2. SUBTRACTION OF COMPOUND NUMBERS.

132. Subtraction of Compound Numbers is the process of finding the difference between two similar compound numbers.

WRITTEN PROBLEMS.

(1.) PROCESS. From 63 lb. 4 oz. 18 dwt. 13 gr. Take 27" 6" 4 " 16"

35 lb. 10 oz. 13 dwt. 21 gr.

-

Explanation. We write the numbers as in addition of compound numbers, and begin to subtract at the lowest denomination. We cannot take 16 gr. from 13 gr.; we therefore take 1 dwt., equal to 24 gr., which added to 13 gr. equals 37 gr.; 16 gr. from 37 gr. leaves 21 gr.; 4 dwt. from 17 dwt. leaves 13 dwt. We cannot take 6 oz. from 4 oz.; we therefore take 1 lb., equal to 12 oz., which added to 4 oz. equals 16 oz.; 6 oz. from 16 oz. leaves 10 oz.; 27 ib. from 62 lb. leaves 35 lb.

NOTE.-Let the pupil derive the rule.

10. From a barrel containing 31 gal. 2 qt. there leaked out 6 gal. 3 qt. 1 pt.: how much remained?

Ans. 24 gal. 2 qt. 1 pt.

11. A farmer had 126 bu. 3 pk. of seed-wheat, and sold 111 bu. 2 pk. 5 qt. 1 pt.: how much remained?

Ans. 15 bu. 2 qt. 1 pt.

12. A pile of wood contained 7 cd.; a teamster hauled 4 cd. 6 cu. ft.: how much remained?

away

Ans. 2 cd. 122 cu. ft.

13. How old was a man who was born Jan. 3, 1832, and died July 1, 1877? Ans. 45 yr. 5 mo. 28 d. 14. A lady was born Nov. 22, 1837: how old was she Sept. 2, 1876? Ans. 38 yr. 9 mo. 10 d. 15. A girl was born Jan. 13, 1862: how old was she Sept. 2, 1877? Ans. 15 yr. 7 mo. 19 d. 16. What is the time from 15 min. past 4 P. M. to 3 min. before 10 P. M. Ans. 5 hr. 42 min. 17. A note was dated Jan. 15, 1877, and was to be paid Aug. 10, 1877: how long from the date of it to the time it was paid? Ans. 6 mo. 25 d.

3. MULTIPLICATION OF COMPOUND NUMBERS.

133. Multiplication of Compound Numbers is the process of finding the product of two numbers, one of which is compound.

WRITTEN PROBLEMS.

1. Multiply 12 £ 6 s. 9 d. by 7.

PROCESS.

12 £ 6 s. 9 d.

Explanation.-7 times 9 d. are 63 d., or 5 s. 3 d.; 7 times 6 s. are 42 s.; 42 s. and 5 s. are 47 s., or 2 £ 7 times 12 £ are 84 £; 84 £ and 2 £ are 86 £. 86 £ 7s. 3 d. Hence, 12 £ 6 s. 9 d. multiplied by 7 equals 86 £

7

7 8.

7 s. 3 d.

NOTE. Let the pupil derive the rule.

8. Multiply 4 gal. 3 qt. 1 pt. by 20. Ans. 97 gal. 2 qt. 9. If a farmer can raise 16 bu. 3 pk. 4 qt. of wheat on an acre, how much can he raise on 40 acres?

Ans. 675 bu.

10. If a horse can haul 17 cwt. 3 qr. 15 lb. 4 oz. of coal in a load, how much can he haul in 16 loads?

Ans. 14 T. 6 cwt. 1 qr. 19 lb.

4. DIVISION OF COMPOUND NUMBERS.

134. Division of Compound Numbers is the process of dividing one number by another, the dividend being compound.

WRITTEN PROBLEMS.

1. Divide 40 bu. 3 pk. 5 qt. by 7.

PROCESS.

7)40 bu. 3 pk. 5 qt. 5 bù. 3 pk. 3 qt.

of 21 qt. is 3 qt.

Explanation. of 40 bu. is 5 bu., and 5 bu., or 20 pk., remaining. 20 pk. and 3 pk. are 23 pk.; of 23 pk. is 3 pk., and 2 pk., or 16 qt., remaining; 16 qt. and 5 qt. are 21 qt. ;

NOTE.-Let the pupil derive a rule.

8. If 8 hens weigh 42 lb., how much does each weigh? Ans. 5 lb. 4 oz.

9. If 12 bags contain 31 bu. 2 pk. of oats, how much does 1 contain? Ans. 2 bu. 2 pk. 4 qt.

NOTE. When both divisor and dividend are concrete numbers, reduce both to the lowest denomination in either, and divide as in simple division.

10. Divide 40 £ 4 s. by 2 £ 10 s. 3 d.

11. Divide 78 lb. 12 oz. avoirdupois by 3 lb. 15 oz.

Ans. 20.

12. A man travels 410 mi. 6 fur. 10 rd. by travelling 16 mi. 3 fur. 18 rd. a day: how many days does he travel? Ans. 25.

13. How many loads of coal, each weighing 1 T. 3 cwt. 27 lb., will weigh 46 T. 10 cwt. 80 lb. ? Ans. 40.

14. A number of boys gather 10 bu. 3 pk. 1 qt. of chestnuts; they divide them equally, and each receives 3 pk. 4 qt. 14 pt.: how many boys were there? Ans. 12.

CHAPTER VII.

PERCENTAGE.

SECTION I.

DEFINITIONS AND PRINCIPLES.

135. Percentage is the name applied to computations in which 100 is the unit or measure.

136. Per cent. is an abbreviation of the Latin phrase per centum, meaning by the hundred.

$5? $10?

3. How many hundredths of $100 are $3?

NOTE.- of any number is 1 per cent. of that number; 1 is

2 per cent. of it; 18 is 3 per cent. of it;

and so on.

is 15 per cent. of it,

4. How many hundredths of a number is 5 per cent. of it? 8 per cent.? 10 per cent.? 20 per cent.?

100 per cent.?

5. How many hundredths of a number is 15 per cent. of it? 75 per cent.? 120 per cent.? 6. What per cent. of a number is 18

of it?

180 of it?

7. What per cent. of a number is .14 of it? .27 of it? .12 of it? 1.19 of it?

Per cent. is usually written %; thus, 25 per cent. is written 25%.

8. How many hundredths is 5%? 15%? 20% ? 40%? 75%? 61%? 121%? 135%?