Which of the following fraction pairs are equivalent fractions?
A 1/2 and 17/32
B 1/2 and 32/64
C 1/2 and 3/4
D 1/2 and 63/128
The correct answer and explanation is:
The correct answer is B: 1/2 and 32/64.
To determine if two fractions are equivalent, you need to check if they represent the same value. This can be done by simplifying one fraction or cross-multiplying the two fractions.
Let’s analyze each option:
- 1/2 and 17/32:
To check if these fractions are equivalent, simplify both fractions or cross-multiply.
Cross-multiplying:
1×32=321 \times 32 = 32
2×17=342 \times 17 = 34
Since 32 is not equal to 34, these fractions are not equivalent. - 1/2 and 32/64:
Simplify 32/64 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 32: 3264=32÷3264÷32=12\frac{32}{64} = \frac{32 \div 32}{64 \div 32} = \frac{1}{2} Since 32/64 simplifies to 1/2, these fractions are equivalent. - 1/2 and 3/4:
Cross-multiply to check:
1×4=41 \times 4 = 4
2×3=62 \times 3 = 6
Since 4 is not equal to 6, these fractions are not equivalent. - 1/2 and 63/128:
Cross-multiply:
1×128=1281 \times 128 = 128
2×63=1262 \times 63 = 126
Since 128 is not equal to 126, these fractions are not equivalent.
Thus, the only pair of equivalent fractions is 1/2 and 32/64.