Answer:
(a)1/2
(b)11/24
Explanation:
Given the difference:
[tex]\frac{10}{12}-\frac{3}{8}[/tex]
Part A
First, we estimate the difference using benchmark values.
[tex]\begin{gathered} \frac{10}{12}\text{ is closer to }\frac{12}{12}=1 \\ \frac{3}{8}\text{ is closer to }\frac{4}{8}=\frac{1}{2} \\ \text{Therefore:} \\ \frac{10}{12}-\frac{3}{8}\approx1-\frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]
Part B
Here, we find the actual difference.
[tex]\begin{gathered} \frac{10}{12}-\frac{3}{8} \\ T\text{ake the lowest co}mmon\text{ multiple of the denominators} \\ =\frac{20-9}{24} \\ =\frac{11}{24} \end{gathered}[/tex]
Part C
Here, the difference between the estimate and the actual value is calculated.
[tex]\begin{gathered} \text{Estimated Value-Actual Value} \\ =\frac{1}{2}-\frac{11}{24} \\ =\frac{12}{24}-\frac{11}{24} \\ =\frac{12-11}{24} \\ =\frac{1}{24} \end{gathered}[/tex]
A reasonable estimate does not exceed the original numbers in the problem. Thus, the estimate for part A was reasonable.
