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DIVISION OF FRACTIONS.

PROBLEMS.

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1. Divide 10 by 5.

Ans. 10 -5== 2. 2. Divide 6 by 3.

Ans. f = 2. 3. Divide 3 by 3.

Ans. = 1.

} 4. Divide 1 by 2.

Ans. 5. Divide 1 by 3.

Ans. 6. Divide 2 by 3.

Ans

.. 7. Divide 3 by 4.

Ans. * 8. Divide 5 by 4.

Ans. $ 11 9. Divide 3 by 2, or divide 4 into two equal parts.

Ans. 3x2 = 1 1. 10. Divide by 2, or divide into two equal parts.

Ans. +2 = $. 11. Divide by 2, or divide 4 into two equal parts.

Ans. 3x2 = . 12. Divide f by 1, or how often is contained in .

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Ans. Evidently twice. 13. Divide } by 4, or how often is contained in £=*.

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Ans. Evidently twice. 14. Divide } by , or how often is } contained in 1. Ans. = f and = *;$==*= 13. je 중 :

11. 15. Divide } by 4, or how often is contained in 1.

An8. } = ਉੱਠ and } = ਝੂਠ ; ਝੂਠ : ਡੂੰਨ = ਟੈ·
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1 ; COR. 1.-The numerator of a fraction is a dividend, the denominator a divisor, and the fraction itself the quotient.

COR. 2.—To divide a fraction by a fraction, reduce both to a common denominator and then divide the

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REM.-When we consider that the numerator of a fraction represents a dividend, and the denominator a divisor, a complex fraction is readily reduced to a simple fraction.

to a simple fraction.
31

2 x 7 .

5 REM.-As the denominator is a divisor, it must be inverted,

1. Reduce

34 to

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371 4. Reduce

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to a simple fraction.
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1001 403 2 1 1 1 5. Multiply Х

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= x x 1007 ^ 601 441^101 Tot xa = 184..

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by Х

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In changing the division to multiplication, the whole divisor must be inverted ; that is, 4 becomes the numerator and it becomes the denominator, with the sign of multiplication; then again the two denominators must be inverted; then they are all in the form of multiplication.

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1 REM.—It is evident that the above expression indicates that to to be divided by .

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35. REM.-By inverting the whole divisor, problem 3d is changed from division to multiplication,

EX A M PLES.

1. Reduce the

to a simple fraction.
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fx} = }} simple fraction.

3 3 2. Reduce

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1. A man spends of his income for board, for clothing, and has 50 dollars left, what is his income?

Ans. 600 dollars. 2. What number divided by I will give for a quotient 4 ?

Ans.

3. What number multiplied by I will give a product of 1?

Ans. 6. 4. In an orchard f of the trees bear apples, peaches,

plums, and 20 trees bear pears. How many trees in the orchard ?

Ans. 80 trees. 5. What are the numbers between 15 and 450 which have the former for their greatest common divisor, and the latter for their least common multiple ?

Ans. 30, 45, 75, 90, 150, 225. 6. What six numbers between 35 and 840 have the former for their greatest common divisor, and the latter for their least common multiple?

Ans. 70, 105, 140, 210, 280, 420.

%. A father bequeathed of his estate to one son, and the rest of his estate to another; the difference of their legacies were 1560 dollars. How much did each receive ?

Ans. The one 7800 dollars, and the other 6240 dollars.

8. A cargo is worth five times the value of the ship. What part of the cargo is B of the ship and cargo ?

Ans. 4.

REM.—2 is what part of 3? Ans. š. 3 is what part of 4? Ans. . 1 is what part of ģ. Ans. i x = = 4.

9. If A can do a piece of work in 4 days, and B can do it in 5 days, what part can each do in a day? What part of it can both do in a day? How many days will it take both to do it?

Ans. A can do 4 in a day, B 3, both , and both can do it in 2 days.

10. A and B bought a barrel of flour, for which A paid 5 dollars, and B paid 6 dollars. What part of the flour should each have?

Ans. A and B 11: 11. Three men, A, B, and C, bought 640 acres of land. A paid 4000 dollars, B paid 5000 dollars, and C 7000 dollars. How many acres should each receive?

Ans. A 160 acres, B 200 acres, and C 280 acres. 12. A man left ] of his property to his wife, to each of his two daughters, 1 to his son, and the remainder, which was 500 dollars, to his servant. What was the value of his whole estate?

Ans. 6000 dollars. 13. If 3650 is p of some number, what is of the same number?

Ans. 5256. 14. A sold of a ship for 3650 dollars, and B owns io of the ship. What is it worth at the same rate ?

Ans. 5256.

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