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SUBTRACTION OF DECIMALS. Rule-Write down the largest of the two numbers first, then write down the smallest under it, observing to place the separatrix under each other; then subtract exactly as in Simple Subtraction.

Examples.
234•101
91.91

141.1 7.00044 145.164321 81•11234 98.3 5.19864

88.936679

MULTIPLICATION OF DECIMALS.

RULE.Multiply exactly as in whole numbers, and from the right of the product point off as many figures for decimals as are equal to the decimal figures in the multiplicand and multiplier, counted together; If at any time there are not so many figures in the product, as this rule requires, supply the defect by prefixing cyphers, to the left of the products.

Eramples
11.23

•1213
•1321

1

117.8

8984 7861 1123 1123

1213 2426 3639 1213

1322.894 pro.

•01602373 pro.

Note. In the first example there being three decimal figures in the two factors, three figures are pointed off for decimals in the product; in the second example there are eight decimal figures in both factors, and the product consists only of seven figures, therefore I prefixed one cypher and pointed all off for decimals.

No.
1.
2.
3.

Multiplic.

1.23 10.4

123 ·002

ХХХХ

Multiplier.
by 17.8
by 123
by 1:45
by .661

Product.
21.894
1279.2
178.35
·001322

Practical Questions. 1. How much is the product of 29.5 multiplied by .96 ?

Ans. 28o32. 2. How much will 1000 pounds of butter come to, at 114 cents per pound?

Ans. $115. 3. How much will 64.5 bushels of corn come to at $112 cts

Ans. $72.24 cts.

DIVISION OF DECIMALS. RULE.-Divide exactly as in whole numbers, and from the right hand of the quotient point off as many figures for decimals, as the decimal figures in the dividend exceed the decimal figures in the divisor; if there are not so many figures in the quotient as this rule requires, the defect must be supplied by prefixing cyphers to the left of the quotient; if there are more decimal figures in the divisor than in the dividend, place as many cyphers to the right of the dividend, as will make them equal, and the quotient is whole numbers till the dividend is all brought down; if a remainder still remains annex cyphers. and continue the division and the quotient thence arising will be decimals.

Examples.
1. It is required to clivide 34-21 by 12.1.

12.1134-21(2-8 Ans.

242

2001
968

33 rem.

NOTE.There being one more decimat figure in the dividend, than in the divisor, one figure is pointed off from the right of the quotient fox decir

mals ; cyphers might have been annexed to the remainder

and the quotient carried to a greater degrec

of exactness.
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 ; in 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(.1999 Ans. NOTE 3.- In this example there are 3 decimal figures in the dividend, and the divisor is whole numbers i therefore I pointed off 3 figures from the quotient, for decimals. 4. Required to divide .4567 by 333.

333)-4567(*0013311 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. .714.*
6. Divide 00444 by 222. Ans. .00002.
7. Divide .9023 by •11, Ans 8.2021:
8. Divide 15.735 by 12. Ans. 1.3111

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* This mark (t) signifies that there is a remainder which is mot noticed in the answer.

REDUCTION OF DECIMALS.

CASE I. To reduce Vulgar Fractions to Decimale. 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

ܪ

Ans. .5.

*8337 Ans.
2. Reduce to a decimal of the same value,
3. Reduce I to a decimal of the same value.

Ans. •25.
4. Reduce to a decimal of the same value.

Ans. 75.
CASE, II.
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 be

of quotient as before ; proceed thus through all the denominations, the last quotient is the decimal

sought.

D 2

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

24/16*0000
2012-66667
12 0.63337

ch

5

0527+ Ans. 2. Reduce 6 oz. 12 pwt. 15 grs. to the decimal of a pound, Troy weight.

24|15.000

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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
2012

•1432t 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. .93827 6. Reduce 3 roods, 30 rds. 29 yds. to the decimal of an acre, Land measure.

Ans. .94347 7. Reduce 56 gal. 3 qts. 1 pt. to the decimal of a hhd. allowing 63 gal. to a hhd. Ans. •9027.

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