SUBTRACTION OF DENOMINATE NUMBERS. 1. John has 3s 6d and gives ls 4d for a knife: how much has he left? Ans. 2s 2d. 2. James has 4s 8d and gives 2s 3d for a bunch of quills: how much has he left? Ans. 2s 5d. 3. What is the difference between £27 16s 8d and Set down the 11, and carry 1 to 17 making 18: then say, 18 from 36 leaves 18: set it down and carry one to 19 making 20: 20 from 27 leaves 7. Or we may set down the minuend as on the right: £26 35s 20d. Then 9 from 20 leaves 11; 17 from 35 leaves 18; and 19 from 26, 7 remains. § 72. Hence; for the subtraction of denominate numbers we have the following RULE. I. Set down the lesser number under the greater, placing the same denominations directly under each other. II. Begin with the lowest denomination, and if the number expressing that denomination be less than the number directly over it, make the subtraction as in simple numbers. But if it be greater, subtract it from the upper number increased by so many units as make one unit of the next higher denomination, and carry this one which has been borrowed to the next higher denomination, as in subtraction of simple numbers. III. Do the same for all the denominations, and set down the several remainders, and they will form the true remainder. PROOF. Add the remainder to the subtrahend—their sum should be equal to the minuend. Q. How do you write down the numbers for subtraction? Where do you begin to subtract? When the number to be subtracted is less than the one above it, what do you do? When it is greater, what do you do? How do you prove Subtraction? 7. From 38mo. 2wk. 3da. 7hr. 10m., take 10mo. 3wk. 2da. 10hr. 50m. Ans. 27mo. 3wk. 20hr. 20m. 8. From 176yr. 8mo. 3wk. 4da., take 91yr. 9mo. 2wk. 6da. Ans. 84yr. 11mo. 5da. 9. From 6 tuns, take 3hhd. 15gal. 3qt. Ans. tuns. gal. qt. Ans. 1lb. 11oz. 19pwt. 4gr. Ans. 3 3 9. 12. From 8b, take 1b 13 23 27. 13. From 9T., take 1T. 1cwt. 2qr. 20lb. 15oz. 14dr. Ans. 7T. 18cwt. 1qr. 7lb. Ooz. 2dr. 14. From 3 miles, take 3fur. 19rd. Ans. 2mi. 4fur. 21rd. APPLICATIONS IN ADDITION AND SUBTRACTION. 1. Sold a merchant one quarter of beef for £2 7s 9d; one cheese for 9s 7d; 20 bushels of corn for £4 10s 11d; and 40 bushels of wheat for £19 12s 81d: how much did the whole come to? Ans. £27 0s 11 d. 2. Bought of a silversmith a teapot, weighing 3lb. 4oz. 9pwt. 21gr.; one dozen of silver spoons, weighing 2lb. loz. 1pwt.; 2 dishes weighing 167b. 10oz. 15pwt. 16gr.: how much did the whole weigh? Ans. 22lb. 4oz. 6pwt. 13gr. 3. Bought one hogshead of sugar, weighing 9cwt. 2qr. 277b. 14oz.; one barrel weighing 3cwt. 271b., and a second barrel weighing 2cwt. 3qr. 261b. 4oz.: how much did the whole weigh? Ans. cwt. qr. lb. 0%. 4. A merchant buys two hogsheads of sugar, one weighing 8cwt. 3qr. 21lb.; the other, 9cwt. 2qr. 67b.; he sells two barrels, one weighing 3cwt. 1qr. 127b. 14oz.; the other, 2cwt. 3qr. 15lb. 6oz.: how much remains on hand? Ans. 12cwt. 26lb. 12oz. 5. A man sets out upon a journey and has 200 miles to travel; the first day he travels 9 leagues 2 miles 7 furlongs 30 rods; the second day 12 leagues 1 mile 1 furlong; the third day 14 leagues; the fourth day 15 leagues 2 miles 5 furlongs 35 rods: how far had he then to travel? Ans. 14L. 1mi. 1fur. 15rd. 6. A farmer has two meadows, one containing 9A. 3R. 37P., the other contains 10A. 2R. 25P.; also three pastures, the first containing 12A. 1R. 1P., the second containing 13A. 3R., and the third 6A. 1R. 39P.: by how many acres does the pasture exceed the meadow land? Ans. A. R. P. 7. Supposing the Declaration of Independence to have been published at precisely 12 o'clock on the 4th of July 1776, how much time elapsed to the 1st of January 1833, at 25 minutes past 3 P. M.? Ans. 56yr. 181da. 3hr. 25m. 8. A farmer has three granaries, one for wheat, one for rye, and one for corn: he fills them all. His wheat granary contains 657bu. 3pk. 6qt.; the corn granary 257bu. 1pk. 1qt.: the rye granary 459bu. 2pk. 7qt.; how much grain had he in all, and how much more wheat than In all 1374bu. 3pk. 6qt. Wheat more than rye 198bu. 7qt. rye? Ans. { 9. A father was born on the 8th of December 1759, his first son on the 4th of June 1795: what was the difference of their ages ? Ans. 35yr. 5mo. 27da. 10. A merchant has a bill to pay of £600. He has £250 198 8d in cash, a good note against A for £75 10s 6d and a note against B for £37 11s 9d: how much money does he want to make the payment? Ans. £ s d. 11. A tailor requires lyd. 3qr. 3na. of cloth for a father's coat, and lyd. 1qr. 2na. for each of two sons: the father buys 6 yards, does he buy too much or too little? Ans. lyd. 1qr. Ina, too much. MULTIPLICATION OF DENOMINATE NUMBERS. 1. Charles pays 6d for a pencil: How much will buy two pencils? How much will buy 3 pencils? 4 pencils? 5 pencils? 6 pencils? 2. James puts 1 quart and 1 pint into a measure: How much could he put in a measure of twice the size? In a measure of three times the size? 4 times the size? 5 times the size? 6 times the size? 3. What is the product of 2s 4d multiplied by 2? by 3? by 4? by 5? by 6? by 7? by 8? by 9? 4. What is the product of lyd. İqr. multiplied by 2? by 3? by 4? by 5? by 6? by 7? by 8? by 9? 5. Multiply £3 9s 10d by 4? In this example we say, 4 times 10d are 40d, equal to 3s and 4d. Set down the 4d in the lower line. Then 4 times 9s are 36s and 3s to carry make 39s, equal to £1 and 19s over: set down the 19s. Then 4 times £3 are £12 and £1 to carry make £13. OPERATION. £ s d 3 9 10 4 £12 36s 40d £13 19s 4d We may conclude from the examples that, to multiply a denominate number by a simple one, is to repeat the denominate number as many times as there are units in the multiplier. CASE I. § 73. When the simple number does not exceed 12. RULE. I. Write down the denominate number and set the multiplier under the lowest denomination. II. Multiply the lowest denomination by the multiplier, and see how many units of the next higher denomination are contained in the product, and set down the excess as in addition. III. Multiply the next higher denomination by the multiplier and add the units to be carried from the last product; then reduce the sum to units of the next higher denomination, write down the excess and proceed in the same way for all the denominations, setting down the entire product when you come to the last. Q. What is required when you multiply a denominate number by a simple one? When the simple number does not exceed 12, how do you write it down? How do you begin to multiply? How do you carry? 1. What is the cost of 4 yards of cloth at £1 3s 6d per yard? The amount per yard multiplied by the number of yards will evidently give the entire cost. OPERATION. £1 3s 6d 4 £4 14s 0d Ans. |