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

7⁄8 ÷ 9

12⁄7 ÷ 8

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
= 12^{3}⁄7 x 1⁄8^{2}
= (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

2 ÷ 1⁄3

7 ÷ 4⁄5

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

3⁄5 ÷ 4⁄7

9⁄7 ÷ 3⁄2

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
= 9^{3}⁄7 x 2⁄3^{1}
= (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.

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Exercise on dividing Fractions

Simplify

1⁄2 ÷ 3

3⁄4 ÷ 5

4 ^{3}⁄_{7} ÷ 2

Simplify

4 ÷ 1⁄9

5 ÷ 8⁄11

9 ÷ 3 ^{8}⁄_{9}

Simplify

2⁄5 ÷ 6⁄11

4⁄9 ÷ 9⁄13

3 ^{7}⁄_{8} ÷ 4 ^{5}⁄_{9}

For Answers see at the bottom of the page.

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