SUPPLEMENT TO REDUCTION OF WHOLE NUMBERS. Art. 120.-1. How many dollars in £480 188.?

2. In £332 16s. 8d. how many ninepences?

Ans. $1603.

Ans. 8875 and 5d.

3. How many times will a regular clock strike in 400 years? Ans. 22776000.

4. A man sold four trees standing in the forest, measuring as follows: 6 tons, 5 tons, 4 tons, 3 tons, at 12 cts. per foot. What was their value? Ans. $92.50.

5. A man buys 20 tons of hay, at 45 cts. per cwt. He pays a man 62 cts. a day for himself, and 50 cts. for his team. It takes him 6 days to cart it. How much does the hay cost him? Ans. $186.75. take to cover a wide, and what will it Ans. {$65.34 cost. 990 plank.

6. How many plank one foot wide will it bridge 60 rods in length, and 2 rods cost, at 20 cts. per hundred feet?

7. If a boy be paid for wheeling a bushel of apples over said bridge 1 mill for every revolution of the wheel, which is 5 feet in circumference, how much does he receive?

Ans. 19 cts. 8 m.

8. What will 2 tons of molasses amount to, at 6 pint?

cents a

Ans. $252.

9. A Vermonter, being in Boston, 80 miles from home, sold his dog and returned. At 6 o'clock the following night, the dog left his new master, and at 6 o'clock the next morning stood at the door of his former master. How many steps did he take of 8 inches each?

10. What will the plastering of a room, 15 feet square, the walls 9 feet high, amount to at 23 cents a square yard, deducting for 2 doors, 7 feet by 3, and 2 windows, 5 feet by 3? Ans. $17.71. 11. How much time would a person lose in 20 years, by lying in bed half an hour later every day than he ought? Ans. 152 days, 4 hours, 30 minutes. 12. How many cords of wood would a man draw in 6 weeks, drawing 4 loads a day, and 64 cord feet at a load?

Ans. 117 cords. 13. A merchant failing in trade, owes A. £15 78. 9d.; B. £69 11s. 6d.; C. £102 16s. 11d.; D. £41 19s. 10d.;

E. £139 17s. 5d. His whole estate is valued at £300. How much does he owe more than he is worth?

Ans. £69 13s. 5d.

14. How many shingles will cover the roof of a factory 100 feet in length, one side of the roof being 40 feet in width, if 4 shingles in width cover 2 feet in length, and 2 courses make a foot? Ans. 32,000. 15. How many boxes, each 12 lbs., can be filled from a hogshead of sugar containing 74 cwt.? 16. In 46 bales of cloth, each containing 24 pieces, and each piece 42 ells Flemish, how many yards?

Ans. 70.

Ans. 34,776 yards. 17. The sun travels through 6 signs of the zodiac in half a year. How many degrees, minutes, and seconds?

Ans. 180 deg., 10,800 m., 648,000 sec. 18. How many English crowns, at 6s. 8d. each, in 10 English guineas, at 288. each, and 24 pistoles, at 228. each ?

Ans. 121c. 1s. 4d.

19. The forward wheels of a wagon are 14 feet in circumference, and the hind wheels 153 feet. How many more times will the forward wheels turn round than the hind wheels, in running from Concord to Boston, the distance being 60 miles? Ans. 1734, rejecting fractions.

REDUCTION OF FRACTIONS.

288

Art. 121.-1. Reduce of a pound to the fraction of a penny.

We have seen that integers of a higher denomination are brought into integers of lower, by multiplication, (see Art. 117;) and also that fractions are multiplied either by multiplying the numerator, or dividing the denominator. (Šee Art. 67.) Pounds are reduced to shillings by multiplying by 20, and shillings to pence by multiplying by 12. Therefore, to reduce of a pound to the fraction of a penny, multiply the fraction by 20 and 12, thus:

238×20×12=210=5 Ans.

Or thus:

6 24 288 20 5
12

65= Ans.

As the numerator of the fraction is to be multiplied, place it with its multipliers on the right of the line, and 288, the divisor, on the left. Cross 288 and 12, and write 24 in the place of the larger number; 4 is contained in 20 five times, and in 24 six times. The answer, then, is 5 divided by 6, or , in the lowest terms of the fraction.

OBS.-It will be seen, that the only difference between reducing 1 pound to pence, and of a pound, is, that in the latter case the multiplicand is a number divided; consequently, having multiplied the numerator as we should a whole number, we divide the product by the denominator. To divide the product is the same as to divide the multiplicand.

Art. 122. To change fractions of a higher denomination into fractions of a lower denomination, we have the following

RULE.

Multiply the numerator of the fraction, or divide the denominator by all the denominations between it and that denomination into which it is to be reduced, including the lower denomination.

EXAMPLES.

1. Reduce of a pound to the fraction of a penny.

Ans. .

2. Reduce 336 of a pound to the fraction of a farthing.

Ans. .

3. What part of a pound is 4 cwt.?

Ans. .

4. Reduce of a yard to the fraction of a nail. Ans. }. 5. Reduce 1920 of a pound to the fraction of a farthing.

Art. 123. It has been shown (see Art. 117) that Reduc

Operation.

1920 20

212
A

tion Ascending is the reverse of Reduction Descending, and also, (Art. 68,) that a fraction is divided, either by dividing its numerator or multiplying its denominator. Farthings are reduced to pence by dividing by 4, and pence to shillings by dividing by 12; shillings to pounds by dividing by 20. ThereforeTo reduce of a farthing to the fraction of a pound, divide the fraction by 4, 12, and 20.

2|1=Ans.

1. What part of a pound is of a farthing?

Art. 124. To change fractions of lower, into fractions of higher denominations, we have, then, this

RULE.

Multiply the denominator of the fraction by all the denominations between it and that into which it is to be reduced, and write the product under the numerator of the given fraction.

2. Reduce of a penny to the fraction of a pound.

As the denominator of the fraction is to be multiplied for a divisor, place it with its multipliers on the left of the line. Then, by cancelling, 5 on the right of the line, and 20 on the left, equal therefore cross 5 and 20, and write 4 on the left. Multiply the remaining numbers on the left together, for a divisor. We have, then, the answer in the lowest terms of the fraction,.

3. Reduce of a penny to the fraction of a pound.

Ans. £0.

4. Reduce of a farthing to the fraction of a pound.

Ans. 3360°

5. What part of a cwt. is of a pound?
6. Reduce of a nail to the fraction of a yard.

Ans. 14.

Ans. 504

QUESTION.-1. What would be your multipliers in reducing the fraction of a pound

to the fraction of a penny?

REDUCTION ASCENDING AND DESCENDING.

EXAMPLES.

Art. 125.-1. Reduce 1440 Art. 126.-2. Reduce of a pound to the fraction of a