Part A
We need to estimate the subtraction between the two fractions below:
[tex]\frac{10}{12}-\frac{3}{8}[/tex]To do that we need to estimate a more appropriate value for each expression, using benchmarks. We will use the benchmark values 1 and 1/2. We can then approximate each function:
[tex]\frac{10}{12}\cong1[/tex]Since the numerator 10 is very close to the denominator 12, we can estimate that its value is very close to 1.
[tex]\frac{3}{8}\cong\frac{1}{2}[/tex]We can estimate that the fraction 3/8 is very close to 1/2, because the numerator is one unit off being half of the denominator. With these estimations we can quickly calculate the estimate for the whole subtraction:
[tex]1-\frac{1}{2}=\frac{1}{2}[/tex]We estimate that the subtraction is approximately equal to 1/2.
Part B.
Now we need to actually solve the problem, the first step we will take is to simplify both fractions as much as we can:
[tex]\frac{10}{12}=\frac{5}{6}[/tex]Now we can actually subtract them:
[tex]\begin{gathered} \frac{5}{6}-\frac{3}{8}=\frac{4\cdot5-3\cdot3}{24} \\ \frac{5}{6}-\frac{3}{8}=\frac{11}{24} \end{gathered}[/tex]The actual value for the subtraction is 11/24.
Part C
Now we need to calculate the difference between our estimate and the actual value, for that we will subtract the actual value from the estimate:
[tex]\frac{1}{2}-\frac{11}{24}=\frac{1}{24}[/tex]The difference between the two is 1/24 of a unit, which means that our estimate was very close to the actual value, therefore it was reasonable.