Numbers: Fractions
Addition and subtraction of fractions
We have seen how we can add fractions with like denominators. However, it can very often be useful to add fractions that do not have like denominators. In the action plan below we will show how this works.
Addition and subtraction of fractions
Action plan 
Example  
We would like to add two fractions. 
#\frac{3}{4} + \frac{1}{6}=\dots#


Step 1  We write the fractions with like denominators. 
#\dfrac{3}{4} = \dfrac{18}{24} \text{ and }\dfrac{1}{6} = \dfrac{4}{24} # 
Step 2  We add the fractions with like denominators. 
#\dfrac{18}{24} + \dfrac{4}{24} = \dfrac{22}{24}# 
Step 3  If possible, we simplify the answer. 
#\dfrac{22}{24}=\dfrac{11}{12}# 
#{{8}\over{9}}+{{3}\over{5}}=# #{{67}\over{45}}#
#\begin{array}{rcl}\displaystyle {{8}\over{9}}+{{3}\over{5}}&=&\dfrac{40}{45}+\dfrac{27}{45} \\ &&\phantom{xxx}\blue{\text{created fractions with like denominators, new denominator is }9 \times 5=45} \\
&=& \dfrac{67}{45}\\
&&\phantom{xxx}\blue{\text{added the numerators while the denominators remain the same}} \\
\end{array}#
#\begin{array}{rcl}\displaystyle {{8}\over{9}}+{{3}\over{5}}&=&\dfrac{40}{45}+\dfrac{27}{45} \\ &&\phantom{xxx}\blue{\text{created fractions with like denominators, new denominator is }9 \times 5=45} \\
&=& \dfrac{67}{45}\\
&&\phantom{xxx}\blue{\text{added the numerators while the denominators remain the same}} \\
\end{array}#
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