How to add or subtract fractions with unlike denominators

Question

tafzijdeq · Accepted Answer

Step 1
When two fractions are to be added or subtracted, the denominators need to be equal. When the denominators are not equal, the least common denominator (LCD) is to be determined. LCD can be obtained by considering the least common multiple (LCM) of the denominators. After obtaining the LCM, both the fraction are multiplied in the numerator and denominator with a number that gives the LCM in both the denominators. Now that both the denominators are same (LCM), the numerators are added or subtracted.
Step 2
Example for the same can be given by:
Here the denominators are 2 and 3 respectively. The LCM of 2 and 3 is 6. To obtain 6 in the denominator of first fraction having 2, it is to be multiplied with 3. Hence, 3 is multiplied to the numerator and denominator of the first fraction. Similarly 2 is multiplied to numerator and denominator of the second fraction. After simplifying, both the denominators have 6. Since, the denominators are equal, the numerators can be added and simplified.

\frac{1}{2} + \frac{1}{3} = \frac{1 (3)}{2 (3)} + \frac{1 (2)}{3 (2)}

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6}

\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6}

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

How to add or subtract fractions with unlike denominators

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