## What you need to know

Things to remember:

• We can have positive, negative, and improper fractions.
• We can convert between mixed numbers and improper fractions to help add and subtract.

Fractions with like denominators are fractions with the same denominator, which we know how to add and subtract; we add and subtract the numerators, the denominators don’t change.

$$\dfrac{2}{9}+\dfrac{3}{9}=\dfrac{2+3}{9}=\dfrac{5}{9}$$

$\dfrac{15}{24}-\dfrac{11}{24}=\dfrac{15-11}{24}=\dfrac{4}{24}=\dfrac{1}{6}$

Write $\dfrac{5}{11}+\dfrac{9}{11}$ as a single fraction and as a mixed number.

$$\frac{5}{11}+\frac{9}{11}=\frac{5+9}{11}=\frac{14}{11}$$

Tip: To turn an improper fraction into a mixed number, we divide like normal. The whole number part of the division is the whole number part of the mixed number, and the remainder goes over the original denominator.

$$\frac{5}{11}+\frac{9}{11}=\frac{14}{11}=1\frac{3}{11}$$

Like with whole number, we can add more than two fractions together.

Write $\dfrac{5}{11}+\dfrac{9}{11}+\dfrac{10}{11}$ as a single fraction and as a mixed number.

$$\frac{5}{11}+\frac{9}{11}+\frac{10}{11}=\frac{5+9+10}{11}=\frac{24}{11}$$

$$\frac{5}{11}+\frac{9}{11}+\frac{10}{11}=\frac{24}{11}=2\frac{2}{11}$$

We do the exact same when subtracting fractions as well.

Write $\dfrac{3}{15}-\dfrac{14}{15}-\dfrac{13}{15}$ as a single fraction and as a mixed number.

$$\frac{2}{15}-\frac{14}{15}-\frac{13}{15}=\frac{2-14-13}{15}=-\frac{25}{15}$$

$$\frac{3}{15}-\frac{14}{15}-\frac{13}{15}=-\frac{25}{15}=-\frac{5}{3}=-1\frac{2}{3}$$

## Example Questions

#### Question 1: Write the following as a single fraction and mixed number$$\frac{3}{5}+\frac{4}{5}+\frac{2}{5}$$

$$\frac{3}{5}+\frac{4}{5}+\frac{2}{5}=\frac{3+4+2}{5}=\frac{9}{5}$$

$$\frac{3}{5}+\frac{4}{5}+\frac{2}{5} =\frac{9}{5}=1\frac{4}{5}$$

#### Question 2: Write the following as a single fraction.$$\frac{19}{24}-\frac{7}{24}-\frac{2}{24}$$

$$frac{19}{24}-\frac{7}{24}-\frac{2}{24}=\frac{19-7-2}{24}=\frac{10}{24}$$