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.

(4/9) ÷ (3)

= (4/9) ÷ (3/1)

= (4/9) x (1/3)

= (4 x 1) ÷ (9 x 3)

= 4 ÷ 27

= 4/27

= (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.

7(2/8) ÷ 4(6/5)

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].

58/8 ÷ 26/5

58/8 x 5/26

= (58 x 5) ÷ (8 x 26)

= 290 ÷ 208

= 1(82/208) [When converted back to a mixed fraction].

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].

5/9 ÷ 11/16

5/9 x 16/11

= (5 x 16) ÷ (9 x 11)

= 80 ÷ 99

= 80/99.

10/9 ÷ 45/5

= 10/9 x 5/45

= (10 x 5) ÷ (9 x 45)

= 50 ÷ 405

= 10 ÷ 81 [Simplified further]

= 10/81.

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.

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.

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]

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.