Answer :
To estimate 77% of 86, we are looking for an approximate value that is close and easy to calculate. Here is a step-by-step guide on how to determine which given option is the most accurate:
1. Calculate 77% of 86:
[tex]\[
77\% \text{ of } 86 = \frac{77}{100} \times 86 = 66.22
\][/tex]
So, 66.22 is our target value.
2. Evaluate the options:
We want to see which of the presented options provides a number closest to 66.22.
- Option 1: [tex]\(\frac{1}{2} \times 88\)[/tex]:
[tex]\[
\frac{1}{2} \times 88 = 44
\][/tex]
- Option 2: [tex]\(\frac{3}{4} \times 88\)[/tex]:
[tex]\[
\frac{3}{4} \times 88 = 66
\][/tex]
- Option 3: [tex]\(\frac{3}{4} \times 89\)[/tex]:
[tex]\[
\frac{3}{4} \times 89 = 66.75
\][/tex]
- Option 4: [tex]\(\frac{1}{2} \times 89\)[/tex]:
[tex]\[
\frac{1}{2} \times 89 = 44.5
\][/tex]
3. Find the closest estimate:
- The difference from 66.22 for each option is calculated as follows:
- Option 1: [tex]\(|66.22 - 44| = 22.22\)[/tex]
- Option 2: [tex]\(|66.22 - 66| = 0.22\)[/tex]
- Option 3: [tex]\(|66.22 - 66.75| = 0.53\)[/tex]
- Option 4: [tex]\(|66.22 - 44.5| = 21.72\)[/tex]
4. Determine the most accurate option:
The option with the smallest difference from 66.22 is Option 2, with a difference of 0.22.
Therefore, the most accurate way to estimate 77% of 86 is [tex]\(\frac{3}{4} \times 88\)[/tex].
1. Calculate 77% of 86:
[tex]\[
77\% \text{ of } 86 = \frac{77}{100} \times 86 = 66.22
\][/tex]
So, 66.22 is our target value.
2. Evaluate the options:
We want to see which of the presented options provides a number closest to 66.22.
- Option 1: [tex]\(\frac{1}{2} \times 88\)[/tex]:
[tex]\[
\frac{1}{2} \times 88 = 44
\][/tex]
- Option 2: [tex]\(\frac{3}{4} \times 88\)[/tex]:
[tex]\[
\frac{3}{4} \times 88 = 66
\][/tex]
- Option 3: [tex]\(\frac{3}{4} \times 89\)[/tex]:
[tex]\[
\frac{3}{4} \times 89 = 66.75
\][/tex]
- Option 4: [tex]\(\frac{1}{2} \times 89\)[/tex]:
[tex]\[
\frac{1}{2} \times 89 = 44.5
\][/tex]
3. Find the closest estimate:
- The difference from 66.22 for each option is calculated as follows:
- Option 1: [tex]\(|66.22 - 44| = 22.22\)[/tex]
- Option 2: [tex]\(|66.22 - 66| = 0.22\)[/tex]
- Option 3: [tex]\(|66.22 - 66.75| = 0.53\)[/tex]
- Option 4: [tex]\(|66.22 - 44.5| = 21.72\)[/tex]
4. Determine the most accurate option:
The option with the smallest difference from 66.22 is Option 2, with a difference of 0.22.
Therefore, the most accurate way to estimate 77% of 86 is [tex]\(\frac{3}{4} \times 88\)[/tex].
