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How to add mixed fractions?
Addition of Mixed fractions:
To add or subtract mixed fractions, first convert them to improper fractions.
(i) If they are like fractions then add or subtract the numerators keeping the denominator unchanged.
For example,
$2 \frac{1}{5} + 3 \frac{2}{5} = \frac{(2\times5+1)}{5} + \frac{(3\times5+2)}{5} = \frac{11}{5} + \frac{17}{5} = \frac{(11+17)}{5} = \frac{28}{5}$.
(ii) If they are unlike fractions then we have to follow the below procedure:
To add or subtract unlike terms, first, we need to convert them to like fractions.
We have to follow the following steps to convert unlike terms to like terms:
1. Find the LCM of the given fractions.
2. Divide each denominator by the LCM and note down the quotients for each case.
3. Now, multiply the numerator and the denominator of each fraction by the
corresponding quotients that you got in the 2nd step.
4. After the multiplication, the denominators of all the fractions are the same, thus the resultant fractions are like fractions.
5. We can now add or subtract the numerators as required.
For example,
$2 \frac{2}{3} + 1 \frac{1}{2} = \frac{(2\times 3+2)}{3} + \frac{(1\times 2+1)}{2} = \frac{8}{3} + \frac{3}{2}$
LCM of 3 and 2 is 6.
$\frac{6}{3}=2$ and $\frac{6}{2}=3$
$\frac{8}{3}=\frac{(8\times 2)}{(3\times 2)} = \frac{16}{6}$
$\frac{3}{2}=\frac{(3\times 3)}{(2\times 3)} =\frac{16}{6}$
Therefore,
$2 \frac{2}{3} + 1 \frac{1}{2} = \frac{16}{6}+\frac{16}{6}= \frac{(16+9)}{6} = \frac{25}{6}$.
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