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COMPOUND SUBTRACTION.

133

COMPOUND SUBTRACTION.

228. When one compound number is taken from another, the process is called Compound Subtraction. It combines subtraction and reduction descending.

229. A person who had 1 cwt. 8 lb. 15 oz. of cheese, sold 3 qr. 19 lb. 7 oz. How much had he left ?

We are here required to find the difference between two compound numbers. Write the subtrahend under the minuend, placing numbers of the same denomination in the same column. Mark the denominations over the top.

cwt. qr. lb. OZ.

1 0

8 15

19 lb.

3

19

Ans.

14

8

Begin to subtract at the right. 7 oz. from 15 oz. leave 8 oz.; set down 8 beneath, in the same column. can not be taken from 8 lb. We therefore take one of the next higher denomination, 1 qr., reduce it to pounds, and add it to 8 lb. 25+8=33;

19 lb. from 33 lb. leave 14 lb. Set down 14.

To balance the quarter added to the minuend, we must add 1 qr. to the subtrahend. This we do, by carrying 1 to the next column.

1 and 3 are 4. 4 qr. can not be taken from 0 qr. We therefore take 1 cwt., reduce it to quarters, and add it to 0 qr. 4+04qr. 4 qr. from 4 gr. leave 0 qr. Carry 1. 1 from 1, 0. Answer, 14 lb. 8 oz. Hence the rule.

230. RULE.—To subtract a compound number, set it under the minuend, placing numbers of the same denomination in the same column.

228. When one compound number is taken from another, what is the process called? What does Compound Subtraction combine?-229. Go through the example, explaining the steps.-230. Give the rule for Compound Subtraction.

134

COMPOUND SUBTRACTION.

Beginning at the right, subtract each denomination separately, and place the remainder in the same column with the number subtracted.

If, in any denomination, the subtrahend is greater than the minuend, add to the latter as many as make one of the next higher denomination. Subtract, and carry 1 to the next denomination of the subtrahend.

PROOF. Add the remainder and subtrahend. If the sum is equal to the minuend, the work is right.

EXAMPLES FOR THE SLATE.

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9. A grocer buys 15 cwt. 20 lb. of sugar, and sells 10 cwt. 23 lb. How much remains unsold? Ans. 4 cwt. 3 qr. 22 lb. 10. From a piece of cloth containing 373 yd., have been cut off 6 yd. for one dress and 10 yd. for another. How many yards remain in the piece? Ans. 21 yd.

4

What is the proof in Compound Subtraction?

EXAMPLES IN COMPOUND SUBTRACTION.

135

11. A person having £20 18s., spends £5 18s. 74d. How much has he left? Ans. £14 19s. 41d.

12. A farmer raises 100 bu. 3 pk. 2 qt. of wheat from one field, and 87 bu. 1 pk. 1 qt. 1 pt. from another. He sells 53 bu. to one person, and 37 bu. 2 pk. 1 qt. to another. How much has he left? Ans. 97 bu. 2 pk. 2 qt. 1 pt.

13. From a pile of wood containing 100 cords, I sold 10 Cd. 100 cu. ft. to one customer, and 18 Cd. 59 cu. ft. to another. How many cords remained? Ans. 70 Cd. 97 cu. ft. 14. The subtrahend is 19 mi. 7 fur. 8 rd. 2 ft. 10 in.; the minuend is 24 mi. 5 fur. 18 rd. 2 yd. 1 ft. 7 in. What is the

remainder?

Ans. 4 mi. 6 fur. 10 rd. 1 yd. 1 ft. 9 in. 15. A printer who has a bale of paper, uses 1 bundle, 1 ream, 5 quires, and 6 sheets. How much remains on hand? 16. A tailor uses 5 gross, 7 dozen, of buttons. How many has he on hand, if he had 1 great gross at first?

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17. Poughkeepsie is 75 miles from New York. A man who starts to walk there, goes 22 mi. 3 fur. 15 rd. the first day, and 19 mi. 5 fur. 30 rd. the second. How much farther has he to go? Ans. 32 mi. 6 fur. 35 rd.

18. A jeweller, having a bar of silver weighing 2 lb. 6 oz., used 5 oz. 7 pwt. 12 gr. for one job, and 1 lb. 18 pwt. 7 gr. for another. How much was left? Ans. 11 oz. 14 pwt. 5 gr.

19. From a barrel of beer containing 54 gallons, a person drew 12 gal. 3 qt. one day, and 9 gal. 2 qt. 1 pt. another. How much was left?

20. From 39 sq. rd. 29 sq. yd. 128 sq. in., subtract 17 sq. rd. 16 sq. yd. 5 sq. ft.

21. A grocer has 1 cwt. 18 lb. of sugar in one barrel, 3 qr. 21lb. in another, and 1cwt. 2 qr. 11 lb. in a third. After selling 1ewt. 3 qr. 15 lb., how much will he have left? Ans. 1 cwt. 3 qr. 10 lb.

136

COMPOUND MULTIPLICATION.

COMPOUND MULTIPLICATION.

231. When a compound number is multiplied, the process is called Compound Multiplication. It combines multiplication and reduction ascending.

232. Multiply 4 bu. 3 pk. 7 qt. 1pt. by 27.

27 being the product of 9 and 3, it is best to multiply by the factors in turn. Set 9, the first multiplier, under the lowest denomination of the multiplicand.

Begin to multiply at the right. 9 times 1 pint` is 9 pt.; which, by dividing by 2, we reduce to 4 qt. 1 pt. Set 1 pt. in the column of pints, and carry 4qt. to the next product.

9 times 7 qt. is 63 qt., and the 4 qt. carried make 67 qt., equal to 8 pk. 3 qt. Set 3 in the column of quarts, and carry product.

bu.

pk. qt. pt. 4 3 7 1

9

44 3 3 31

3

134

2 2 2 1

8 pk. to the next

9 times 3 pk. is 27 pk., and the 8 pk. carried make 35 pk., equal to 8 bu. 3 pk. Set 3 in the column of pecks, and carry 8 bu. to the next product.

9 times 4 bu. is 36 bu., and the 8 bu. carried make 44 bu. Set down 44.

Now multiply this product by 3, reducing and carrying in the same way. Answer, 134 bu. 2 pk. 2 qt. 1 pt.

233. Had we multiplied by 27 at once, we should have proceeded in the same way. As, however, we could not then have multiplied and divided in the mind, we should have had to write out the figures elsewhere, and set the results only under the line.-Multiply by 12 or less at once, in one line.

231. When a compound number is multiplied, what is the process called? What does Compound Multiplication combine ?-232. Go through the example, explaining the steps.-233. Had we multiplied by 27 at once, how should we have proceeded? How must we multiply by 12 or less?

COMPOUND MULTIPLICATION.

137

234. RULE.-Set the multiplier under the lowest denomination of the multiplicand.

Multiply each denomination in turn, and set the product under the number multiplied, unless it can be reduced to a higher denomination. If so, divide it by the number that it takes to make one of that denomination; set the remainder under the number multiplied, and carry the quotient to the next product.

PROOF.-When factors have been used in multiplying, multiply by the factors in reverse order. If the results agree, the work is right.

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6. Multiply 5 cubic yards, 21 cubic feet, 643 cubic inches Ans. 69 cu. yd. 13 cu. ft. 804 cu. in.

by 12.

7. How much cloth will it take for 7 suits of clothes, if each suit requires 7 yd. 3 qr.? Ans. 54 yd. 1 qr.

8. How much wood can a horse draw in 13 loads, if he draws 1 Cd. 1 cd. ft. each load?

234. Recite the rule for Compound Multiplication. What is the mode of proof, when factors have been used in multiplying?

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