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5. Divide 5 by .

6. Divide 12 by 2.

7. Divide 16 by .

Ans. 1111.

8. Divide 100 by 17.

9. I have 50 square yards of cloth; how many yards, of a yard wide, will be sufficient to line it? Ans. 83 yards.

10. A. Poor can walk 37 miles in 60 minutes; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance? Ans. 73 minutes.

6)17

2,

161. To divide a mixed number by a whole number. Ans. 248.

Ex. 1. Divide 17 by 6.

Having divided the whole number as in simple division, we have a remainder of 5g, which we reduce to an improper fraction, and divide it by the divisor, as in Art. 159. Annexing this That is, we

OPERATION.

43

58 = 2; 8 x 6 2+18=248.

result to the quotient 2, we obtain 248 for the answer.

Divide the integral part of the mixed number; and the remainder, reduced if necessary to a simple fraction, divide as is in Art. 159.

EXAMPLES FOR PRACTICE.

by 7.
by 8.

2. Divide 17
3. Divide 18
4. Divide 271

5. Divide 31

by 12.

6. Divide 78
7. Divide 1891 by 4.

8. Divide 107 by 3.

Ans. 25.
Ans. 16.
Ans. 32.

43 48

Ans. 218.
Ans. 217.

Ans. 3.

Ans. 2.

Ans. 617.

Ans. 4713.

Ans. 35.

Ans. $2.

9. Divide $143 among 7 men.

Ans. $133.

10. Divide $ 1067 among 8 boys.

Ans. $0.3413.

11. What is the value of 1⁄2 of a dollar? 12. Divide $1077 among 4 boys and 3 girls, and give each of the girls twice as much as each of the boys?

Ans. Boy's share, $ 104; Girl's share, 21. of a ton of copperas, what quan Ans. 1cwt.

by 9.

by 11.

tity will $1 purchase?

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13. If $14 will purchase

161. How do you divide a mixed number by a whole number?

OPERATION.

48 25

5 5

162. To divide a whole number by a mixed number. Ans. 51.

Ex. 1. Divide 25 by 43.

23) 125 (518

115

10

Reduce the divisor and dividend to the same fractional parts as are denoted by the denominator of the fraction in the divisor, and then divide as in whole numbers.

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We first reduce the divisor and dividend to fifths, and then divide as in whole numbers.

2. Divide 36 by 97.
3. Divide 97 by 1311.

4. Divide 113 by 214.

63 =

The divisor and dividend were both multiplied by the same number, 5; therefore their relation to each other is the same as before, and the quotient is not changed. (Art. 115, Note.) Hence,

Ans. 3. Ans. 6184. Ans. 5. Ans. 23

5. Divide 342 by 14T

6. There is a board 19 feet in length, which I wish to saw into pieces 23 feet long; what will be the number of pieces?

Ans. 714 pieces.

EXAMPLES FOR PRACTICE.

163. To divide a fraction by a fraction. Ex. 1. Divide 7 by .

FIRST OPERATION.

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63

63

8 X4 32

= =

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}÷1=}×}=}}=1}}•

Since 1 is contained in, times, is contained in 9 times times, or times; and is contained in 7, of times, which is , or 1, times.

Ans. 13.

SECOND OPERATION.

That is, we have multiplied the denominator of the dividend by the number denoting the numerator of the divisor, and the numerator of the dividend by the number denoting the denominator of the divisor, hence, for convenience, as in the second operation, we can simply invert the terms of the divisor and proceed as in Art. 156.

162. How do you divide a whole by a mixed number? How does it appear that this process does not alter the quotient?-163. How do you divide a fraction by a fraction? Give the reason why this process divides the fraction of the dividend.

RULE. Invert the divisor, and then proceed as in multiplication of fractions.

NOTE 1.-Factors common to numerator and denominator should be canceled.

NOTE 2. When the divisor and dividend have a common denominator their denominations cancel each other, and the division may be performed by simply dividing the numerator of the dividend by that of the divisor.

EXAMPLES FOR PRACTICE.

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72=41; 34 = 24. 2 X 24=34 = 238.

EXAMPLES FOR PRACTICE.

2. Divide 78 by 41. 3. Divide 3 by 73. 4. Divide 114 by 5%. 5. Divide 4 by 17.

164. To divide a mixed number by a mixed number. Reduce them to improper fractions, and proceed as in Art. 163. Ex. 1. Divide 7 by 33.

Ans. 288

OPERATION.

6. Divide 116 by 144.

7. Divide 814 by 91.

8. Divide of 5 of 7 by of 3%.

Ans. 148.
Ans. 3.

Ans..

Ans. 23.

Ans. 6.

Ans. 4.

Ans. 6.

Ans. 24. Ans. 183. Ans. T

Ans. 33.

Ans. 138.
Ans. 75.

Ans. 2

Ans., 25.

Ans. 833.

Ans. 813
Ans. 11.

163 The rule for dividing one fraction by another? How may fractions be divided when they have a common denominator? Does this process differ in principle from the other? 164. How do you divide a mixed number by a mixed number?

Ex. 1. Reduce

COMPLEX FRACTIONS.

165. To reduce complex to simple fractions.

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fractions. (Art. 163.)

Ex. 2. Reduce

Ex. 3. Reduce

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OPERATION.

= { × 3 = 42 = 17 ·

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4. Reduce

6. Reduce

to a simple fraction.

8

44

Ans.

Since the numerator of a fraction is the dividend, and the denominator the divisor (Art. 132), we simply divide the numerator, , by the denominator, , as in division of

12

OPERATION.

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to a simple fraction.

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RULE. · Reduce the terms of the complex fraction, if necessary, to the form of a simple fraction. Then divide the numerator of the complex fraction by its denominator.

Ans. 17.

We reduce the numerator, 8, and the denominator, 4, to improper fractions, and then proceed as in Ex. 1.

Ans. 14.

=

NOTE. Another method is to multiply both terms of the complex fraction by a common multiple of their denominators.

We reduce the denomi

Inator, of, to a simple fraction, and then proceed as before.

91

5. Reduce to a simple fraction.

14

EXAMPLES FOR PRACTICE.

to a whole number.

to a simple fraction.

Ans. 28.

Ans. g.

Ans. 1.

165. The rule for reducing complex to simple fractions? How does this process differ from division of fractions?

1

7. Reduce

8. Change

9. Change

11

82

}

93

10. Reduce

121

11. If 7 is the denominator of the following fraction,

is its value when reduced to a simple fraction?

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81

634

to a simple fraction.

62

7. Divide

12. If is the numerator of the following fraction, its value when reduced to a simple

to a simple fraction.

7

2. Add and together.

iz

to a mixed number.

to a simple fraction.

44

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166. Complex fractions, after being reduced to simple ones, may be added, subtracted, multiplied, and divided, like them.

EXAMPLES FOR PRACTICE.

12

take

31 5

take

together.

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84/ 5. Multiply of by 4 of

63

6. Multiply

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61

by 2

of 12 by

Ans. T

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16

Ans.

of 83.

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166. How do you add, subtract, multiply, and divide complex fractions?

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