2. Begin at the right hand, and take the number in each denomination of the lower line from the number standing above it, and set down their remainders below them. 3. But if the number below be greater than that above it, increase the upper number by as many as make one of the next higher denomination, and from this sum take the number in the lower linc, and set down the remainder as before. 4. Carry the unit borrowed to the next number in the lower line, and subtract as before ; and so on, till the whole is finished ; and all the several remainders taken together, as one number, will be the whole difference required. The method of proof is the same as in simple sub traction. EXAMPLES. Μ Ο Ν Ε Υ. S. ibo d. . d. From 275 13 en 45.4 14 27 Take 176 276 175 S. ' d. 274 14 25 85 15 71 Mls. fur. pol. yd. ft. in. Mls. fur. pol. yd. ft.in. Mls. fur. pol. yd. ft.in. From 14 3 17 I 2 70 7 13 I I 2 70 3 10 14 2 2 7 17 3 II I Take 10 h 302 IO 20 pe.gal. L. qr. bu.pe. gal.pot. L. gr. bu. pe. gal. L. gr. bu. From 9 4 7 1 13 3 5 2 27 5 3 7 3 7 10 2 2 1 1 I 1 Take 2 2 COMPOUND MULTIPLICATION. Compound Multiplication teacheth to find the amount of any given number of different denominations by repeating it any proposed number of times. RULE.* 1. Place the multiplier under the lowest denomination of the multiplicand. • 2. Multiply the number of the lowest denomination by the multiplier, and find how many ones of the next higher denomination are contained in the product. 3. Write down the excess, and carry the ones to the product of the next higher denomination, with which proceed as before ; and so on, through all the denominations to the highest, whose product, together with the several excesses, taken as one number, will be the whole amount required. The method of proof is the same as in simple multiplication. EXAMPLES The product of a number consisting of several parts, or de nominations, by any simple number whatever, will evidently be expressed by taking the product of that simple number and each part by itself, as so many distinct questions : thus, 251. 128. 6. multiplied by 9 will be 225l. 108s. 54d. = (by taking the shillings from the pence, and the pounds from the shillings, and placing them in the shillings and pounds respectively), 230l. 12s. 6d. which is the same as the rule ; and this will be true, when the multiplicand is any compound number whatever. il. 45. 41d. the answer. 2. 3lb. of green tea, at 9s. 6d. per lb. Ans. Il. 8s. 6d. 3. sib. of loaf sugar, at is. 3d. per lb. Ans. 61. 35. 4. gcwt. of cheese, at il. 11s. 5d. per cwt. Ans. 141. 25. od. 5. 12 gallons of brandy, at 9s. 6d. per gallon. Ans. 51. 145. CASE I. If the multiplier exceed 12, multiply successively by its component parts, instead of the whole number at once, as * in simple multiplication. EXAMPLES. 1. 16cwt. of cheese, at il. 18s. 8d. per cwt, il 18s. 8d. 4 £30 18 8 the answer. 2. 28 yards of broad cloth, at 198. 4d. per yard. Ans. 271. Is. 4d. 3. 96 quarters of rye, at il. 35. 4d. per quarter. Ans. 1121, 4. 120 dozen of candles, at 55. od. per doz. Ans. 34!. Ios. 5: 132 yards of Irish cloth, at 25. 4d. per yard. Ans. 151. 8. 6. 144 reams of paper, at 135, 4d. per ream. Ans. 961. 7. 1210 |