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

1.	Leave the numerator as it is.
2.	Multiply the denominator by the whole number you are dividing by.
3.	Simplify the fraction if necessary.

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

1.	Leave the denominator as it is.
2.	Divide the numerator by the whole number you are dividing by.
3.	Simplify the fraction if necessary.

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.