How to divide fractions


Before reading about how to divide fractions, please read the primer on fractions.


Let's kick off with this simple example of dividing fractions


1/3     ÷     1/2


Change the division sign (÷) to a multiplication sign (x) and 'flip' the second fraction

1/3     x     2/1


It may help to imagine a pancake marked on one side with the fraction 1/2 - 'flip' the pancake to reveal the fraction 2/1 on the other side!



Now follow the rules for multiplying fractions -


multiply the numerators

1  x  2   =   2

multiply the denominators

3  x  1   =   3


The resulting fraction is 2/3.


So

1/3  ÷  1/2   =   1/3  x  2/1   =   (1 x 2) / (3 x 1)   =   2/3


i.e.   one third divided by a half equals two thirds.


Next consider


1/7     ÷     1/2     ÷     2/3


Change the division signs (÷) to multiplication signs (x) and 'flip' the second and third fractions

1/7     x     2/1     x     3/2


Now multiply the numerators

1  x  2  x  3   =   6

and multiply the denominators

  7  x  1  x  2   =   14


Simplify the resulting fraction 6/14 to the equivalent fraction 3/7 by dividing numerator and denominator by factor 2



Bringing everything together


1/7     ÷     1/2     ÷     2/3

=

1/7     x     2/1     x     3/2

=

(1 x 2 x 3) / (7 x 1 x 2)

=

6/14

=

3/7


i.e.   one seventh divided by a half divided by two thirds equals three sevenths.


Have a go at the following


3/4     ÷     3/4     ÷     1/2     ÷     1/2


5/3     ÷     2/2     ÷     1/2     ÷     2/3     ÷     1/2


Don't worry about how many fractions are involved or the improper fractions (5/3 and 2/2, numerator greater than or equal to denominator). Apply the same technique as shown in the previous examples of how to divide fractions.


To recap, change the division signs (÷) to multiplication signs (x) and 'flip' all the fractions except the first fraction. Then follow the rules for multiplying fractions - multiply the numerators and multiply the denominators.


The answers/workings out are as follows



3/4     ÷     3/4     ÷     1/2     ÷     1/2

=

3/4     x     4/3     x     2/1     x     2/1

=

(3 x 4 x 2 x 2) / (4 x 3 x 1 x 1)

=

48 / 12

(48 divided by 12)

=

4


i.e.   three quarters divided by three quarters divided by a half divided by a half equals 4.



5/3     ÷     2/2     ÷     1/2     ÷     2/3    ÷     1/2

=

5/3     x     2/2     x     2/1     x     3/2     x     2/1

=

(5 x 2 x 2 x 3 x 2) / (3 x 2 x 1 x 2 x 1)

=

120/12

(120 divided by 12)

=

10


i.e.   five thirds divided by two halves divided by a half divided by two thirds divided by a half equals 10.


Feeling more confident about how to divide fractions?


Using the technique you've just learned, go ahead and divide fractions with confidence - regardless of the number of fractions or whether they're proper or improper!


For more on fractions click here:

Math fractions

Equivalent fractions

Simplifying fractions

Adding fractions

How to subtract fractions

Multiplying fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent

Percent to fraction


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