Numbers: Fractions
Adding and subtracting 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
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
\[ \frac{\orange1}{\blue5} + \frac{\orange3}{\blue{5}} = \frac{\orange{1}+\orange{3}}{\blue{5}} = \frac{4}{\blue{5}} \]
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
\[ \frac{\orange5}{\blue7} - \frac{\orange3}{\blue{7}} = \frac{\orange{5}-\orange{3}}{\blue{7}} = \frac{2}{\blue{7}} \]
#\begin{array}{rcl}\displaystyle {{1}\over{12}}+{{7}\over{12}}&=&\dfrac{8}{12} \\ &&\phantom{xxx}\blue{\text{adding the numerators while the denominators remain the same}} \\ &=& \displaystyle {{2}\over{3}} \\ &&\phantom{xxx}\blue{\text{simplified by dividing numerator and denominator by }4} \end{array}#
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