Question

9/8>11/12 what benchmark fraction is the closest

Answer 1

The closest benchmark fraction to 9/8 would be 1 since it is slightly greater than a whole. The comparison involves understanding reciprocal relationships and the effect of multiplication and division on fractions.

Step-by-step explanation:

The question asks which benchmark fraction is closest to 9/8 when comparing it to 11/12. One approach to understanding fractions is to relate them to division and multiplication. For instance, calculating one eighth of 1,000 involves multiplying 1,000 by the reciprocal of 8, which results in 125, a "125-like" number.

When dealing with fractions, we know that division is multiplication by the reciprocal. Therefore, dividing by 8 means multiplying by 1/8. Similarly, the reciprocal of 2.5 is like a "4-like" number because the entry for 2.5 would be 4. In the context of determining a benchmark fraction, 9/8 is greater than 1 and 11/12 is less than 1. When comparing fractions to benchmarks such as 1/2 or 1, 9/8 can be associated with the benchmark of 1, since it's more than a whole. However, 11/12 is closer to 1 than 1/2, yet not quite a whole, putting it near the benchmark of 1 as well.

Answer 2

We can have more info about those fractions if we take them to share the same denominator, for that we use the minimum common multiple of 8 and 12 which is 96, so we multiply and divide each fraction for a certain number that gets the fraction to denominator 96:
9/8 = (12/12)(9/8) = 12*9/12*8 = 108/96
11/12 = (8/8)(11/12) = 8*11/8*12 = 88/96
So we can write the equivalence:
9/8 > 11/12
108/96 > 88/96
we can see that the inequality is true, there are a lot of fractions yet to have them closest, 108 to 88