Which of the following pairs of fractions is equivalent?

Rationale

2/3 and 10/15 are equivalent fractions.

Both fractions represent the same value when simplified. The fraction 10/15 can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 5, resulting in 2/3. Therefore, these two fractions are indeed equivalent.

A (5/9 and 45/72) YOUR ANSWER

To determine if these fractions are equivalent, we can simplify 45/72 by dividing both the numerator and denominator by their greatest common divisor, which is 9. This results in 5/8, not 5/9; hence, they are not equivalent.

B (4/5 and 7/4) YOUR ANSWER

These fractions are not equivalent as they represent different values. The fraction 4/5 is less than 1, while 7/4 is greater than 1. Their different values indicate that they cannot be equivalent fractions.

D (3/8 and 8/13) YOUR ANSWER

Similar to the previous choices, these fractions are not equivalent. When evaluated, 3/8 is approximately 0.375, while 8/13 is approximately 0.615. Since the values differ, they do not represent the same fraction.

Conclusion

The equivalence of fractions is determined by whether they simplify to the same value. Among the options provided, 2/3 and 10/15 are equivalent, as shown by the simplification process. The other pairs do not yield the same values upon evaluation, confirming that they are not equivalent fractions. Understanding how to simplify fractions is crucial for identifying equivalencies accurately.

Which of the following pairs of fractions is equivalent?

2/3 and 10/15 are equivalent fractions.

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