Dividing fractions by whole numbers

​​In a nutshell

Dividing fractions by whole numbers is a case of either multiplying the denominator of the fraction by the whole number, or dividing the numerator of the fraction by the whole number - whichever is easier! Always try to simplify at the end.

Fractions reminder

Remember that a fraction represents one number divided by another number, specifically, the numerator divided by the denominator. So

​$$\dfrac49 = 4 \div 9$$​​

There are two different methods you can use to divide a fraction by a whole number. 

Multiply the denominator

Procedure

Example 1

Solve the following question:

​$$\dfrac49\div2$$​​

Leave the numerator as it is, and multiply the denominator by $$2$$​.

​$$\dfrac49\div2 = \dfrac{4}{9\times2}=\dfrac{4}{18}$$​​

Simplify the fraction (if necessary) to reach the final answer.

$$\dfrac{4}{18}=\underline{\dfrac{2}{9}}$$​​​​

Divide the numerator

Procedure

Example 2

Solve the following question:

​$$\dfrac49\div2$$​​

Leave the denominator as it is, and divide the numerator by $$2$$​.

​$$\dfrac49 \div 2 = \dfrac{4\div2}{9} = \underline{\dfrac{2}{9}}$$​​

Note: As you can see, in this case, the second method was quicker as there was no simplifying needed.  However, both methods resulted in the same answer.