Mathematics

Adding and Subtracting Fractions with Different Denominators

This lesson demystifies fractions with different denominators by showing how to find a common language (a common denominator) to allow for addition and subtraction.

\frac{1}{3} + \frac{1}{4} = ?

Imagine trying to add two different types of pizza slices. If you have a third of a pizza and a quarter of another, you cannot easily say how much you have total because the pieces are different sizes. We need a common size to count them together.

Step-by-step solver

(Solution) Identify the denominators

To add or subtract fractions with different denominators, we must first find a common denominator by calculating the Lowest Common Multiple (LCM) of the given denominators.

\text{LCM}(3, 6, 4) = 12

(Solution) Convert to equivalent fractions

Convert each fraction so that it has the common denominator of 12.

\frac{2}{3} = \frac{8}{12}, \quad \frac{5}{6} = \frac{10}{12}, \quad \frac{1}{4} = \frac{3}{12}

(Solution) Combine the fractions

Perform the operations on the numerators while maintaining the same denominator.

\frac{8}{12} + \frac{10}{12} - \frac{3}{12} = \frac{15}{12}

(Solution) Simplify

Reduce the fraction by dividing both the numerator and the denominator by their highest common factor, then convert to a mixed number.

\frac{15 \div 3}{12 \div 3} = \frac{5}{4} = 1\frac{1}{4}

Original question

Explain how to add and subtract fractions with different denominators, with a worked example."

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