Adding Fractions with Unlike Denominators

Front

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.

Front

What does it mean to have unlike denominators in fractions?

Back

Unlike denominators are denominators that are not the same. For example, \(\frac{1}{3}\) and \(\frac{1}{4}\) have unlike denominators.

Front

How do you add fractions with unlike denominators?

Back

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.

Front

What is a common denominator?

Back

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 the fractions.

Front

What is the first step in adding \(\frac{1}{3}\) and \(\frac{1}{4}\)?

Back

The first step is to find the least common denominator (LCD) of the two fractions, which is 12.

Front

Convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 12.

Back

To convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 12, multiply the numerator and denominator by 4: \(\frac{1 \times 4}{3 \times 4} = \frac{4}{12}\).

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Convert \(\frac{1}{4}\) to an equivalent fraction with a denominator of 12.

Back

To convert \(\frac{1}{4}\) to an equivalent fraction with a denominator of 12, multiply the numerator and denominator by 3: \(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\).

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What is the sum of \(\frac{4}{12}\) and \(\frac{3}{12}\)?

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The sum is \(\frac{4 + 3}{12} = \frac{7}{12}\).

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What is the formula for adding fractions?

Back

The formula for adding fractions is: \(\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d}\) where \(a\) and \(c\) are the numerators, and \(b\) and \(d\) are the denominators.

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What is the result of adding \(\frac{1}{2}\) and \(\frac{3}{8}\)?

Back

To add \(\frac{1}{2}\) and \(\frac{3}{8}\), convert \(\frac{1}{2}\) to \(\frac{4}{8}\) and then add: \(\frac{4}{8} + \frac{3}{8} = \frac{7}{8}\).