Adding and subtracting fractions with like denominators

Numbers: Fractions

Adding and subtracting fractions with like denominators

Fractions with like denominators

The fractions $\tfrac{1}{\blue 5}$ and $\tfrac{3}{\blue 5}$ have the same denominator.
When fractions have the same $\blue{\text{denominator}}$ , we call them fractions with like denominators.

Example

$\tfrac{2}{\blue 7}$ and $\tfrac{3}{\blue 7}$ have like denominators

Adding fractions with like denominators

When adding fractions with like denominators, the $\blue{\text{denominator}}$ does not change.

The numerators do change. We add the $\orange{\text{numerators}}$ to each other.

In general:

When adding fractions with like denominators, we add the numerators while the denominator stays the same.

Example

$\frac{\orange1}{\blue5} + \frac{\orange3}{\blue{5}} = \frac{\orange{1}+\orange{3}}{\blue{5}} = \frac{4}{\blue{5}}$

If you find it difficult to remember this, imagine a pizza with $\blue5$ slices. If you have $\orange1$ slice, and you take $\orange3$ more, you will have a total of $\frac{\orange1}{\blue5}+\frac{\orange3}{\blue5}=\frac{4}{\blue5}$ of the entire pizza.

Subtracting fractions with like denominators

When subtracting fractions with like denominators, the $\blue{\text{denominator}}$ does not change.

The numerators do change. We subtract the $\orange{\text{numerators}}$ from each other.

In general:

When subtracting fractions with like denominators, we subtract the numerators while the denominator stays the same.

Example

$\frac{\orange5}{\blue7} - \frac{\orange3}{\blue{7}} = \frac{\orange{5}-\orange{3}}{\blue{7}} = \frac{2}{\blue{7}}$

If you find it difficult to remember this, imagine a pizza with $\blue7$ slices. If you have $\orange5$ slices, and you eat $\orange3$ of them, you will have a total of $\frac{\orange5}{\blue7}-\frac{\orange3}{\blue7}=\frac{2}{\blue7}$ of the entire pizza left.

Calculate:
${{3}\over{4}}+{{3}\over{4}}$
Simplify your answer as much as possible. Give your answer in the form of a fraction.

${{3}\over{4}}+{{3}\over{4}}=$ ${{3}\over{2}}$

$\begin{array}{rcl}\displaystyle {{3}\over{4}}+{{3}\over{4}}&=&\dfrac{6}{4} \\ &&\phantom{xxx}\blue{\text{adding the numerators while the denominators remain the same}} \\ &=& \displaystyle {{3}\over{2}} \\ &&\phantom{xxx}\blue{\text{simplified by dividing numerator and denominator by }2} \end{array}$

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