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How to add mixed unlike fractions?
Addition of mixed fractions:
To add mixed fractions with different denominators,
First, we need to convert them to improper fractions.
Addition of Unlike Fractions:
To add 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 the numerators as required.
$1 \frac{2}{3} + 2 \frac{1}{2} = \frac{(1\times 3+2)}{3} + \frac{(2\times 2+1)}{2} = \frac{(3+2)}{3} + \frac{(4+1)}{2} = \frac{5}{3} + \frac{5}{2}$
LCM of 3 and 2 is 6.
$\frac{6}{3} = 2$ and $\frac{6}{2} = 3$
$\frac{5}{3} = \frac{(5\times 2)}{(3\times 2)} = \frac{10}{6}$
$\frac{5}{2} = \frac{(5\times 3)}{(2\times 3)} = \frac{15}{6}$
Therefore,
$\frac{5}{3} + \frac{5}{2} = \frac{10}{6} + \frac{15}{6} = \frac{(10+15)}{6} = \frac{25}{6}$.
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