Fractions

A fraction is part of a whole number. The denominator tells your child how many parts the whole number has been cut into and the numerator indicates how many parts we have.

In the example, the circle represents the whole which is cut up into \textcolor{darkturquoise}{4} equal parts.

The numerator then tells us \textcolor{darkturquoise}{3} of the parts are shaded in.

To help your child understand fractions, go through the following examples of finding fractions of amounts.

Equivalent fractions are fractions that are equal but have different numerators and denominators.

Example: What is the simplest equivalent fraction to \dfrac{2}{8} ?

First, find the greatest number that divides into both the numerator and the denominator. In this case both 2 and 8 are divisible by 2.

Divide the numerator and denominator by \textcolor{red}{2}.

\dfrac{2 \textcolor{red}{\div 2}}{8 \textcolor{red}{\div 2}} = \dfrac{1}{4}

Example: What is the simplest equivalent fraction to \dfrac{27}{63} ?

Both the numerator and denominator are divisible by 9.

Divide the numerator and denominator by \textcolor{red}{9}.

\dfrac{27 \textcolor{red}{\div 9}}{63 \textcolor{red}{\div 9}} = \dfrac{3}{7}

Your child may come across improper fractions in their revision and exams. Improper fractions have a numerator that is greater than the denominator and this indicates that the number is greater than \bold{\textcolor{red}{1}}.

Mixed numbers are another way of expressing a fraction that is greater than \bold{\textcolor{red}{1}}. Your child may be asked to convert between improper fractions and mixed numbers.

Example: Convert \dfrac{13}{5} into a mixed number.

\dfrac{13}{5} = 13 \div 5

First, find how many whole times 5 goes into 13.

13 \div 5 = \textcolor{green}{2} r \textcolor{purple}{3}

The mixed number can then be found by writing the number of whole times 5 goes into 13 as a big number at the front.

Then, the remainder of the calculation as the numerator of the fraction with the denominator staying as 5.

So, the answer becomes:

\dfrac{13}{5} = \textcolor{green}{2} \dfrac{\textcolor{purple}{3}}{5}

If two fractions have the same denominator or common denominator, then adding and subtracting is simple.

Add or subtract the numerators and keep the denominators the same.

Example: \dfrac{7}{\textcolor{red}{9}} - \dfrac{2}{\textcolor{red}{9}}

The denominator of both fractions are the same, in order to subtract the fractions, your child needs to subtract one numerator from the other.

\dfrac{7}{\textcolor{red}{9}} - \dfrac{2}{\textcolor{red}{9}} = \dfrac{7 - 2}{\textcolor{red}{9}}=\dfrac{5}{\textcolor{red}{9}}

When the denominators are different, your child needs to use their skills of finding equivalent fractions to make the denominators the same.

Example: \dfrac{3}{5} + \dfrac{4}{15}

In this example, the denominators are different so multiply the numerator and the denominator of \dfrac{3}{5} by \textcolor{red}{3}.

\dfrac{3}{5} \times \textcolor{red}{\dfrac{3}{3}} = \dfrac{9}{15}

Now the fractions both have a denominator of 15 so they can be added as normal.

\dfrac{9}{15} + \dfrac{4}{15} = \dfrac{13}{15}

Multiplying fractions by whole number:

In their exam your child may be asked to multiply a fraction by a whole number. In order to do that, multiply the numerator by the whole number and leave the denominator as it is.

Example: \dfrac{3}{11} \times 5

The numerator is 3

\dfrac{3 \times 5}{\textcolor{purple}{11}} = \dfrac{15}{\textcolor{purple}{11}}

Multiplying fractions by another fraction:

When multiplying a fraction by another fraction your child needs to multiply the numerators together and multiply the denominators together.

Example: \dfrac{6}{7} \times \dfrac{5}{8}

Multiply the numerators and denominators together.

\dfrac{\textcolor{orange}{6}}{\textcolor{purple}{7}} \times \dfrac{\textcolor{orange}{5}}{\textcolor{purple}{8}} = \dfrac{\textcolor{orange}{6 \times 5}}{\textcolor{purple}{7 \times 8}} = \dfrac{30}{56}

The fraction \dfrac{30}{56} can be simplified by finding an equivalent fraction.

30 and 56 both divide by 2 so simplify the fraction by dividing the numerator and denominator by 2.

\dfrac{30 \textcolor{red}{\div 2}}{56 \textcolor{red}{\div 2}} = \dfrac{15}{28}

When dividing fractions by a whole number, your child needs to multiply the denominator by the whole number.

Example: \dfrac{5}{12} \div 6

The denominator is \textcolor{purple}{12} so to find the new denominator, multiply \textcolor{purple}{12} by \textcolor{red}{6}.

So, the calculation becomes:

\dfrac{5}{\textcolor{purple}{12}}  \textcolor{red}{\div 6} = \dfrac{5}{\textcolor{purple}{12}  \textcolor{red}{\times 6}} = \dfrac{5}{72}