How to Divide Fractions

In this article, I would present you 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

Example #1: 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

Example #2: 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.

Mixed Fractions by Mixed Fractions

Example #3: 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].

Example #4: 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].

Fractions by Fractions

Example #5: 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.

Example #6: 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.

Fractions by Mixed Numbers

Example #7: 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.

Example #8: Divide 12/11 by 13(2/5)

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.

Fractions by Variables

Example #9: Divide 13/16 by ab/z

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]

Example #10: Divide 99/25 by pq/tl

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]

And with this, we come to the conclusion of this article. I am sure that you could follow these simple examples, cited above. Once you get a hold of the idea, you can go on with practicing with some more numbers of greater value and complex combination.