4. Which of the following statements best explains why 3/4 and 6/8 are equal?
Answer: D
The point on a number line that represents 3/4 also represents 6/8.
Both 3/4 and 6/8 represent the same point on a number line, confirming that they are equal fractions. When plotted, both values correspond to the same location between 0 and 1.
A) The denominators are both multiples of 2.
While it is true that both denominators (4 and 8) are multiples of 2, this statement does not directly explain the equality of the fractions. It fails to address how the numerators relate to the denominators in establishing that 3/4 and 6/8 are equivalent.
B) 3/4 of a pizza is the same size as 6/8 of a brownie.
This statement may seem plausible in a real-world context, but it does not mathematically explain why the two fractions are equal. The comparison of different items does not provide a valid justification for their equivalence.
C) 4 is the greatest common factor of the denominators.
This statement is incorrect. The greatest common factor of the denominators 4 and 8 is actually 4, but this information alone does not clarify the relationship between the two fractions or why they are equal. It does not illustrate their equivalency on a number line.
D) The point on a number line that represents 3/4 also represents 6/8.
This statement accurately explains the equality of the two fractions. When both fractions are plotted on a number line, they occupy the exact same position, thereby demonstrating their equivalence.
Conclusion
The correct answer, which identifies that the point on a number line representing 3/4 also represents 6/8, clearly illustrates the mathematical concept of equivalent fractions. Other options either provide irrelevant information or fail to accurately represent the relationship between the two fractions. Hence, only option D effectively explains their equality.