Adding and subtracting fractions

If you eat $\frac{1}{8}$ of a pizza and your sister eats $\frac{3}{8}$ of the same pizza, together you have eaten $\frac{4}{8}$ , half the pizza! Adding fractions with the same denominator is as easy as adding the numerators.

What is this?

When two fractions share the same denominator, they are made of pieces of the same size. We can simply count the pieces.

$\frac{1}{8} + \frac{3}{8} = \frac{1+3}{8} = \frac{4}{8} = \frac{1}{2}$

The denominator stays the same because the size of the piece does not change. We just count how many pieces we have in total.

Subtraction works the same way. If you had $\frac{5}{8}$ of a chocolate and gave away $\frac{2}{8}$, you are left with:

$\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$

After adding, always check if the answer can be simplified. $\frac{4}{8}$ becomes $\frac{1}{2}$. The answer is the same, just dressed in simpler clothes.

What about adding when denominators are different? First change them to equivalent fractions with the same denominator, then add. For example:

$\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

The same trick , make the denominators match, then count the pieces.

Worked examples

Example 1. Add $\frac{2}{7} + \frac{3}{7}$.

• Same denominator → add the tops.
• $\frac{2+3}{7} = \frac{5}{7}$.

Example 2. $\frac{7}{10} - \frac{3}{10}$.

• $\frac{7-3}{10} = \frac{4}{10}$.
• Simplify by dividing top and bottom by 2 → $\frac{2}{5}$.

Example 3. Ramu walks $\frac{1}{4}$ km to the shop and $\frac{1}{2}$ km to school. How much did he walk in all?

• Change $\frac{1}{2}$ to $\frac{2}{4}$.
• $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ km.

Try it

1. $\frac{1}{5} + \frac{2}{5}$.
2. $\frac{5}{9} - \frac{2}{9}$.
3. $\frac{3}{8} + \frac{4}{8}$ (simplify if possible).
4. $\frac{1}{3} + \frac{1}{6}$.
5. Asha ate $\frac{2}{6}$ of a cake. Her brother ate $\frac{3}{6}$. How much cake did they eat together? How much is left?

Hands-on

Roti share. Take a sheet of paper as a "roti". Cut it into 6 equal parts. Pick 2 pieces for yourself and 1 piece for a friend. Together you took $\frac{2}{6} + \frac{1}{6}$. Count out the answer.

Chocolate maths. Find a chocolate bar with 12 squares. Eat $\frac{4}{12}$ today and $\frac{3}{12}$ tomorrow. How much chocolate did you eat in total? How much remains?