Final answer:
Ben should use 40 as the common denominator to compare 5/8 and 3/5. Upon conversion, 5/8 becomes 25/40, and 3/5 becomes 24/40. Thus, 5/8 is greater than 3/5 when they have the same denominator.The correct answer is option D.
Step-by-step explanation:
Ben needs to compare the fractions 5/8 and 3/5 by finding a common denominator. To find a common denominator for these two fractions, we should look for the least common multiple (LCM) of their denominators. The denominators are 8 and 5.
To find the LCM of 8 and 5, we can list their multiples:
- Multiples of 8: 8, 16, 24, 32, 40, 48, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
The smallest common multiple of 8 and 5 is 40. Therefore, the common denominator that Ben should use is 40.
To compare 5/8 and 3/5 using the new common denominator, we convert each fraction:
For 5/8: (5 × 5) / (8 × 5) = 25/40
For 3/5: (3 × 8) / (5 × 8) = 24/40
Now that both fractions have the common denominator of 40, it is easy to see that 25/40 is larger than 24/40, so 5/8 is greater than 3/5.The correct answer is option D.