Multiply $3 / 4 \times 16 / 9$.
A. $64 / 27$
B. $4 / 3$
C. $27 / 64$
D. $3 / 4$
Answer (2)
Multiply the numerators: $3
\times 16 = 48$.
Multiply the denominators: $4
\times 9 = 36$.
Write the fraction: 36 48 .
Simplify the fraction: 36 48 = 3 4 .
3 4
Explanation
Problem Analysis We are asked to multiply two fractions, 3/4 and 16/9 .
Multiplying Numerators and Denominators To multiply fractions, we multiply the numerators and multiply the denominators: 4 3 × 9 16 = 4 × 9 3 × 16
Calculating the Products Now we perform the multiplications: 3 × 16 = 48 and 4 × 9 = 36 . So we have: 36 48
Simplifying the Fraction To simplify the fraction, we look for common factors in the numerator and the denominator. Both 48 and 36 are divisible by 12. Dividing both by 12, we get: 36 ÷ 12 48 ÷ 12 = 3 4
Final Answer Therefore, the product of the two fractions is 3 4 .
Examples
In baking, if a recipe calls for 3/4 of a cup of flour and you want to make 16/9 times the recipe, you would multiply these two fractions to find out how much flour you need. This ensures accurate scaling of ingredients for consistent results.
The result of multiplying 4 3 × 9 16 is 3 4 after simplifying the fraction. Therefore, the correct answer is option B. 3 4 .
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