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Example of Contrasting Subtraction and Multiplication of rac{3a}{4} and rac{8}{9}
This example contrasts the procedures for subtracting and multiplying the fractions rac{3a}{4} and rac{8}{9}. The first step is to identify the operation, which determines whether a common denominator is needed.
ⓐ Subtracting rac{3a}{4} - rac{8}{9}: Subtraction requires a least common denominator (LCD). The LCD for and is . First, rewrite each fraction as an equivalent fraction with the LCD: rac{3a \cdot 9}{4 \cdot 9} = rac{27a}{36} and rac{8 \cdot 4}{9 \cdot 4} = rac{32}{36}. Then, subtract the numerators and place the difference over the common denominator: rac{27a - 32}{36}. Because there are no common factors to remove between the numerator and denominator, this expression is fully simplified.
ⓑ Multiplying rac{3a}{4} \cdot rac{8}{9}: Multiplication does not require a common denominator. We simply multiply the numerators and denominators: rac{3a \cdot 8}{4 \cdot 9}. Before multiplying out, rewrite showing common factors: rac{3a \cdot 2 \cdot 4}{4 \cdot 3 \cdot 3}. Removing the common factors of and from both the numerator and denominator simplifies the expression to rac{2a}{3}.
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
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