RULE. Write the decimals so that the points are in the same vertical line.

Add as in whole numbers.

Place the point in the sum in the same vertical line with the points in the decimals.

9. Change to decimals and add: 3, †, 3, 12, 64, 13.

10. 3.13, 2.121, 37, 4.015, 3.17.

32. To subtract decimals.

RULE. Write the decimals so that the points are in the same vertical line.

Subtract as in whole numbers.

Place the point in the remainder in the same vertical line with the points in the decimals.

ILLUSTRATIVE EXAMPLE.

Subtract 2.12 from 14.3.

14.30

2.12 12.18

Adding ciphers to a decimal does not change its value.

33. To multiply decimals.

RULE. Multiply as in whole numbers.

Point off so that the decimal places in the product are equal to the sum of the decimal places in the multiplier and multiplicand.

34.

DIVISION OF DECIMALS.

DIVISION is the reverse of multiplication.

Therefore,

processes in division should be the reverse of those in multiplication. As we added the decimal places in multiplication to get the number of places to point off in the product, so we subtract in division to get the number of places to point off in the quotient.

Point off as many places in the quotient as the decimal places in the dividend exceed those in the divisor, or add as many ciphers to the quotient as the decimal places in the divisor exceed those in the dividend.

NOTE 1. - In practice it is not necessary to carry the division farther than the 4th decimal place. If the dividend does not contain figures enough to give this number of places, and the last figure in the dividend gives a remainder in dividing, annex ciphers to the dividend so as to continue the division, and consider the quotient figures arising from the use of these ciphers as so many decimal places in the quotient.

NOTE 2. If the places in the dividend are less than those in the divisor annex enough ciphers to the dividend to make them equal. The quotient arising from the use of all these places will be a whole number. If there be a remainder now annex ciphers so as to continue the division. The quotient arising from the use of these ciphers will be decimal.

NOTE 3. - When the dividend is less than the divisor annex ciphers to the dividend in order to divide. The quotient in this case will be entirely decimal.

NOTE 4.

When the quotient contains less figures than the rule requires to be pointed off make up the lack by prefixing ciphers.

MISCELLANEOUS PROBLEMS IN FRACTIONS AND DECIMALS. 35. 1. Sold 4 pieces of carpet. The first contained 31 yds., the second 37 yds., the third 49% yds., and the fourth 44 yds. How many yards were sold in all?

2. A grocer packed in a box for shipment 15ğ lbs. sugar, 19 lbs. coffee, 2 lbs. tea, 173 lbs. ham, and 25 Ibs. bacon. What was the total weight of the contents of the box?

3. I bought 4 bbls. of sugar, the net weight of each being respectively 275ğ lbs., 285 lbs., 291 lbs., and 2697 lbs. What was the total net weight?

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4. A man inherited of an estate in his own right, and bought the shares of two fellow-legatees who had inherited