Adding Fractions with Unlike Denominators

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What is a fraction?

Back

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction \(\frac{1}{2}\), 1 is the numerator and 2 is the denominator.

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What does it mean to have unlike denominators?

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Unlike denominators are denominators that are not the same. For example, in the fractions \(\frac{1}{3}\) and \(\frac{2}{5}\), 3 and 5 are unlike denominators.

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How do you add fractions with unlike denominators?

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To add fractions with unlike denominators, first find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators.

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What is a common denominator?

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A common denominator is a number that is a multiple of the denominators of two or more fractions. It allows you to add or subtract fractions easily.

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What is the first step in adding \(\frac{1}{3}\) and \(\frac{2}{5}\)?

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The first step is to find a common denominator. The least common multiple (LCM) of 3 and 5 is 15.

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Convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 15.

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To convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 15, multiply both the numerator and denominator by 5: \(\frac{1 \times 5}{3 \times 5} = \frac{5}{15}\).

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Convert \(\frac{2}{5}\) to an equivalent fraction with a denominator of 15.

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To convert \(\frac{2}{5}\) to an equivalent fraction with a denominator of 15, multiply both the numerator and denominator by 3: \(\frac{2 \times 3}{5 \times 3} = \frac{6}{15}\).

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What is the sum of \(\frac{5}{15}\) and \(\frac{6}{15}\)?

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The sum is \(\frac{5 + 6}{15} = \frac{11}{15}\).

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What is the formula for finding the sum of two fractions?

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The formula for adding two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\) is: \(\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d}\).

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What is the importance of simplifying fractions?

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Simplifying fractions makes them easier to understand and work with. It involves reducing the fraction to its lowest terms.