# Adding and subtracting negative fractions

Lesson

We have covered a number of chapters that dealt with adding and subtracting negative integers, (Moving Up The Number Line, and Moving Down the Number Line), and we have seen where negative fractions fall on a number line and how to order them, (Where are negative fractions?).

Well now we combine these concepts together to add and subtract fractions.

Remember to add or subtract fractions we need to have common denominators, so that is usually your first step. After that, follow your rules incorporating negative numbers.

subtracting a negative is the same as addition e.g. $\frac{2}{4}-\left(-\frac{3}{4}\right)=\frac{2}{4}+\frac{3}{4}$24(34)=24+34 = $\frac{5}{4}$54

adding a negative is the same as subtraction e.g.$\frac{2}{4}+\left(-\frac{1}{4}\right)=\frac{2}{4}-\frac{1}{4}$24+(14)=2414  $=$= $\frac{1}{4}$14

subtracting a positive is the same as subtraction e.g. $\frac{2}{4}-+\frac{1}{4}=\frac{2}{4}-\frac{1}{4}$24+14=2414 $=$= $\frac{1}{4}$14

#### Worked Examples

##### QUESTION 1

Evaluate $\frac{4}{11}-\frac{7}{11}$411711, writing your answer in its simplest form.

##### QUESTION 2

Find the difference between $\frac{4}{9}$49 and $-\frac{5}{9}$59.

State the difference as a positive value, writing your answer in its simplest form.

##### QUESTION 3

Evaluate $\frac{-6}{11}-\frac{4}{11}$611411, writing your answer as a simplified fraction.

### Outcomes

#### 9D.NA2.01

Simplify numerical expressions involving integers and rational numbers, with and without the use of technology