Numbers: Fractions
Convenient addition and subtraction of fractions
We have seen how to add and subtract fractions. The most convenient way to do this, is to use the least common multiple. That way, fewer steps are needed to simplify the result.
Convenient addition and subtraction of fractions
Action plan 
Example  
We would like to add two fractions. 
#\frac{2}{4} + \frac{2}{6}=\dots#


Step 1  We write the fractions with like denominators using the #\mathrm{lcm}#. #\mathrm{lcm}(4,6)=12#, so the new denominator is #12#. 
# \begin{array}{rcl} 
Step 2  We add the fractions with like denominators. 
#\dfrac{6}{12} + \dfrac{4}{12} = \dfrac{10}{12}# 
Step 3  If possible, we simplify the answer. 
#\dfrac{10}{12}=\dfrac{5}{6}# 
#{{1}\over{9}}+{{9}\over{10}}=# #{{91}\over{90}}#
#\begin{array}{rcl}\displaystyle {{1}\over{9}}+{{9}\over{10}}&=&\dfrac{10}{90}+\dfrac{81}{90} \\ &&\phantom{xxx}\blue{\text{created fractions with new like denominator }\mathrm{lcm}(9,10)=90} \\
&=& \dfrac{91}{90}\\
&&\phantom{xxx}\blue{\text{added the numerators while the denominators remain the same}} \\
\end{array}#
#\begin{array}{rcl}\displaystyle {{1}\over{9}}+{{9}\over{10}}&=&\dfrac{10}{90}+\dfrac{81}{90} \\ &&\phantom{xxx}\blue{\text{created fractions with new like denominator }\mathrm{lcm}(9,10)=90} \\
&=& \dfrac{91}{90}\\
&&\phantom{xxx}\blue{\text{added the numerators while the denominators remain the same}} \\
\end{array}#
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