# DIVIDING FRACTIONS MADE EASY -LUCID EXPLANATION OF FRACTION PROBLEMS OF DIVISION

Fractions before dividing Fractions
if you have not already done so.

There we studied about half, quarter, three fourth with examples and exercises.

There we studied about concept of fraction in general with examples and exercises.

The knowledge of

Equivalent Fractions

and

Conversion of Improper to Mixed and Mixed to Improper Fractions

is also used here.

Learn/Teach
Fractions through Fun Games.
For details, see near

Here, we explain division of fractions, in a lucid way with solved examples and problems for practice with answers.

## Division of Fractions

In order to divide a fraction (dividend fraction) by another fraction (divisor fraction), we multiply the dividend fraction by the reciprocal of the divisor fraction.

Thus dividing is nothing but multiplying with reciprocal.

### Solved Example 1 of dividing Fractions

Simplify

1. 7⁄8 ÷ 9
2. 12⁄7 ÷ 8
3. 3  79 ÷ 5

Solution :

(i) 7⁄8 ÷ 9 = 7⁄8 x 1⁄9 (since divding is mutiplying with reciprocal)
= (7 x 1)⁄(8 x 9) = 7⁄72. Ans.

(ii) 12⁄7 ÷ 8 = 12⁄7 x 1⁄8 = 123⁄7 x 1⁄82 = (3 x 1)⁄(7 x 2) = 3⁄14. Ans.

(iii) 3  79 ÷ 5 = (3 x 9 + 7)⁄9 ÷ 5 = 34⁄9 x 1⁄5 = (34 x 1)⁄(9 x 5) = 34⁄45. Ans.

### Solved Example 2 of dividing Fractions

Simplify

1. 2 ÷ 1⁄3
2. 7 ÷ 4⁄5
3. 12 ÷ 2  38

Solution :

(i) 2 ÷ 1⁄3 = 2 x 3⁄1 = 2 x 3 = 6. Ans.

(ii) 7 ÷ 4⁄5 = 7 x 5⁄4 = ( 7 x 5)⁄4 = 35⁄4. Ans.

(iii) 12 ÷ 2  38 = 12 ÷ ( 2 x 8 + 3)⁄8 = 12 ÷ 19⁄8
= 12 x 8⁄19 = (12 x 8)⁄19 = 96⁄19 = 5  119. Ans.

### Solved Example 3 of dividing Fractions

Simplify

1. 3⁄5 ÷ 4⁄7
2. 9⁄7 ÷ 3⁄2
3. 1  23 ÷ 3  45

Solution :

(i) 3⁄5 ÷ 4⁄7 = 3⁄5 x 7⁄4 = (3 x 7)⁄(5 x 4) = 21⁄20 = 1  120 Ans.

(ii) 9⁄7 ÷ 3⁄2 = 9⁄7 x 2⁄3 = 93⁄7 x 2⁄31 = (3 x 2)⁄(7 x 1) = 6⁄7. Ans.

(iii) 1  23 ÷ 3  45 = ( 1 x 3 + 2)⁄3 ÷ ( 3 x 5 + 4)⁄5 = 5⁄3 ÷ 19⁄5
= 5⁄3 x 5⁄19 = (5 x 5)⁄(3 x 19) = 25⁄57. Ans.

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## Word Problems

For Application of various topics of Fractions including dividing Fractions to Word Problems go to

Fraction Word problems.

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### Exercise on dividing Fractions

1. Simplify
1. 1⁄2 ÷ 3
2. 3⁄4 ÷ 5
3. 4  37 ÷ 2
2. Simplify
1. 4 ÷ 1⁄9
2. 5 ÷ 8⁄11
3. 9 ÷ 3  89
3. Simplify
1. 2⁄5 ÷ 6⁄11
2. 4⁄9 ÷ 9⁄13
3. 3  78 ÷ 4  59
For Answers see at the bottom of the page.

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### Answers to Exercise on dividing Fractions

Answers to problems on dividing Fractions :

1.
1. 1⁄6
2. 3⁄20
3. 2  314
1. 36
2. 6  78
3. 2  1135
1. 11⁄15
2. 52⁄81
3. 279⁄328

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