How to Divide Fractions

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.

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

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.

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].

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].

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.

Solution:

10/9 ÷ 45/5

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

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.

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.

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]

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.