Question

Which difference will be closest to 1/2?

A) 7/8 - 5/6
B) 45 - 1/10
C) 7/12 - 1/6
D) 9/10 - 1/8

Answer 1

Upon evaluating all the options by finding common denominators and performing the subtractions, Option D (9/10 - 1/8) results in the difference closest to 1/2.

Step-by-step explanation:

To find which difference will be closest to 1/2, we need to compare the differences between the pairs of fractions (and numbers) provided. Let's evaluate each option:

1. 7/8 - 5/6: To subtract these fractions, we need a common denominator. The least common multiple of 8 and 6 is 24, so 7/8 becomes 21/24 and 5/6 becomes 20/24. The difference is 1/24, which is much less than 1/2.
2. 45 - 1/10: Subtracting 1/10 from 45 leaves us with 44.9, which is much larger than 1/2.
3. 7/12 - 1/6: The common denominator between 12 and 6 is 12, so we rewrite 1/6 as 2/12. Then, 7/12 - 2/12 equals 5/12, which is close to 1/2 but a little more.
4. 9/10 - 1/8: Finding a common denominator for 10 and 8, which is 40, we get 36/40 minus 5/40, which results in 31/40. This difference is the closest to 1/2 as it is slightly more than 3/4 and less than 1.

Option D, 9/10 - 1/8, will provide the difference closest to 1/2 when compared to the other options presented.