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Les cartes, planches, tableaux, etc., peuvent dtre film6s d des taux de reduction diffdrents. Lorsque le document est trop grand pour §tre reproduit en un seul cliche, il est filmd d partir de Tangle sup^rieur gauche, de gauche & droite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivants illustrent la mdthode. 1 2 3 22X 1 2 3 4 5 6 GRUMM'ETTS -♦-♦.- The Newest and most Ccmpiete SELF INSTRUCTOR — FOR — All who desire to advance them- selves in Figures. « — BY — J"ose3I3h: o-:RTris/cjb/L-jsirrT. :)C. Olaij PREFACE. '■"g discoveries have been . """^ ''»^'- «'^PWaed that any eh,-,; J*"' '°8«»«^ ""dso .-''w«gthe4Jl;';"f«-^».iH -'-to, lea™ .,/;^7'.;'"'-'-y other ^«'y short tiB.e. *^'' l-^ok » a JOSEPH GRDMMETT ««". November, 1877. > ». ADDITION, i? s caicuJations ^"^ and start- ^ the foJJow. ^hods in the etiier and so inary mind, ^»* any other ^ooJc in a "1^* »n the *»even. hv »ty of Wat culture. Various suggestions have been made refer- ring to improved methods of addition. In practice I have found no better or quicker method than the following : — KuLE. — Commence at the bottom of tlie right hand column ; add thus— 15, 19, 21) ; set down the 9 in tens place and carry the two tens to the second column, then add thus — ^4, 10, 18, 28 ; set down 8 in tens place and carry two hundreds to the third column, and add so on to the end. Never add in tliis manner — 8 and 7 are 15, and 4 are 19, and 3 are 22, and 7 are 29 ; it is just as easy to name the sum at once, and save time and labour. 4687 6423 ♦ ' 5684 4567 4328 25689 K-TTHiE :DNro. 2. MULTIPLICATWK When the multiplier is any number be- tween 11 and 20, the process is sihiply to multiply by the unit figure of the multiplier, set down one figure to the right hand of the multiplicant and add in the multiplicant. * . • What is the cost of 26 yards of goods at 14c per yard 1 26x14 [J- $3.64 ¥ •< a Process. — 4 times 6 are 24, set down 4 to the right of the 6, carry 2, add it to 6 makes 8, then carry 8 ; then 4 times 2 are 8, and 8 to carry makes 16, set down 6, add the 1 to narrv fn the figure 2 crives 3, then make S3. 64c the sum. i1 :ruil,-bi IsTO. 3. MULTlPLICAriON. s.» V To multiply any number of two figures ty 11. I Rule. — Place the sum of the two figures between them. Multiply 45 by 11 — 4 and 5 are 9 ; place the 9 between the 4 and .5, makes 495 the sum. Multiply 87 by 11—8 and 7 are 15 ; set 5 between the 8 and 7- then one to carry add it to 8 makes 9, gives 957 the sum. tl jBxrXi:E3 isro. 4. MULT1PLWAT10N. To multiply anynumber by It N.. RULE.-Brmg down the right hand figuw 8 ; tlien add 8 and 7 are 15, bring down 6, carry 1 to 7 makes 8 ; then 8 and 5 are 13, bring .lown 3 and carry 1, add it to 5 makes fi • then 6 and 3 are 9, bring down 9, you have none to carry ; then bring down the 3, makes 39358 the sum. 3578x11 39358 !* i MUL TfPL 10 A TIOX. Lt. b hand figure ring down 5, and 5 are 13, it to 5 makes r down 9, you y down the 3, t'^ \ K*. i To multiply when the sum of tlie units inf 10 and the tens are alike. .Rule.— Multiply the figure in tens, place by the next larger number, and the tens by themselves. Jpjat is thini^t of 86 yards- of goods at t cents per yard: 84 cents per yard: 86 84 $72.24 Multiply 91 by 99. w 91 99 9009 MULTrPLWATION. When the unite of any two numbers are alike. Rule.— Multiply units into units, then the sum of the tens by the units, then the tens together. What is the cost of 62 yards of Calico at 32 cents per yard 1 62 32 $19.84 . PR0CBs8.-^Twice 2 are 4, set the 4 in units place ; then twice 9 are 18, set down 8, carry 1 : then 3 times fi ar>t\ l« a-nA *y^ «« makes 1 9— making $ 1 9.84 cents the sum. B e. i^tjxjE zsro, 7. numbers are inits, then the hen the tens f Calico at 32 bhe 4 in units town 8, carry the sum. MULT J PLICA TfON. Whon the tens of any two numbers are alike. t I KuLE.— Multiply units together ; then the sum of the units by the tens ; then the tens together. What is the cost of 64 lbs. of Sugar at 66 cents per pound ? 64 66 $42.24 PROCES8.-r-6 times 4 are 24, set down 4 and carry 2 ; then 6 times 10 are 60, and carried 2 makes 62. set down 2 and carry 6 ; then 6 times 6 are 36, and carried 6 makes 42. rnVp^ $42.24c the sum. B I^"c^XiE isro. a. h MUL T! PLICA TION. To Multiply by 25 or J. What is the cost of 64 yards of goods at ^5 cents per yard 1 Rule. — Annex two ciphers to the number of yards and divide by 4, and you will have the answer in cents. 4)64.00 $16.00 Half yard 4)64.50.00 116.12.50 8. IRTJXiE IvTO. 9. MUL TIP Lie A TION. ot\. , To multiply by 50 or J. ds of goods at to the number you will have What is the cost of 79 yards of calico at 50 cents per yard 1 Rule. — Annex two ciphers to the number of yards and divide by 2, and you will have the answer in cents. 2)79.00 $39.50 ^juarter yard 2)79.25.00 139.62.50 ;; lEaux^s isro. lo. MUL T I PL 10 A TION. To Multiply by 12^ or J. What cost 88 pounds of goods at 12J cents per pound ? , Rule.— Annex two ciphers to the number of pounds and divide by 8, and you will have the answer in cents. 8)88.00 1.00 * laXTLE 3SrO. 11, MULTIPLICATIOK To multiply by 1.25 oi|. What is the cost of 96 yai-ds of jroods at .25 per yard? the number ou will have RULE.-3- Annex threff ciphera to the num- ber of yards and divide by 8, and you will have the answer in cents. 8)96.000 $120.00 ' J.' uii ^aru o^yo.ou.UUO 1120.62.50 . II IRTJXiE 2SrO- 12. M UL riPL TO A TION. To Multiply by 250 or J. What is the cost of 48 yards of goods at $2.50 pel yard 1 Rut.E. — AnnrO. 14. TABLE OF ALIQUOT PARTS. 83J is r'ff of 1,000 62^ « tV {( « 66i (( tV « « 125 (( i cc « 250 « (( (« 375 « (( tt 625 << ({ <( 876 (( (( « i To multiply any number by an aliquot part of 1000. Rule.— Annex three ciphens and divide by the fractional part. rs. I^TJIiE liTO, 15. ^ MULTIPLICATION. To multiply a whole number and a half together. KuLE.— To the product of the whole num- ber add half their sum plus J. What will ^ yards of tape cost at 4J cents per yard ? ' ' - D aliquot d divide Process.— The sum of 6 and 4 are ten- half this sum is 5 ; then 4 times 6 are 24 and 6 are 29 ; to this add J. ' 29Jc i^TJXlE nsro. is. MUL TIP Lie A TION. To multiply a whole number and a half together. Rule. — When the sum is an odd number take half the next number below it then the fraction in the answer will be f . What will 9J yards of goods cost at $2.50 per yard 1 Process. — The sum of 9 and 2 are 11 ; the next number below 11 is 10, half of 10 is 5 ; then twice 9 are 18 and 5 to carry makes 23, to this add f . ^ 2| $23| nd a half i number then the ;at 82.50 K^UXiE 2^» The base of this rule is 6 per cent. Findj^the Interest on $ 5 for 6 days or one week 6 mills. 1 cent. 2 cents. 4 centH. 5 cents. For 12 days nuiltiplv by 2 " 18 " *' ■ * 3 24 " ** 4 '30 •' ** 5 For one dav divide by 6, and yon will have tlu* answer in mills. If yon have dollars and cents together, the answer will be in hundreds of ntills. In actual business a month is eqnivalent to 30 days, a year to 360 dayn. Custom has made this nawful. For months multiply the dollars by half the number of months a»^d you will have the answer in cents. If you have dollars and cents together, multiply by half the number of n)onths and you will have the answer in hundreds of cents. It is all 6 per cent, as a base. For 1 per cent, divide bv (, " 7 " add " 8 . " add " 9 '- add " 10 " add i "11 " add %■ 1 If 1 3 I C( 12 18 24 30 (t multiply by 2 t* tt 5 at^ I lial] ans I^TJXiE ITO. 19 8. 8. 8. To find the price of a lonrl of hay or straw. Iiavo tli»' tlier, the snt to HO iiade ihirt half the le answer together, and yoii 8. What is the cost of 19.50 pounds of Jiay at $14 per ton. Rule. — Multiply thouuinbcir of pounds by half the price per ton, and you will have the answer in mills. 19.50 i .3.65.0 IRTJX^E Isl O. 20. The practice of buying or seJling grain by the 100 pounds or the cental system, has many advantages over the bushel. To find the value per cental when the price per bushel is given. ^ t5' Hulk- Het down the price por bushel, and divide by the number of pounds in the T>U8heI. If wheat is 11.20 per bushel how much is that a centJil or 100 pounds. 60)$1.20 i^TJXiE 2sro. 21. grain by item, has the price shel, and I in the To find the value per bushel when the price per cental is given. KuLE. — Set down the price per cental, and multiply by the number of pounds in the bushel i? wheat is $2 per cental how much is that much is per bushel 1 $2.0 o i^ 11.20 l=lJJXj-:Ei IsTO. 22, BUSHEL MEASURE, The following table shows the legal nnniher of puiinds per bushel : — *' 34 pounds — bushel of oats. 48 pounds — bushel of buckwheat. 48 poundvs — bushel of barley. GO pounds — bushel of beans. j 56 pounds—bushel of Rye or Indian corn. | 60 pounds — bushel wheat, peas or clover seed. *