 72 , 14 21 28 42 4U 56 !63 70 77 84 - 16 Mi' 40 48 56 64 80 88 96 9 18 27 45 -")1 68 72 81 90 99 108 10 20 40 :,d C)() 70 80 90 100 110 120 11 22 33 44 55 66 . i 88 99 110 121 132 1-2 24 36 48 60 12 84 96 108 120 132 144 //>. The following squares of numbers should also be memorized : 12 XI10RT METHODS 13 X 13 == 169 19 X 19 361 14 X 14 = 196 20 X 20 == 400 15 X 15 = 225 21 X 21 =- 441 16 X 16 256 22 X 22 == 484 17 X 17 == 289 23 X 23 529 18 X 18 = 324 24 X 24 576 25 X 25 = 625 14. To multiply any number const stint/ of two digits by 11. RULE. \Vrite the *inn of the digit* between ilieiti, ilie number fltii* e.vpre^ned ?'s I lir product. EXAMPLES. 11 times 24 = 264, 11 " 36 == 396, 11 " 57 == 627. XOTK. \Ylu-ii tin-it- -tun is 10 or inure, carry one to tin- liutulivd's di-it. EXERCISES. 15. 1. Multiply 45 by 11. 4. Multiply 75 by 11. 2. 38 by 11. 5. 96 by 11. 3. 92 by 11. 6. 88 by 11. 16. To multiply any number by 11. RULE. Write the unit's iigurc; next, -write the sum of the ^l-nits and tens, tJifit i lie ^nin of 1/ir fi-n* and hundreds, etc., writing flic left IKI'IK/ figure last, carrying i^lien uec:es?:r\'. EXAMPLE. 11 times 12345 == 135795. 5 4 j 5 9 :i 4 - 7 2 3 5 1-2 3 1 7.Y ARITHMETIC. 13 EXERCISES. /;. 7. Multiply 663 by 11. 4. 6731 by 11. 938 by 11. .7. 9884 by 11. 734 by 11. 6. 72596 by 11. 18. To multiply by 22, 33, etc. Rl'LK. Mil hi ply h\> 11 //>- ,>r<>, ami rhru !>\' ?, .V, <>r 4, etc. EXAMPLE. 22 times 234 =. 2574 X 2 = 5148. XOTK. The work should be done mentally, only results being; written. EXERCISES. W. 7. Multiply 64 by 22- 4. 374 by 55. 65 by 33. .J. 874 by 66. 46 by 44. V. 336 by 77. 20. To multiply by ant/ tuttnbet* betirecn 12 and 2O. RULE. Multiply by the unifs figure only, i.'rir- mg the r<\riln> innitlx>r r<> tin' n'-hr, thru ,i,J ////' number -' v i '/. J. Multiply 25 by 65. 4. 45 by 35. 2. 25 by 85. 5. 65 by 35. 3. 105 by 25. H. 75 by 65. 32. To find the product of two numbers whose tens 9 digits are identical and the sum of the units 9 digits is 10. RULE. Multiply the tens' digit by OTIC greater and annexe the product of the, unit*' ss ten* and one more than the grfutcr, . 84 bv 76. #6*. To jitttt the product of tiro numbers tcheti their fats' (lif/its are the sattte. Rl'LK. Ta,he the prmluct <>f tin' unir*, ne.\~r rhe print ncr ;/s riling the sum <>f tli-e unit*, then flu' pr>J i/ cr nf i/ir rcn*, always r,i ~rr\-i m? rli*' r'7;s, if itii v. EXAMPLE. 73 times 75 5 3 8" 7 7 7 5475 15 write 5, carry 1 56 carry 5. 4V) 5475 EXERCISES. /. Multiply 74 by 72. 85 by 83. 67 bv 65. 4. 97 by 94. .5. 88 by 89. '/. 79 bv 78. V#. To /r tt ft the product of two tttrtttbet's trhett the units 9 digits are iflettfieftt. Rl'LE. Talif r/i.,' pnnlitcr of the nn.it ^ the sum <>f t lir ten* times the liuit*, mul the product of the tens, currying i^'In'n necessary. KXAMPLK. 44 times 74 3256. EXERCISES. / Multiply 46 by 56. 54 by 34. 43 bv 53. 4- 73 by 63. 6. 87 by 47. n. 98 bv 28. OF THE i8 XIIORT METHODS 40. To find the product of fntt/ two num- bers consisting of two digit*. RULE. Take the product of the units, th-e sum of the products of each ten times the other unit, and the product of the tens, carrying if necessary. EXAMPLE. 47 times 36. 6 X 7 ~- 42 6X4 a <" 7 = 45 4X3= 12 1692 EXERCISES. 41. 1. Multiply 35 by 27. 4. 68 by 34. 2. 47 by 34. 5. 78 by 46. 52 by 46. 6. 39 by 35. 42. To find th e produ ct of numbers wh <> 1 t one part of the multiplier is a factor of the other. RULE. Multiply by the factor, then tliit? product by the quotient of the factor into tin- oilier part, ny cipln'r* r - t<\, ami (lie multiplier. EXAMPLE. 423 times 996 423000 4 >< 423. ._ 1(51)2 421308 EXERCISES. ,-T.V. L Multiply 993 by 624. J. 9994 by 425. 0. 997 by 529. / mi tlnni. t he git 'ru nt-u fri pi irr, and iii>tr<'icr ?'rs ne-tenth. EXAM PI. K. 454 times 72 454 80 36320 product by 80 3632 " " 8 32688 " " 72 EXERCISES. ,7,7. /. Multiply 4(5 by 18. 5. 288 by 54. 75 by 27. r>. 384 by 63. 82 by 36. 7. 772 by 75. 4. 144bv 45. 8. 1244 bv 81.5 OI .76*. To multiply by complements. P'roiu eitliLT number subtract the comf>li' of the Other, prly oi]ihi-rs To maki- tht-m the same. p]>ly oi]i EXAMPLES. 94 comp. 6 999 comp. 1 97 comp. 3 999 comp. 1 9118 998001 A'd EXERCISES. ,7;. /. Multiply 92 by 87. 4. 996 by 995. 94 by 75. 5. 993 byi9\L. 99 by 93. n. 998 by 895. 22 SHORT METHODS 58. To find the product of two tt a in hers, each of which is a little over 1OO. RULE. From the sit-in, of the numbers snl>rrf-r - 56M 11/16 " = 6834 13 /16 " 81J4 9334 1>2. To multiply by an rtfiquot part of 100. Anin\\- ti.'o ciphers, . J Multiply 125 by 48. 5. 112 by 62V 2 . 0. 1236 by 3331/3. 4- 192 by 83V 3 . 66. To multiply by (t little more or a lit- tle Jess than- an aliquot part. RULE. Multiply by the nearest alit parr, . 120 by 137K. o. 84 by 1142/ 7 . 345 by 116%. 6. 106^4 by 144. This same principle may be carried to more than 100 and an aliquot; to 200, 300, and even to thousands. The student will find much in this field for original investigation. DIVISION 70. To divide by 5. RULE. Multiply by 2 and cut off one fig it re. EXAMPLE. 125 divided by 5 == 125 X 2 = 25.0. EXERCISES. 71. 1. Divide 135 by 5. 4. 265 by 5. & 145 by 5. 6. 325 by 5. 3. 175 by 5. 6\ 875 by 5. 72. To divide by 25. RULE. Multiply by 4 and cut off two figures. EXAMPLE. 125 divided by 25 == 125 X 4 = 5.00. EXERCISES. 73. 1. Divide 275 by 25. 4. 875 by 25. . 325 by 25. 5. 925 by 25. 475 by 25. 6. 975 by 25. 74. To divide by 125. R ULE. Multiply by 8 and cut off three figures. Ex. 375 divided by 125 = 375 X 8 ^ 3.000. L\ ARITHMETIC. 27 EXERCISES. M. 1. Divide 500 by 125. S. 875 by 125. 625 by 125. 4. 1125 by 125. ;6*. To dh'ide ht/ an aliquot part of 10O. Mn hi ply by the denominator of the frac- tion expressing the alf<{nt part, Divide In' tJie numerator and a/r off'neo iigurcs. EAMFLES. 240 -r- 5 = 240 X 20 48.00. 840 H- 25 := 840 X 4 33.60. 1200 *- 12^ == 1200 X 8 = 96.00. 1350 -f- 16^/3 == 1350 X 6 = 81.00. EXERCISES. ;;. Divide 245 by 25. 820 by S 268 by 20. 725 by 83^. 475 by 33^3 446 by 125. in iitoii denoin iitatr. EXAMPLE. V 7 - 2/7 + % = %. EXERCISES. ,ai. /. Add 2 9 % T ( , . f>6*. To rff7^ f*ro fractions tton RULK. ^Inltiplv tlir ^uin of the denominator s by O'imnon ninii> : r 1 over 2X3 = % % (3 5) X 2 over 15 = 16 /i 5 - EXERCISES. f>;. 1. Add 3 4 ^. -7 r> ii. % - 3 /7- ^ 6 /7 + 6 /H- 5 -f % & 10 ia - 10 /7- 30 SHORT METHOD* 98. To add fractions not having a com- mon numerator nor common denominator. RULE. Multiply each numerator into all the denominators except its own for new numerators, and take the prod^lct of all the denominators for a common denominator, then add. EXAMPLES. % + % = ^jt-" 19 /i5- 12 -r 1<> IS EXERCISES. .9.9. ^. Add % 4- y 7 . A V 2 % % %-f 6 /n. 4- %-h 3 /7 r 8 /n. NOTE. When .several fractions whose denominators are not prime to each other are to be added, reduce them to their least common deuominaior and add. TOO. To add mixed numbers. RULE. Add ivhole numbers and fractions sepa- rately and tlien unite results. EXAMPLE. 8% -f 12%. 8 r 12 20 % %-=' 1 % 5 - His EXERCISES. 101. L Add 91/2+141/3- 4- 283/ 5 + 3 5 4/ 5 . ^. 18%-J 252/7. 5. 431/5 72y 7 . 21%1275/y. ft 66%- 231/4+ 17y 5 . 102. To subtract fractions h rinr/ a co tn- RULE. Take the difference of tli<> 1 eu EXAMPLE. % - 2/ 7 = EXERCISES. /OJ. /. Solve: % 3/ 7 . ,;. s/^ _ 8/ 15 . % - % 5. ~ 5 ll. 6'. *. 7V> subtract fractions had it f/ neither numerators nor comnton denom- inators. RULE. Mu I tiply ench numerator into the other (If/loin iii'i r<>rs, take the difference un-n-aU-r than tliaT of the min- uend subtract a unit from the minuend and add it to tin- traetion before taking the difference. EXAMPLE. 8% 5% 8 5 := 3 % ~ % Vlo 11 - 8 - 3 IVa ~ V 2 % 3%. EXERCISES. Solve: 22% 16%. 5. 89% - 35%. 75% _ 48%. ^ 9 5 i/ 6 __ 7434. XOTE. A g\.od method is to take the complement of the diiference of th fractions when the subtrahend fraction is the greater. EXAMPLE. S 1 /^ 2% 42 2 % 2 VG write the complement % EXERCISES. 110. 1. Solve: 8i/i - 51/3. S. 25% -- 17%. . 2. 15% - 4%. 4. 44% - 313/ 4 . . To fl-nt? the square of ff nti.rert num ber whose fr et ion is 1/2. RULE. Multiply the. integer by tin- next li-igliei number a-nd a>miex %. EXAMPLES. 2% X 2^ == 2 X 3 -f- ^ == 3^ X 3^ - 3 X 4 < = " IX ARITHMETIC. 33 EXERCISES. >. /. Multiply 4V 2 by 4V 2 . & 8V 2 by 8V 2 . 51/2 by 5%. ^. 9V 2 by 9%. To /iwd f/if product of two wired n anthers n'ltose fractions arc 17 2 . Rl~LE. *To rlif pr 4- 3 X 14== 3V 2 >: 4V 2 = 3X4 - 3V 2 + ^4 = 15%. XOTE. The fraction will be ooe-fparth if the sain of the two integers i .-ii : if the sum is odd thi- fraction is three-fourths. EXERCISES. 114. 1. Multiply 21/2 by 6V 2 . ',. Sifeby 3V 2 by 5V 2 . 4. 41/2 by To find the ptoduct of two mixed s whose integers are identical and the sutn of whose fractions is a unit. RULE,. ^Multiply the inrrgrr by the. nr.\-f In'glirr TininbtT ami 4 ^ ( 3^ == 123/ 16 . EXERCISES. / /6\ /. Multiply 4% by 43/ 5 . ^. 9y 7 by 93/ 7 . ?. 5% by 5i x 5 . 5. 12% by 10%. 63/ 8 by 6%. 6. 153/n by 158/ii. I IT. To find the product of two n anthers whose integers are consecutive and the snnt of whose fractions is a unit. 34 SHORT METHODS RULE. Multiply the greater number increased by 1, by the less; and for the fraction annex ilir complement of the square of the fraction of tli-r greater number. EXAMPLE. 4/ 3 X 3^ = 5 X 3 -f- % ?= 15%. XOTK. The .square of one-third equal.-* one-ninth, its complement is eight-ninths. EXERCISES. 118. 1. Multiply 514 by 4%. 4. 9% by 8%. 2. 63/5 by 5%. 5. 12% by 11%. 8. 83/7 by 7y 7 . . 205/12 by 19% 2 . 119. To find the prod net of tico iHi.red numbers whose inteyei's are identical. RULE. To the product of the Integers add tlic product of the siim of the fractions times tJic com- mon integer and the product of the fraction*. Ex. 6y 2 X 6 l /3 = 6 X 6 + 6 X % + % X # - 36 + 5 -: V 6 =~ 41^. EXERCISES. 120. 1. Multiply 8 1X 2 by S^i 4. 24% by 24%- . 12 1/ 3 by 12%. o. 351/5 by 353/ 5 . 8. 142/7 by 146/7. 6. 45% by 45%. 121. To find the product of ttro mixed numbers when the fractions are identical. RULE. To tlic product of the integers add the product of the sum of the integers times the com- mon fraction and the product of the fractions. Ex. 41/3 X 8i 3 = 4 X 8 X 12 X 1X 3 - 1X 3 X 17 3 32 4 i' EXERCISES. 122. 1. Multiply 6^ by 18^. .1 36 17 8 by 44 1/ 8 - 3. 91/3 by 15%. 4. 721/9 by 36%. WO. IX .\RIT1I MET 1C. 35 To multiply by (in aliquot pftrt of RULE. AII.II.CJ; two ciphers to the multiplicand nnd tube such a part of it as the multiplier is a part of 100. EXAMPLE. 24 < 16% 2400 ~6 400. EXERCISES. 124. 1. Multiply 39 by 33V 3 . 4- 54 by 66%. 2. 48 by 12> 2 5. 72 by 37 1 ,> 64 by 8V 3 . fj. 144 by 83V 3 . 12Z. To Multiply a f fact to it by a frac- tion. RULE. Cancel all common factors in numer- ators and denominators and divide the product of those remaining in the numerator by the prod^lct of those in the denominator. EXAMPLE. 3 4 :\ :\ _ \/ ___ \/ ___ N,/ ^__ -- _ 4 2 6 7 2 i0 2S EXERCISES. 126. 1. Multiply % by % by % 5 . 2. % by 2i/ 25 by 27/ 32 . 7^7. To fit ride a fraction, by a fraction. RULE. Invert the divisor and proceed as in multiplication of fraction *. EXAMPLE. % X % + 7 /io X 9 /i 6 = 2 3 4 10 1C) :-l-2 11 X X X ~ 1 4 $ 7 -03 -21 L>1. EXERCISES. 128. L Solve : % X 7/ 10 X % -f- 2 V 2 4 X 15 / 28 . ^. 6 /7 X H12 -*- 22 /49 X % X % PERCENTAGE 119. To find the percentage when the rate is an aliquot part of 200. RULE. Take such a part of the iimnbcr as tlie rate is a part of 100. EXAMPLE. 12M per cent of 64 == }i of 64 = 8. EXERCISES. 13O. 1. Find 50 per cent, of 38. Of 346. 2. 33^ " " 42. Of 543. 8. 160 " " 96. Of 186. 4- 12# " " 128. Of 4168. 131. To find the percentage tc/teit the rate is an aliquot part of WOO. the number by 10, and ta-hr. *ucli a part of it as the rate is a part of 1000. Ex. 830 per cent of 144 = 17 i 2 of 1440 ^ 120. EXERCISES. 132. 1. Find 333 ^ per cent of 27. Of 279. & 1660 " " 66. Of 576. 3. 83V 3 " 96. Of 3612. 4- 62^ " " 288. Of 1624. fX ARITHMETIC. 37 133. To find the percentage when the rate is ant/ number. RULE. ^Multiply the base bv the rate and point off tu'o places. Ex. 12 per cent of $400 = 400 < .12 = $48.00. EXERCISES. 134. 1. Find 15 per cent of 500- Of 1879. 22 " " 750. Of 4321. 18 " " 560. Of 8765. 4. 27 " " 1340. Of 9876. 135. To find the bff.se , the rate an. 1. Rate 4 per cent, Percentage 52, Ba.^e ? 2 " 9 " " 144 " ? .;. " 12 " 176 " ? 13 7. To find the rate, the percentage and base behif/ f/iren. KULE. Divide tlte percentage by rlie base. EXAMPLE. Base = 400, Percentage = 36. 36 -T- 400 = .09, or 9 per cent. EXERCISES. 138. 1. Base 500, Percentage 35, Rate = ? . " 1200, " 72, " = ? -;. " 1800, 144, " 3 8 SHORT METHODS 139. To find the rate of loss or t/nhi. RULE. Divide the loss or gain by the cost. EXAMPLE. Cost == $250, Selling price = $300. $300 $250 = $50, Gain, $50 -^ $250 =* 20 per cent., rate of gain. EXERCISES. 140. Find Rate of Gain or Loss : 1. Cost = $400, Selling Price, $500. 2. " ^$279, " $540. 2. " = $720, " $600. 14,1. The following formulas are a very good illustra- tion of the problems of percentage : FORMULAS OF PERCENTAGE. Base X Rate == Percentage. Percentage -~ Base = Rate. Percentage -~ Rate == Base. Amount -f- 1 Rate := Base. Difference -=- 1 -- Rate Base. By applying the formulas above to these applications, problems of Percentage are very readily solved. IX ARITHMETIC. 39 ^ o c 2. =r = = X R 7T ^ M X Cfl ^ n o 3 3 c I- ~. 7: c ~ c -2. r D i j-i a -- Efl 3' ?' 7 3 or 5 . . ' y. r^ ^-^- ? r = 1" ~ -r y - ^ *""" ' y ^ c pQ c ^1 \J r|ii - -. - - i X'aliK' X ~ l. P n - gj o' r r n \ i I i -. - ~ : 1 -^ " ~ PQ rr |o. ))i:>| pr - pa n 2 ij ~ pc ~' p^- pa s H 1 CO J= i-. 5 1" O __; ~ . ^ r-r ~ ". .___ o - - 5 ^ -r *^n ^ c 17 c - r ^ 2- -^ E b | - ' - - /. - . c 0!~ B 5 S' - _ - 3 3 C 2 f r ^ "* x ~ C = ?' El ? ^^ t f-* * ? - L J '* = 5 171 ". - i = |: > 1 c " 5 ' I = W "-* 1 ? < __ / 3 ^ '~ c* * ? 5' 2 x K n x 7' h INTEREST r . " CANCELLATION METHOD. '143. EXAMPLE. Find the interest on $420 for 30 days, at 7 per cent. 35 $00 30 days .07 $2.45 interest. A us. EXAMPLE. Find the interest on $540 for 7 months at 9 per cent. 45 7 months .09 $28.35 interest. A-ns. RULE. \Vrite the principal, rate and time , or r< nnmrli.-- f (t month. XOTE. When the number of day* is ;t multiple of I* it shorten- th,- vvork hv using 1 months ;\nd tenths of ;i month. ABBREVIATED METHOD. The cancellation method may be somewhat shortened by omitting the rate and using instead of 360 as a divisor the quotient of the rate into 360. Thus : When the rate is 2 per cent. use 180. ; ( tt 3 (i 120. . 4 ti 90. a 5 tt 72. .. 6 n 60. a ti 8 (I a 45. tt it 9 tt it 40. a 10 tt a 36. a 12 30. 18 " " 20. 4 a *1IORT METHODS EXAMPLE. What is the interest on $720 for 33 days at 5 per cent? 10 $:>.: : >() interest. EXAMPLE. What is the interest on $1260 for 66 days at 8 per cent ? 1$ \ 85 $1200 0022 $18.70 interest. EXERCISES. 147. Find the interest : 1. Of $840 for 18 days at 6 per cent. 2. Of $960 for 27 days at 8 per cent. 3. Of $1240 for 36 days at 4 per cent. 4. Of $3260 for 63 days at 9 per cent. BANKERS' METHOD. 148. EXAMPLE. What is the interest on $1344 for 75 days at 6 per cent ? $13.44 = interest for 60 days. 3.36 interest for 15 days. $16 80 = interest for ~75~days. IiULE. Point off two places, ivhich -will give the interest for the rate and corresponding time as fol ioius : IX ARITHMETIC. '2 per ceu i for ltf(. 3 4 90 5 72 6 60 - 45 .f t/// EXERCISES. Find the interest : /. Of $810 for 90 days at 4 per cent. Of $648 for 45 days at 8 per cent. Of $1232 for 36 days at 10 per cent. Of $7200 for 37 days at 9 per cent. Of $963.75 for 80 days at 6 per cent. o. Of $2140.50 for 90 days at 8 per cent. V. Of $5235.60 for 66 days at 6 per cent. 7. Of $4840.40 for 72 days at 10 per cent. PROBLEMS I.N INTEREST. 1.5O* The following formulas are illustrative of the four problems of interest. 4- Principal > Rate Time Interest. .',. Interest -~ Principal Rate ~= Time. .'. Interest : Principal Time = Rate. /. Interest ~ Time ~ Rate Principal. 131. Applications of Percentage involving the ele- ment of time are as follows : Interest, Discount. Partial Payments, Insurance, and Stock Investments. 44 XII ORT METHODS To find the timv when t/te principal, rate and interest is given. EXAMPLE. Principal - $900; Rate = 8 per cent.; Interest, $6.00; to find the Time. 300 $<>.00 $000 oO days, the tune. EXAMPLE. Principal $720; Rate 6 per cent.; Interest $25.20. Find the time. n 00 (?) .00 7 months. RULE* Use the cancellation inetJiod :i'pt that tJi>' Tim? and Rut? is us?,>. To find the Rank Discount of any sum. EXAMPLE.^; Find the bank discount of $840 for 63 days discounted at bank at 10 per cent. $?<40 70 03 21 300 10' I An*. $14.70 bank discount. ItL'LK. Kititl tin 1 sfmpl? iii.r.?r?st. fr the given tiii)<' an 1 1 r//<> the rate for the given time t th to tin' unit as follows: If 4 hats cost $20, 1 hat will cost ^ of $20, or $5. The second step is to reduce to a number: If 1 hat cost $5, 7 hats will cost $35. The third step combines the first and second: If 7 coats cost $84, 1 coat will cost $12 ; 4 coats will cost $48. EXERCISES. 258. If 13 hats cost $39, what will 7 hats cost? 2. If 11 pairs of shoes cost $46.50, what will 7 pairs cost? 3. If y* of a ton of hay cost $10, what will J^ of a ton cost? 47 15 & Reduce the following first to the fractional unit, then to the integral unit, then to the required number of fractions. EXAMPLE. If % of a ton of hay cost $12, what will fe of a ton cost ? % of a ton cost $12, l / 5 of a ton will cost $3, % or 1 ton will cost $15, r /6 will cost /s of 15 or *%, ~> will cost 7'times i5/ 8 =i05/ 8=: EXERCISES. 1(>0. /. If 73 of a bushel of wheat is worth 72 cents, what are 10 bushels worth? 2. If 9/io of an acre of land cost $108, what will % O f an acr*e cost at the same rate? .}. If y?> of ^ of a cord of wood is worth $3.50, what is of % of a cord worth ? 1(>1. To find interest on overdrafts. EXAMPLE. Overdrafts for the week were as follows : 7. 1200 1500 Interest at 10 per cent. IbOU 1600 1850 9500 -*- 360/ 10 $2.64. RULE. Divide the sum of the daily overdrafts by 360 divided by tlie rate, and point off two decimal places. 48 102. How to find ert-ors s/towtt by a trial balance. I. See that your former baln-ncc of Imlnm'cs is in balance. ;'. Be sure that your additions are correct. Find the exact amount out of balance, and look for it and its one-half among the ledger items. Jf. If the error is 9 or a multiple of 9, look for reversed figures. EXAMPLE. 65 written 56 would make a difference of 9 ; 57 written 75 would make a difference of 2 times 9, or 18 ; 63 written 36 would make a difference of 27, etc. This may occur in any or all columns. 5. If there is an error of 1 in any column, look tor er- rors in addition. #. If the error is small, look for it in Interest or Dis- count. 7. Examine the Bills Receivable and Bills Payable ac- counts and note that the Debit and Credit entries are ex- actly alike as far as posted. 8. See if your cash account in the Ledger or Cash Book agrees with your Banking Ledger and cash on hand. 9. If the error is in cents column, it is not necessary to add the dollars column. 10. If the above tests will not indicate to you the er- rors, it will be necessary for you to re-check everything from the previous balance of balances. Do not go over the work without checking, you will .waste your time if you do. J/ U. C. BERKELEY LIBRARIES