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

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

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

Also study Fractions Made Easy.

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
the bottom of this page.

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  ⁷⁄₉ ÷ 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  ⁷⁄₉ ÷ 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  ³⁄₈

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  ³⁄₈ = 12 ÷ ( 2 x 8 + 3)⁄8 = 12 ÷ 19⁄8
= 12 x 8⁄19 = (12 x 8)⁄19 = 96⁄19 = 5  ¹⁄₁₉. Ans.

Solved Example 3 of dividing Fractions

Simplify

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

Solution :

(i) 3⁄5 ÷ 4⁄7 = 3⁄5 x 7⁄4 = (3 x 7)⁄(5 x 4) = 21⁄20 = 1  ¹⁄₂₀ 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  ²⁄₃ ÷ 3  ⁴⁄₅ = ( 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.

Word Problems

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

Fraction Word problems.

Learning/Teaching Math Can Be Fun

Here is a collection of kids math
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This Collection of Fun Math Games
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For more information or to have
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click HERE.

Exercise on dividing Fractions

1. Simplify
   
   1. 1⁄2 ÷ 3
   2. 3⁄4 ÷ 5
   3. 4  ³⁄₇ ÷ 2
2. Simplify
   
   1. 4 ÷ 1⁄9
   2. 5 ÷ 8⁄11
   3. 9 ÷ 3  ⁸⁄₉
3. Simplify
   
   1. 2⁄5 ÷ 6⁄11
   2. 4⁄9 ÷ 9⁄13
   3. 3  ⁷⁄₈ ÷ 4  ⁵⁄₉

Answers to Exercise on dividing Fractions

1.  
   1. 1⁄6
   2. 3⁄20
   3. 2  ³⁄₁₄
2. 1. 36
   2. 6  ⁷⁄₈
   3. 2  ¹¹⁄₃₅
3. 1. 11⁄15
   2. 52⁄81
   3. 279⁄328