18. Write 46 tenths.

SOLUTION.-46 tenths-18=4=4.6.

19. Write 124 hundredths.

20. Write 4986 thousandths.

154. By annexing 0 to a decimal, both terms of the fraction are really multiplied by 10, and the value of the decimal is not changed.

Thus, .5 .50; that is, ; etc.

PRINCIPLE.

1. Annexing O's to a decimal does not alter its value.

155. By prefixing 0 to a decimal, the denominator is multiplied by 10. The value of the fraction is therefore divided by 10.

Thus, 5; but .05-50; and T8 is one tenth of

PRINCIPLE.

2. Prefixing 0's to a decimal divides the decimal by 10 as many times as there are O's prefixed.

21. Change .4 to hundredths.

22. Change .56 to millionths. 23. Divide .8 by 10.

24. Divide .34 by 100.

25. Divide .49 by 1000.

26. Divide .456 by 100.

REDUCTION OF DECIMALS.

CASE I.-To reduce a decimal fraction to a common fraction.

156. 1. Reduce .8 to a common fraction.

SOLUTION..81%=1.

2. Reduce .08 to a common fraction.

SOLUTION.-.08=180=25.

Rule.-Erase the decimal point. Write the denominator, and reduce to lowest terms.

NOTE.-When the decimal point is erased, the 0's at the left of a decimal become valueless, and should be omitted. Thus, 08=8. But .08 does not equal 8.

CASE II.-To reduce a common fraction to a decimal fraction.

of 30 tenths is 7 tenths, 20 hundredths. of 20 of 3, or 4,7 tenths+5

SOLUTION. 1=10 tenths. is of 10 tenths, which is 0 tenths, with a remainder of 10 tenths; 10 tenths=100 hundredths; of 100 hundredths is 6 hundredths, with a remainder of 4 hundredths; 4 hundredths=40 thousandths; of 40 thousandths is 2 thousandths, with a remainder of 8 thousandths; 8 thousandths 80 ten-thousandths;

of 80 ten-thousandths is 5 ten-thousandths. O tenths+6 hundredths +2 thousandths+5 ten-thousandths=.0625. That is, 1.0625.

Rule.-Annex O's to the numerator. Divide this result by the denominator. Place the decimal point at the left of the quotient. If necessary, prefix ciphers to the quotient, in order that there may be as many decimal orders in the quotient as there have been O's annexed to the numerator.

15. Reduce to a decimal.

SOLUTION.-Annex O's and divide by the denominator, according to the rule. Proceed thus as far as may be desirable, and annex the sign. Thus, =.333+.

Reduce to decimals of 4 figures each:

What is a decimal fraction? Are the denominators of decimal fractions usually written? Why is it not necessary to write them? What is the decimal point? Why is it sometimes called the separatrix? Repeat the rule for reading decimals. Rule for writing decimals. What are the two principles of decimals given? How may a decimal fraction be reduced to a common fraction? How may a common fraction be reduced to a decimal fraction?

ADDITION AND SUBTRACTION OF DECIMAL

FRACTIONS.

ORAL.

158. 1. Add .6 and .9.

SOLUTION.-The sum of 6 tenths and 9 tenths is 15 tenths, equal to

1 and 5 tenths, or 1.5.

2. Add .7 and .4.

3. Add .21 and .12.

4. Add .3 and .05.

SOLUTION.- .3 .30; .30+.05=.35.

5. Add .5 and .09.

6. Add .12 and .014.

159. The principles of addition and subtraction of decimal fractions and of integers are the same, because both are decimal; that is, 10 units of any order are equal to 1

unit of the next higher order. When numbers are to be added or subtracted, figures of the same order should be written in the same column; that is, units should be written under units, tenths under tenths, hundredths under hundredths, etc. All the decimal points will, of course, be in column.

WRITTEN.

7. Add 8.5, 25.8395, 69., 4.37, and .075.

PROCESS.

8.5 25.8395

69.

4.37

.075

SOLUTION.-Write the numbers so that the decimal points shall all be in the same column. This will place figures of the same order in column.

Add as integers, writing the decimal point between the integer and the decimal fraction in the result.

107.7845

8. From 237.5 subtract 68.625.

PROCESS.

237.500 68.625

168.875

SOLUTION.-Write the numbers so that figures of the same order shall stand in the same column. Subtract as in integers, placing the decimal point on the left of the tenths in the remainder.

NOTE.-In the process, the .5 have been reduced to .500 by annexing two 0's. It is not necessary, however, to write the O's.

Rule.-Write the numbers so that figures of the same order shall stand in the same column. Add or subtract as in integers. Place the decimal point at the left of the tenths

in the result.

9. Add 83.4, 9.64, 324.5, and .8946.

10. Add .375, .0049, 6.2, 54., and 3.03.

13. From the sum of 845, 9.64, and .04, subtract the sum of 4.3 and 50.656.

160. In United States money, the dollar is the unit;

cents are hundredths, and occupy the two places on the right of the decimal point; mills are thousandths, and occupy the third decimal place. The sign of U. S. money is $.

Thus-One dollar is written

One cent is written

Ten cents are written

One mill is written

Ten dollars, thirty-seven cents and five

mills are written

(For fractional parts of a dollar, see page 95.)

$1.00 or $1. .01 or 14.

.10 or 10¢.

.001

$10.375 or $10.37.

14. Add $25.50, $8.75, $492.00, and $3.25. 15. Add $50., $125.875, $.625, and $35.00. 16. Add $310., $3.10, $49., $.10, and $.007.

17. Add $71, $34, $101, and $3.

SUGGESTION. Change the fractions to decimals, in accordance with the table, page 95. Thus, $74=$7.50; $3-$3.25; etc.

18. Add $247.50, $29.75, $84, and $9§. 19. Find difference of $100. and $75.

20. Add $1.374, $2.25, $.12 and $34.

SUGGESTION. Change the fractions of a cent to mills.

21. Add $.50, $.80, $.064, $.37, and 8.1675.

22. From $25 subtract $15.62.

23. A horse was bought for $150. and sold for $170.50. What was the gain?

24. A man bought a load of hay for $18.75, another for $13.25. He sold the two loads for $35. Did he gain or lose, and how much?

25. A house was bought for $3420.75. must it be sold to gain $1751?

For how much