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(5x)/(6y)*(3)/(10 y) Which expression is equivalent to the product for all y > 0 ? Choose 1 answer: (A) (x)/(2) (B) (25 x)/(9) (C) (x)/(2y^(2)) (D) (x)/(4y^(2))

5x6y⋅310y \frac{5 x}{6 y} \cdot \frac{3}{10 y} \newlineWhich expression is equivalent to the product for all y>0 ?\newlineChoose 11 answer:\newline(A) x2 \frac{x}{2} \newline(B) 25x9 \frac{25 x}{9} \newline(C) x2y2 \frac{x}{2 y^{2}} \newline(D) x4y2 \frac{x}{4 y^{2}}

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Q. 5x6y⋅310y \frac{5 x}{6 y} \cdot \frac{3}{10 y} \newlineWhich expression is equivalent to the product for all y>0 y>0 ?\newlineChoose 11 answer:\newline(A) x2 \frac{x}{2} \newline(B) 25x9 \frac{25 x}{9} \newline(C) x2y2 \frac{x}{2 y^{2}} \newline(D) x4y2 \frac{x}{4 y^{2}}
  1. Write and Identify Operation: Write down the given expression and identify the operation to be performed.\newlineWe have the expression (5x6y)×(310y)(\frac{5x}{6y}) \times (\frac{3}{10y}) and we need to multiply the two fractions.
  2. Multiply Numerators and Denominators: Multiply the numerators and the denominators of the fractions separately.\newline(5x×3)/(6y×10y)=(15x)/(60y2)(5x \times 3) / (6y \times 10y) = (15x) / (60y^2)
  3. Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.\newline15x15x and 60y260y^2 have a common divisor of 1515.\newline(15x)/(60y2)=(1515)x/(6015)y2=x4y2(15x) / (60y^2) = (\frac{15}{15})x / (\frac{60}{15})y^2 = \frac{x}{4y^2}
  4. Compare with Choices: Compare the simplified expression with the given choices.\newlineThe simplified expression is x4y2\frac{x}{4y^2}, which matches choice (D).

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