# Addition and Subtraction of Like Fractions

Lesson

A fraction describes a part of a whole. The denominator (bottom number) tells us how many parts the whole is divided into (e.g. halves, thirds or quarters), while the numerator (top number) tells us how many parts we need to add or subtract.

Let's start by looking at how we add parts of a whole:

$1$1 part + $1$1 part = $2$2 parts

Now let's add in the language of fractions. You may have already looked at how to do this using a diagram or a number line. Let's say we wanted to add thirds together.

$1$1 third + $1$1 third = $2$2 thirds

We can write this using only numbers as well

$\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$13+13=23

Now play around with this applet. What do you notice about the number on the numerator and the number on the denominator?

#### Worked Examples

##### Question 1

$\frac{1}{6}+\frac{1}{6}+\frac{2}{6}=\editable{}$16+16+26=

Think: The grid above is divided into $6$6 pieces. If we coloured in the grid as the number sentence tells us, how many sixths would be shaded?

Do: $\frac{1}{6}+\frac{1}{6}+\frac{2}{6}=\frac{4}{6}$16+16+26=46 (this is equivalent to $\frac{2}{3}$23 but we'll learn more about that later).

##### Question 2

1. $+$+$=$=

##### Question 3

Find the value of $\frac{4}{7}-\frac{3}{7}$4737.

### Outcomes

#### NA3-1

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.