Year 7AC9M7N06

Adding and Subtracting Fractions

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.

You can only add pieces that are the same size. Make the bottoms match, add the tops, and leave the bottom alone.

Builds onYr 7 · Comparing and Ordering Fractions

Method

The bottom never changes when you add

\frac{2}{7} + \frac{3}{7} = \frac{5}{7}

You are counting sevenths. The size of a seventh does not change.

Adding the bottoms is the classic error

\frac{2}{7} + \frac{3}{7} \neq \frac{5}{14}

That would make the answer smaller than what you started with.

Different bottoms: find the LCD first

Rewrite both fractions, then add. Never add across as they are.

Mixed numbers: whole parts and fraction parts separately

Or turn both into improper fractions. Either works — pick one and stick to it.

Worked example

e.g.

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

The bottoms are different, so find the lowest common denominator. $LCM(3, 4) = 12$
Rewrite the first fraction over 12. $\frac{2}{3} = \frac{8}{12}$
Rewrite the second fraction over 12. $\frac{1}{4} = \frac{3}{12}$
Add the tops. Leave the bottom alone. $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$
Simplify if you can. $\frac{11}{12} \text{ is already simplest}$
Check it looks sensible. The answer should be a bit less than 1. $\frac{2}{3} \approx 0{,}67 \quad \frac{1}{4} = 0{,}25 \quad \text{sum} \approx 0{,}92 \quad\checkmark$

Practice

Find the LCD first. Simplify your answer.

\frac{3}{8} + \frac{1}{8}

Answer

\frac{4}{8} = \frac{1}{2}

\frac{1}{2} + \frac{1}{5}

Answer

\frac{7}{10}

\frac{5}{6} - \frac{1}{4}

Answer

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

\frac{3}{4} + \frac{2}{3}

Answer

\frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1\frac{5}{12}

2\frac{1}{3} + 1\frac{1}{2}

Answer

3\frac{5}{6}

\text{Why is } \frac{1}{3} + \frac{1}{3} = \frac{2}{6} \text{ wrong?}

Answer

\text{The bottom must stay } 3. \text{ The answer is } \frac{2}{3}.