Question

which of the following pairs of fractions is equivalent to 5/6 and 7/8? 10/16 and 14/16 10/12 and 14/12 20/24 and 21/24 20/48 and 42/48

Explanation:

Step1: Find common denominator for 5/6 and 7/8

The least common denominator of 6 and 8 is 24.

Step2: Convert 5/6 to denominator 24

Multiply numerator and denominator by 4: $\frac{5\times4}{6\times4}=\frac{20}{24}$

Step3: Convert 7/8 to denominator 24

Multiply numerator and denominator by 3: $\frac{7\times3}{8\times3}=\frac{21}{24}$

Step4: Check each option

• Option 1: 10/16 and 14/16. Denominator 16, not 24. Incorrect.
• Option 2: 10/12 and 14/12. Denominator 12, not 24. Incorrect.
• Option 3: 20/24 and 21/24. Matches converted fractions. Correct.
• Option 4: 20/48 and 42/48. 42/48 simplifies to 7/8? No, 7/8 is 42/48? Wait, 7×6=42, 8×6=48, but 5/6 is 40/48, not 20/48. So incorrect.

Answer:

20/24 and 21/24 (the third option)