mals cyphers might have been annexed to the remainder and the quotient carried to a greater deof exactness.

gree

2. It is required to divide 1302 by 101.

101)1302 000(12891.089 Ans.

NOTE 2. In this example the dividend is whole numbers, and the divisor has 3 figures in decimals ;~~~ I therefore annexed 3 cyphers to the right of the dividend before I divided; and after the dividend: was all brought down, I annexed 3 cyphers to the remainder, and continued the division, and got the decimal part of the quotient, viz. ⚫089.

3. Required to divide 263 146 by 1320.

1320)263-146(*1990 Ans.

NOTE 3.-In this example there are 3 decimal. figures in the dividend, and the divisor is whole numbers; therefore I pointed off 3 figures from the quotient, for decimals.

4. Required to divide 4567 by 333..

333)-4567(001323 Ans.

NOTE 4. In this example, there are 4 figures in decimals in the dividend, and the divisor is whole numbers; the quotient has but 2 figures; I therefore prefixed 2 cyphers to the left of the quotient, and pointed all off for decimals.

5. Divide 07912 by 111.

Ans. 71f.*

*

This mark (†) signifies that there is a remainder which is not noticed in the answer.

REDUCTION OF DECIMALS.

CASE I.

To reduce Vulgar Fractions to Decimals. RULE.-Annex cyphers to the numerator, and divide by the denominator; the quotient is the decimal sought.

NOTE. A vulgar fraction is expressed thus ; the top figure is a remainder left after division and is called the numerator; the bottom figure is a divisor used in division, and is called the denominator,

Examples.

1. Reduce to a decimal of the same value.

6)5,000

833 Ans.

2. Reduce to a decimal of the same value.

Ans. 5.

3. Reduce to a decimal of the same value.

Ans. 25.

4. Reduce to a decimal of the same value.

CASE, II.

Ans. 75.

To reduce numbers having different denominations to decimals.

RULE. Write down the several denominations under each other; beginning. with the lowest and ending with the highest; on the left of these draw a perpendicular line, and on the left of the line, place such numbers for divisors, against each denomination, as it takes of the lowest to make one of the next higher: annex cyphers to the top figures. and divide by the number standing against it on the left of the line; set the quotient (decimally) against the next denomination below; divide the next below by the number standing against it; set the quotient as before; proceed thus through all the denominations, the last quotient is the decimal sought.

Examples.

1. Reduce 16 gr. 12 pwt. to the decimal of 4 pound, Troy weight.

24/16.0000

20 12.6666+

12 0.6333+

0527 Ans.

2. Reduce 6 oz. 12 pwt. 15 grs. to the decimal of a pound, Troy weight.

24/15.000

20 12.625+ 10

12 6.6312

⚫5526 Ans.

3. Reduce 2 cwt. 3 qrs. 12 lb. 12 oz. 11 dr. to the decimal of a ton, Avoirdupois weight.

16/11.
16 12.

28/12

4 3.

20 2.

•1432+ Ans.

4. Reduce 3 qr. 3 na, to the decimal of a yard, Cloth measure.

•9375 Ans.

5. Reduce 2 miles 6 fur. 20 rds. 12 ft. 6 in. 2 bar. to the decimal of a league, Long measure. Ans. •9382+

6. Reduce 3 roods, 30 rds. 29 yds. to the decimal

of an acre, Land measure.

Ans. ⚫9434t.

7. Reduce 56 gal. 3 qts. 1 pt. to the decimal of a hhd. allowing 63 gal. to a hhd.

Ans. 9027.

8. Reduce 39 feet 1727 inches to the decimal of 4 ton of round timber. Ans. 9999t. 9. Reduce 1 pk. 2 qts. 1 pt. to the decimal of a chaldron. Ans. 0001t. 10. Reduce 12 months, 3 weeks, 6 days, 23 hours, 59 minutes, 12 seconds, to the decimal of a year. Ans. 9999+.

measure.

A

11. Reduce 2 minutes to the decimal of of a month, allowing 28 days to a month: Ans. 00004+. 12. Reduce 1 pint to the decimal of a hhd. wine Ans. 0019t 13. Reduce 1 week to the decimal of a year, allowing 13 months to a year. Ans. 01923†. 14. Reduce 1 minute to the decimal of a year, allowAns. 000001f. 15. Reduce 1 dram to the decimal of a ton, AvoirduAns. 000001†.

ing 360 days to a year.

pois weight.

CASE III.

To express the value of any decimal' in the several denominations of the integer.

RULE. Multiply the decimal by the next denomination, point off as many figures for decimals as is required by the rule in multiplication of decimals; then multiply the last decimal by the next denomination, and so on to the last; the figures on the left of the separatrix are the value of the decimal in the denominations of the integer.

Examples.

1. Required the value of -0527 of a lb. Troy weight.

Hb. 0527
12

oz. 6324

20

pwt. 12.6480

24

grs. 15:5520

Answer 12 pwt. 15 grs.

2. Required the value of 5526 of a lb. Troy weight. Ans. 6 oz. 12 pwt. 14+ grs.

3. What is the value of 1432 of a ton?

Ans. 2 cwt. 3 qr. 12 lb. 12 oz. 4t dr. 4. What is the value of 9017 of a lb. Apothecaries weight? Ans. 10 oz. 6 dr. 1 sc. 13+ grs. 5. What is the value of 9376 of a yard, Cloth measure? Ans. 3 qr. 3 na. 6. What is the value of 9436 of a league, Long measure?

Ans. 2 mi. 6 fur. 25 rds. 4 yds. 2 ft. 1f in. 7. What is the value of 9436 of an acre, Land measure? Ans. 150 rods. 8. What is the value of •9999 of a ton of round timber? Ans. 39 ft. 1721 in. 9. What is the value of 0099 of a chaldron ?

10. What is the value of lowing 28 days to a month?

Ans. 1 pk. 3 qts.. 0002 of a month, alAns. 8 min. 3 sec..

COMPOUND MULTIPLICATION. DEFINITION.-Compound Multiplication is a rule much used in business; and teaches, by having the price of one article given, to find the price of any number of the like kind.

CASE I.

When the quantity is whole numbers. RULE.-Multiply the price and quantity together the product is the answer; if there are dimes, cents and mills in the price, point off for decimals according to the rule of multiplication of decimals.

Examples.

1. How much will 1000 lbs. of butter come to at 11. cts. 5 mills per pound?

1000 lbs. x 115 $115.000 Ans.