Question

Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and for the solution.

Answer 1

The estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.

Explanation:

The given expression is

`(10)/(12)-(3)/(8)`

Case 1: Let the benchmark value be 1/2.

10/12 > 3/4 so we round it to 1.

1/4 ≤ 3/8 ≤ 3/4 so we round it to 1/2.

Estimating the solution:

1 - 1/2 = 1/2

Case 2: Let the benchmark value be 1/4.

5/8 ≤ 10/12 < 7/8 so we round it to 3/4.

3/8 ≤ 3/8 < 5/8 so we round it to 2/4.

Estimating the solution:

3/4 - 2/4 = 1/4

Case 3: Let the benchmark value be 1/8.

13/16 ≤ 10/12 < 15/16 so we round it to 7/8.

5/16 ≤ 3/8 < 7/16 so we round it to 3/8.

Estimating the solution:

7/8 - 3/8 = 1/2

Therefore the estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.