Select the best answer for the question. What is the product of [tex]$7 / 16, 4 / 3$[/tex], and [tex]$1 / 2$[/tex]? A. [tex]$2^{13} / 48$[/tex] B. [tex]$7 / 12$[/tex] C. [tex]$21 / 32$[/tex] D. [tex]$7 / 24$[/tex]
Answer (2)
Multiply the numerators: 7 × 4 × 1 = 28 .
Multiply the denominators: 16 × 3 × 2 = 96 .
Simplify the resulting fraction: 96 28 = 24 7 .
The product of the fractions is 24 7 .
Explanation
Understanding the Problem We need to find the product of the fractions 16 7 , 3 4 , and 2 1 . This means we need to multiply these three fractions together.
Multiplying the Fractions To find the product, we multiply the numerators together and the denominators together: 16 7 × 3 4 × 2 1 = 16 × 3 × 2 7 × 4 × 1
Simplifying the Result Now we simplify the fraction: 16 × 3 × 2 7 × 4 × 1 = 96 28 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 96 ÷ 4 28 ÷ 4 = 24 7
Final Answer Therefore, the product of 16 7 , 3 4 , and 2 1 is 24 7 .
Examples
Understanding fraction multiplication is essential in many real-life scenarios. For instance, when baking, you might need to halve a recipe that calls for 3 4 cups of flour. This requires multiplying 2 1 by 3 4 . Similarly, if you're calculating how much of your monthly budget ( 16 7 of your income) you'll spend on groceries, and you only spend half of that amount, you're essentially multiplying 16 7 by 2 1 . These calculations help in managing resources and planning effectively.
The product of the fractions 16 7 , 3 4 , and 2 1 is 24 7 . Therefore, the correct answer is option D. Simplifying the resulting fraction gives us the final result.
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