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 in fractions?

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

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

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The first step is to find the least common denominator (LCD) of the two fractions. The LCD of 3 and 4 is 12.

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

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To convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 12, multiply both 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.

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To convert \(\frac{1}{4}\) to an equivalent fraction with a denominator of 12, multiply both 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 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 simplest form.

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How do you simplify the fraction \(\frac{6}{8}\)?

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To simplify \(\frac{6}{8}\), divide both the numerator and denominator by their greatest common divisor (GCD), which is 2: \(\frac{6 \div 2}{8 \div 2} = \frac{3}{4}\).