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Troy Weight.

1. In 13lb. how many grains?

2. In 22lb. 6oz. 10pwt. how many grains?

1. In 74880grs. how many pounds?

2. In 129540gr. how many pounds? Avoirdupois Weight.

1. In 4 tons how many ounces?

2. In 7cwt. Sqr. how many drams?

3. In 1961b. how many "Dunces?

1. In 143360oz. how many pounds?

2. In 222 208 drams, how many cwt.?

3. In $136oz. how many pounds? Long Measure.

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1. In 143 yards how many

rods?

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Circular Measure.

1. In 6 signs how many minutes?

2. In 47° 28′ 15′′ how many seconds?

1. How many signs in 10800 minutes?

2. In 170595" how many degrees?

REDUCTION OF DECIMALS.

141. 1. Reduce 4 ounces to the decimal of a pound. 4oz. lb. As 1 lb. is 16)4.0(.25 16 oz. 4 oz. are of a pound,

32

and

80

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80

reduced

decimal,

(130) is..25 of a
pound.

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142. 1. How many ounces are 0.25 of a pound?

.25

16

150

25

oz. 4:00

Pounds are reduced to ounces by multiplication, (139) and .25 lb. multiplied by 16, the ounces in a pound, the product (122) is 4 ounces.

2. How many inches are 0.0833+-of a yd

3

of

0.0833

0.2499

12 2.9988

=0.25 ft. and 0.25
ft. are reduced to
yards by dividing
them by 3, (140).
The sign denotes
that more decimal

0.0833+ figures may be had
Ans. by adding more ci-
phers.

3. Reduce 8 hours 24 min. to the decimal of a day.

then 8h. 24m.-8.4h.

Yards are reduced to feet

by multiplying them by 3, and feet to inches by multiplying by 12, (139.) Here it will be seen, by comparing this with the example at the left hand, that there is a loss of 12 ten thousandths of an inch, on account of the decimal being incomplete.

3. In 0.35 of a day, how many hours and minutes?

0.35

24

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140

70

24)8.40

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0.35d.

0.35 of a day.

h. 8.40

60

m. 24.00

To reduce days to hours, we multiply by 24, and the product is 8.4 h. and .4 multiplied by 60 gives 24 minutes; then 0.35 d. 8 b. 24.min.

The above methods of changing decimals to integers of a different de

pemination, and the reverse, are salled the Reduction of Decimals

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143. To reduce compound numbers to decimals of the highesi denomination.

RULE.-Divide the lowest denomination (annexing one or more cipher, as shall be found necessary) by the number which it takes of that to make one of the next higher denomination,(126) and write the quotient as a decimal of the higher; divide this higher denomination by the number which it takes to make one still higher, and so continue to do till it is brought to the decimal required.

47

144. To find the value of a decimal in integers of a lower denomination.

RULE.-Multiply the decimal by that number which it takes of the next lower denomination to make one of the denomination in which the decimal is given, and point off as in the multiplication of decimals.(122) Multiply the decimal part of the product by the number it takes of the next lower denomination to make one of that, and so on; the several numbers at the left of the decimals will be the

answer.

QUESTIONS FOR PRACTICE.

1. Reduce 2 yards, 2 feet, 1. Reduce 0.5303 rod to and 9 inches to the decimal | yards, feet and inches.

of a rod.

12)9.00(0.75 ft.

3)2.75(0.9166 yd.

5.5)2.9166(0.5303 rd. Ans. 2. Reduce 10s. 3d. to the decimal of a pound. 3d. s. 0.25s. and 10.25s.19.251.=0.51251.

3. Reduce 3qrs. to the decimal of a shilling.

4. Reduce 12s. 9d. 3qr. to

the decimal of a pound.

0.5303X5.5=2.91665yd. 0.91665X3=2.74995ft. 0.74995X12-8.9994in or 2yds. 2ft. 9in. nearly, Ans.

2. In 0.51251. how many shillings and pence?

3. What is the value o 0.0625s.?

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145. In computing interest, it is common to consider 30 days one month, and 12 months a year.

Reduce 8 months 21 days to the decimal of a year. 21d. m. 0.7m. and 8m. 21-7-0.725yr. Ans.

Reduce 0.725 year to

months and days.

$

0.725X12 8.7mo. and 0.7X30-21d.

3. ADDITION.

146. 1. A person gave £2 17s. and 8d. for a load of hay, £1 5s. 3d. for 5 bushels of wheat, and 10s. 4d. for a load of wood; what did the whole cost?

l. s. d.

2 17 8 1 53 10 4

4 13 3 Ans.

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As we may very evidently add pence to pence, shillings to shillings, &c. we write down the numbers so that pence shall stand under pence, shillings under shillings, and so We then add the pence, and find their sum to be 15d. but as 12d. Is. 15=1s. 3d. We therefore write down 3d. under the column of pence, and reserve the Is. to be joined with the shillings. We now add together the shillings, which, with the 1s. reserved, amount to 33s. 4 13 3 proof. =£1 13s. we therefore write 13s. under the column of shillings, and reserve the £1 to be joined with the pounds. Lastly, we add the pounds, and joining the £1 reserved, write the amount, £4, under the column of pounds; and thus we find the whole cost to be £4 13s. Bd. The above process is called Compound Addition.

COMPOUND ADDITION

147. Is the uniting together of several compound numbers into one sum.(48)

RULE

148. Place the numbers to be added so that those of the same denomination may stand directly under each other.

Add the numbers of the lowest denomination, and carry for that number which it takes of that denomination to make 1 of the next higher, writing the excess, if any, at the foot of the column. Proceed with each denomination in the same way, till you arrive at the last, whose amount is to be set down as in Simple Addition.

PROOF. The same as in Simple Addition.

QUESTIONS FOR PRACTICE.

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