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2. Reduce .6, .75, .089, to similar decimals.

3. Reduce .15, .0406, .0035, .051, to similar decimals. 4. Reduce .0045, .3846, .51, .51040, to similar decimals. 5. Reduce 3.35, .345, to similar decimals.

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206. To reduce a decimal to a common fraction.

1. If 5 tenths be written as a common fraction what will be the numerator? What will be the denominator?

2. What is the numerator and what the denominator of the decimal 18 hundredths, when expressed as a common. fraction?

3. Express the value of the decimal 50 hundredths, by a common fraction in its smallest terms.

4. Express by a common fraction in its smallest terms, the following decimals: 20 hundredths. 30 hundredths. 50 hundredths. 250 thousandths. 375 thousandths.

WRITTEN EXERCISES.

1. Reduce .75 to its equivalent common fraction.

PROCESS.

.75=75%=

100

ANALYSIS.-.75 expressed as a common fraction is, which, being reduced to its smallest terms, equals .

RULE.-Omit the decimal point, supply the denominator, and reduce the fraction to its lowest terms.

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53

inator also to sevenths, the expression becomes 88, or 3,50.

Change the following to equivalent common fractions, or to

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207. To reduce a common fraction to a decimal.

1. One half of an apple is equal to how many tenths of an apple?

2. How many tenths are there in ? ?

3. How many hundredths are there in ? ? ? ? ? 4. How many hundredths are there in?? 27? 23? 5. How many hundredths are there in, or 100 hundredths divided by 2? How many in ?

6. How many hundredths are there in , or 400 hundredths divided by 5? How many in ?

7. How many thousandths are there in sandths divided by 8? How many in

89

or 5000 thou

? How many in ?

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remaining. 4 hundredths are equal to 40 thousandths, and of 40 thousandths is 5 thousandths. Hence is equal to 6 tenths+ 2 hundredths+5 thousandths, or .625.

Or we may multiply both terms of the fraction by 1000 and divide the resulting terms by 8, and obtain the decimal 625, or .625.

1000

RULE.-Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places in the quotient as there are ciphers annexed.

In many cases the division is not exact. In such instances the remainder may be expressed as a common fraction, or the sign + may be employed after the decimal to show that the result is not complete; thus:.1663, or .166+.

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ADDITION.

208. 1. What is the sum of and ?

and .7?

40

and ? .3

30

2. What is the sum of 4 and 180? 26 and 200? .12 and .20?

3. What is the sum of 10 and 1000? 10 and 188? -.005 and .043?

4. Find the sum of and 18. Of .5 and .06. .7 and .19.

5. Find the sum of .6, .31, .004. Of .5, .08 and .006.

209. PRINCIPLES.-The principles are the same as for addition of integers.

WRITTEN EXERCISES.

1. What is the sum of .36, 2.136 and 4.5004?

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all the decimals have the same number of places.

It is not usual to make the decimals similar, for if they are written so that decimals of the same order stand in the same column it is unnecessary to supply the ciphers.

RULE.-The rule is the same as for addition of integers.

What is the sum of

2. 4.15, 3.86 and .487?
3. 3.9, 4.84 and .0507?
4. .004, 5.86 and 3.05?

5. 6.843, 48.25 and 17.286?
6. .35, .046 and .00435?
7. 106, .106, 1.06 and 10.6?

8. What is the sum of $5.18, $3.09, $46. and $54.185? 9. Find the sum of $18.23, $12.08, $31.255 and $6.625. 10. Add $34.73, $206.357, $1200.18, $3816 and $137. 11. Express as decimals and add 61, 3, 5, 61 and 93. 12. A laborer earned $7.25 in one week, $7.12 in another, $9.18 in another, and $8g in another. How much did he earn during that time?

13. What is the sum of 18 thousandths, 15 millionths, 81 hundredths, 146 ten-thousandths, 834 hundred-thousandths?

14. What is the sum of 8 dollars 5 cents, 13 dollars 19 cents, 18 dollars 3 cents 8 mills, 25 dollars 37 cents 5 mills, 12ğ dollars, and of a dollar?

15. Mr. A. paid the following bills for repairs upon his premises, viz: carpenter-work, $381.45; plastering, $215.385; plumbing, $323.94; and other expenses, $181.57. How much did he pay for repairs?

16. A farmer purchased cloth for $137, boots for $85, crockery for $101, and groceries for $15:49. How much did he pay for all his purchases?

SUBTRACTION.

210. 1. From take. From .9 take .5.

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2. Find the difference between 18 and 180; 1 and 10; .19 and .08.

3. Find the difference between 100 and 1000; 10% and 1000; .007 and .005.

4. What is the difference between 2 and 180? .5 and .06? .7 and .09?.

5. What is the difference between .16 and .03? .15 and .08? .45 and .3?

211. PRINCIPLES.-The principles are the same as for the subtraction of integers.

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