fourth as many pence as farthings, one-twelfth as many shillings as pence, and one-twentieth as many pounds as shillings. COR.—A lower denomination is reduced to a higher one by division. Reduce 1095 farthings to pence, shillings, and pounds. 4 ) 1095 farthings. 12 ) 273 ... 3 far. 20) 22 9d. £1 28. 9d. 3 far. The first remainder is farthings, the second pence, and the third shillings. Reduce £1 2s. 9d. 3 far. to farthings. 20 12 273 pence. 4 1095 farthings. In reducing a higher denomination to a lower one, begin by multiplying by the number of the next lower denomination that makes one of the higher, and if it be a compound number, add to the product the number of the lower denomination, and continue this process until you reach the lowest denomination. In reducing a lower to a higher denomination, divide by the number of the lowest denomination that makes one of the next higher, and if there be a remainder, it will be of the lowest denomination, etc. COR.-In the computation of compound numbers, instead of carrying a unit to a higher order for every ten, as in abstract numbers, a unit is carried to a higher denomination as often as the sum reaches the number that it takes of the lower denomination to make one of the next higher denomination; thus, as 4 farthings make 1 penny, as often as the sum of the farthings reaches four, one must be carried to the pence; and as 12 pence make 1 shilling, in computing pence as many must be carried to shillings as the number of times 12 is contained in the number of pence; 1 from shillings to pounds for every 20. In division, the order is reversed, as then we begin with the highest denomination and descend. The sum of the first column is 9 farthings, which is 2 times 4 and 1; the 1 is farthings, and must be placed under the farthings; the 2 is carried to the next denomination and added with the pence, the sum of which is 35; that is, 2 times 12 and 11, that is, 2 shillings and 11 pence; the 2 is added with the shillings, making the sum 45, which is £2 58.; the shillings are placed under the shillings and the 2 carried to the pounds, the sum of which is 24. £25 18s. 10d. 2 far. As you cannot subtract 3 farthings from 1 farthing, you must borrow 1 penny, which is 4 farthings; this 4 and the 1 make 5; then 3 from 5, 2 remains; the 1 penny borrowed must be carried to the 6, which makes 7, which cannot be subtracted from 5; 1 shilling, that is, 12 pence, must be borrowed and added to the 5, which makes 17; 7 from 17, 10 remains; 1 shilling to carry to 7 makes 8, which cannot be taken from 6; 1 pound, that is, 20 shillings, must be borrowed and added to the 6, making 26, from which subtract 8 and 18 remains; and £1 to carry to 28, making 29, which is subtracted from 54 and 25 remains. REM.—When the subtrahend is less than the minuend, the difference can be taken directly. · 4 5 3 5 5 21 20 ) 32 25 4) 15 £1 12s. 3 3d. 3 far. 12) 28 28. 4d. COR.—Multiply each denominate number, and divide the product by the number of this denomination that it takes to make one of the higher, and carry the number of times it is contained to the higher denomination, and place the remainder under its kind. 4. Multiply £48 12s. 7d. 2 far. by 6. £1 68. 6d. 37 far. 4 is contained in 5, once and £l over; this £1 is 20 shillings, which added to the 6 shillings make 26 shillings, into which 4 is contained 6 times and 2 shillings over; this 2 shillings is 24 pence, which added to tà: pence, makes 27 pence, in which 4 is contained 6 times and 3 pence over, which is 12 farthings, and I more make 13, in which 4 is contained 31 times. 6. Divide £754 15s. 9d. 3 far. by 27. 27 ) £754 158. 9d. 3 far. ( £27 54 214 189 25 20 2 27 £ 7. Muigiply £5 48. 6. 1 far. by 35. 35 35 35 4) 35 6 8d. 3 far. 210 8 12) 218 140 18s. 2d. 18 REM.- Observe these solutions carefully; for if they are understood, there is no further difficulty in denominate numbers; the principle is the same in all, the tables alone differ. EXAMPLES 1. In 2 dollars, how many cents? How many mills ? $2 x 100 = 200 cents. 2. In 5 dollars, how many cents? How many mills ? 3. In 7 dollars, how many cents? How many mills ? 4. In 5 dollars 15 cents, how many cents? How many mills ? $5 = 500 cents. 15 5. In 6 dollars 15 cents and 3 mills, how many mills ? many $5, Ans. 7. In 625 cents, how many dollars and cents ? Ans. $6.25. 500 100 |