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Sagot :
Answer:
[tex]\begin{gathered} A\text{. 1/2} \\ B\text{. 11/24} \\ C\text{. }\frac{1}{24} \\ \end{gathered}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Step-by-step explanation:
For part A,
-estimate the fraction 10/12 using 1/2 as our benchmark
The lower range is 1/2 and the upper range is 1
The halfway point is:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{(1+2)}{2} \\ \frac{1}{2}\cdot\frac{3}{2}=\frac{3}{4} \end{gathered}[/tex]Therefore, our range is 1/2 < 3/4 < 1
10/12 ≥ 3/4, we round up to 1
-estimate the fraction 3/8 using the 1/2 as our benchmark:
The lower range is 0 and the upper range is 1/2
The halfway point is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore, our range is 0 < 1/4 < 1/2
3/8 ≥ 1/4, we round up to 1/2
[tex]\frac{2}{2}-\frac{1}{2}=\frac{1}{2}[/tex]For part B, the denominators are 12 and 8, so the LCM would be;
[tex]\text{LCM}=24[/tex]Then, we make a common denominator and subtract the numerators
[tex]\begin{gathered} \frac{10}{12}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24} \\ \frac{10}{12}-\frac{3}{8}=\frac{11}{24} \end{gathered}[/tex]For part C, compute the difference between the two results from parts A and B:
[tex]\frac{1}{2}-\frac{11}{24}=\frac{1}{24}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
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