Difficulty: Easy

Average Score: 77%

Which of the following statements best explains why 3/4 and 6/8 are equal?

Rationale

The point on a number line that represents 3/4 also represents 6/8.

Both fractions, 3/4 and 6/8, are equal because they represent the same point on the number line. When simplified, 6/8 reduces to 3/4, confirming their equivalence in terms of value.

A (The denominators are both multiples of 2.) YOUR ANSWER

While it is true that both denominators (4 and 8) can be divided by 2, this fact does not explain the equality of the two fractions. The multiple relationship does not directly show that the fractions represent the same value or point on the number line.

B (3/4 of a pizza is the same size as 6/8 of a brownie.) YOUR ANSWER

This statement may suggest a comparison of sizes, but it does not provide a mathematical explanation for why the two fractions are equal. The equality of fractions is determined by their numerical values rather than their physical representations in different contexts.

C (4 is the greatest common factor of the denominators.) YOUR ANSWER

The greatest common factor (GCF) of the denominators does not address the equality of the fractions. While the GCF can help simplify fractions, it does not explain why 3/4 equals 6/8; it is the actual values represented by the fractions that matter.

Conclusion

The equality of the fractions 3/4 and 6/8 is best understood by their representation on the number line. Both fractions correspond to the same point, demonstrating their equivalence. Understanding this visual relationship clarifies why they are equal, independent of their denominators or contexts in which they are presented.

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