How to Divide Fractions

Rajib Singha May 13, 2019
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An easy tutorial to the mathematical process of dividing fractions is what this write-up is all about. So keep a pen and paper ready, and jot down the steps.
Here is the basic idea of dividing fractions with the help of some simple examples. These examples will include working with whole numbers, mixed fractions, dividing fractions by fractions, mixed numbers, and variables as well.

Dividing Fractions by Whole Numbers

Divide 4/9 by 3

Solution:

(4/9) ÷ (3)

Step a. 3 can be written as 3/1

= (4/9) ÷ (3/1)

Step b. Replace 3/1 with its reciprocal 1/3 and multiply the fractions. Simplify the result if possible.
= (4/9) x (1/3)
= (4 x 1) ÷ (9 x 3)
= 4 ÷ 27
= 4/27

Divide 9/45 by 3

Solution:

= (9/45) ÷ (3)
= (9/45) ÷ (3/1)
= (9/45) x (1/3)
= (9 x 1) ÷ (45 x 3)
= 9 ÷ 135
= 1 ÷ 15 [9/135 simplified further]
= 1/15.

Dividing Mixed Fractions by Mixed Fractions

Divide 7(2/8) by 4(6/5)

Solution:

7(2/8) ÷ 4(6/5)

Step a: Simplify each of the mixed fractions first. That is, convert them into improper fractions (a fraction whose numerator is larger than the denominator).

7(2/8) = 58/8 [7 x 8 + 2 = 58 and denominator remains the same, i.e., 8]
4(6/5) = 26/5 [4 x 5 + 6 = 26 and denominator remains the same, i.e. 5]
So, we get,

58/8 ÷ 26/5

Step b: Replace 26/5 with its reciprocal 5/26 and multiply the fractions.

58/8 x 5/26

= (58 x 5) ÷ (8 x 26)
= 290 ÷ 208
= 1(82/208) [When converted back to a mixed fraction].

Divide 9(2/3) by 7(5/11)

Solution:

9(2/3) ÷ 7(5/11)

= 29/3 ÷ 82/11
= 29/3 x 11/82
= (29 x 11) ÷ (3 x 82)
= 319 ÷ 246
= 1(73/264) [When converted back to a mixed fraction].

Dividing Fractions by Fractions

Divide 5/9 by 11/16

Solution:

5/9 ÷ 11/16

Step a: Replace 11/16 with its reciprocal 16/11 and simply multiply the fractions.

5/9 x 16/11

= (5 x 16) ÷ (9 x 11)
= 80 ÷ 99
= 80/99.

Divide 10/9 by 45/5

Solution:

10/9 ÷ 45/5

= 10/9 x 5/45
= (10 x 5) ÷ (9 x 45)
= 50 ÷ 405
= 10 ÷ 81 [Simplified further]
= 10/81.

Dividing Fractions by Mixed Numbers

Divide 10/9 by 4(6/9)

Solution:

10/9 ÷ 4(6/9)

= 10/9 ÷ 42/9 [4(6/9) = 42/9]
= 10/9 x 9/42
= (10 x 9) ÷ (9 x 42)
= 90 ÷ 378
= 5 ÷ 21 [Simplified further]
= 5/21.

Divide 12/11 by 13(2/5)

Solution:

12/11 ÷ 13(2/5)


= 12/11 ÷ 67/5 [13(2/5) = 67/5]
= 12/11 x 5/67
= (12 x 5) ÷ (11 x 67)
= 60 ÷ 737
= 60/737.

Dividing Fractions by Variables

Divide 13/16 by ab/z

Solution:

13/16 ÷ (ab)/z


= 13/16 x z/(ab) [Replaced (ab/z) with its reciprocal z/(ab)]
= (13 x z) ÷ (16 x ab)
= 13z ÷ 16ab
= 13z/16ab [The values of a, b and z, if known, can be put in order to get the final answer]

Divide 99/25 by pq/tl

Solution:

99/25 ÷ pq/tl


= 99/25 x (tl)/(pq)
= (99 x tl) ÷ (25 x pq)
= 99tl ÷ 25 pq
= 99tl/25 pq [Put the values of t, l, p and q and derive the final answer]
Once you get a hold of the idea, you can go on with practicing with some more numbers of greater value and complex combination.