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Example of Contrasting Subtraction and Multiplication of rac{4k}{5} and rac{1}{6}
This example contrasts the procedures for subtracting and multiplying the fractions rac{4k}{5} and rac{1}{6}. Identifying the operation determines if a common denominator is necessary.
ⓐ Subtracting rac{4k}{5} - rac{1}{6}: Subtraction requires a least common denominator (LCD). The LCD for and is . First, rewrite each fraction as an equivalent fraction with the LCD: rac{4k \cdot 6}{5 \cdot 6} = rac{24k}{30} and rac{1 \cdot 5}{6 \cdot 5} = rac{5}{30}. Next, subtract the numerators and place the difference over the common denominator: rac{24k - 5}{30}. There are no common factors between the numerator and denominator, so the expression is simplified.
ⓑ Multiplying rac{4k}{5} \cdot rac{1}{6}: Multiplication does not require a common denominator. Multiply the numerators and denominators directly: rac{4k \cdot 1}{5 \cdot 6}. Rewrite to reveal common factors: rac{2 \cdot 2k \cdot 1}{5 \cdot 2 \cdot 3}. Removing the common factor of from both the numerator and denominator simplifies the expression to rac{2k}{15}.
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
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