| XXX | (376) | XXX |
^7^ A R I t H M E T I C K. bottom; and if the work be right, the figures at top and I. Divifion of Integers.
- bottom will agree, or be the lame.
Examp. I. Here call the 9’s out Rule I. From the left-hand part of the dividend of the multiplicand, and place the point off the firll 15428 excefs 7 on the right fide of the crofs; contain the divifor.dividual, viz. fo many figures as will then call the 9’s out of the multiplier, Aik how often the divifor is contained in the diviand place the excefs 2 on the left fide dual,II. and 6032 put the anfwer in the quotient. of the crofs ; next multiply thefe ex- III. Multiply 2262 00 by the figure fet in the quo5 eeffes 2 and 7 into one another, call tient, and fubtradthethedivifor from the dividual, the 9’s out of their product, and IV. To the right ofprodud 28652 the bring down the place the excefs five at the top of the next figure of the dividend forremainder a new dividual; and then crofs; la-ftly, call the 9’s out of the produd, and place proceed as before. the excefs 5 at the foot of the crofs; which being the Examp. I. Here, becaufe the fame with the figure at the top,. you may conclude the divifor 7 is contained in 8, the left- Divi- Divi- Quowork to be right. hand figure of the dividend, point it for. dend. tient. Examp.II. Here, in calling off as the firft dividual, according 7)875(125 the n’s out of the multiplicand, to Rule I; and then fay, How oft. .. 7 and of the produd, begin en 7 in 8 ? Anf. 1 time; which 1 7 2* 8 X* without the pounds, and reduce the let in the quotient, as direded in —— ^ i ■ excefs to Ihillings, and in like Rule II.; then multiply the divifor 7 17 347 6 10 manner excefsto ofpence, the Ihil-7 by this quotient figure 1, and fub14 lings is the reduced and trad the .produd 7 from the divithat of the pence to farthings. The multiplier being an dual 8, as direded in Rule III.; to 35 abllrad number, needs no redudion; but if a multiplier the remainder 1 bring down the fol- , 35 t? be a mixt number, or confift of integers and parts, as lollowing figure of the dividend, for feet and inches, fyc. the excefs of the higher denomina- the fecond dividual, as direded in (°) Rule IV.; then proceed as before, tion mull always be reduced to the lower. and fay. How often 7 in 17? Anf. 2 times; wherefore, fetting two in the quotient, multiply and fubtrad C h a p. V. Division. and find the next remainder to be 3 ; to which bring down the following figure of the dividend, and you have 3 5 for the third dividual; then fay, How often 7 in 3 5 ? Division difcovers how often one number is con- Anf. 5 times; which 5 being placed in' the quotient, tained in another: or, Divifion, from two numbers given, finds a third, which multiply and fubtrad, and o remains; fo the quotient 125. contains unity as often as the given number contains is By reviewing the Heps of the preceding operation, and the other. the dividuals and quotient-figures to their feThe number to be divided, or which contains the o- reducing parate values, the reafon of the rules will be obvious; ther, is called the dividend; the number by which we for, divide, or which is contained in the dividend, is called The feparate value 7)875(100} the divifor; and the number found by divifion, or which expreffes how often the dividend contains the divifor, is of the firftanddividual is 800; the fe-8 iftdividualSoo . partialquots. called the.quotient or quot. value of 1, the 700 As multiplication fupplies the place of many additions, parate figure put in the fo divificn, which is the reverfe of multiplication, firft 100 125 total quot. is 100; for ferves inllead of many fubtradions; as will thus ap- quot, 70 as 8 contains 7 the pear:is,Suppofe it wereoftenrequired to dividein1818,bythe6, divifor
- 2. that
to find how 6 is contained 1 time, fo 800 it 100 times, 2d dividual 170 ^ work by fubtradion will Hand as in the margin-: contains 140 100 remains ; to by which it appears, that 6 is contained 3 times in and which bring down <5 the number 18. But this, by divifion, may be the 30 following figure of the dividend 7, (°)‘ found at one trial: thus, 5 whofe feparate value Set the divifor on the left of the dividend, leaving is 70; and the fe- 3d dividual 35 room on the right hand for the quotient, as in cond dividual is 170; 35 margin; and then fay. How often 6 in 18 ? 6)18(3 the as 7 is contained —
Anf. 3 times : this 3 fet in the quotient; then and 18 multiply times in 17, fo it (o) the quotient figure 3 into the divifor is2 contained 20 times faying, 3 times 6 make 18; which fet down in 170, and 30 remains ; to which bring ffown the next o) 6,below the dividend, and lubtratt it from the or laft figure of the dividend 5 ; and the third dividual dividend, and o remains.
