When you’re multiplying fractions by an integer (or a whole number) you multiply the numerator of the fraction by the whole number, whilst the denominator of the fraction stays the same.
Think about the following example.
If you have an apple and divide it into 8 equal parts or slices, you are dividing it into eighths (⅛). 8 eighths make a whole apple.
If you eat 5 slices of this apple throughout the day, what fraction of the apple have you eaten?
The equal parts that have been eaten are represented in yellow on the bar model above.
To calculate the fraction of the apple that has been eaten, you can add up all 5 parts.
⅛ + ⅛ + ⅛ + ⅛ + ⅛ = ⅝
You have eaten ⅝ of the apple. This method is called repeated addition.
You can also represent this through multiplication. You have eaten 5 slices of apple, and each slice of apple is ⅛ of the apple:
5 × ⅛ = ⅝
As you can see, the numerator (1) is multiplied by 5, but the denominator (8) stays the same.
