Answer :
To find the most accurate way to estimate 48% of 67, we need to consider how close each option is to the actual value of 48% of 67. Here's how we can approach this:
1. Calculate the actual value:
- The actual calculation for 48% of 67 is [tex]\( 0.48 \times 67 \)[/tex].
- This results in 32.16.
2. Evaluate each estimation option:
- Option 1: [tex]\( \frac{1}{2} \times 66 \)[/tex]
- Calculate this: [tex]\( 0.5 \times 66 = 33 \)[/tex].
- Option 2: [tex]\( \frac{2}{3} \times 69 \)[/tex]
- Calculate this: [tex]\( \frac{2}{3} \times 69 = 46 \)[/tex].
- Option 3: [tex]\( \frac{1}{2} \times 69 \)[/tex]
- Calculate this: [tex]\( 0.5 \times 69 = 34.5 \)[/tex].
- Option 4: [tex]\( \frac{2}{3} \times 66 \)[/tex]
- Calculate this: [tex]\( \frac{2}{3} \times 66 = 44 \)[/tex].
3. Find the absolute difference between the actual value and each estimate:
- Difference for Option 1:
- [tex]\( |32.16 - 33| = 0.84 \)[/tex].
- Difference for Option 2:
- [tex]\( |32.16 - 46| = 13.84 \)[/tex].
- Difference for Option 3:
- [tex]\( |32.16 - 34.5| = 2.34 \)[/tex].
- Difference for Option 4:
- [tex]\( |32.16 - 44| = 11.84 \)[/tex].
4. Determine the most accurate option:
- The smallest difference indicates the most accurate option.
- Comparing these differences, [tex]\( 0.84 \)[/tex] is the smallest.
Therefore, the most accurate way to estimate 48% of 67 is Option 1: [tex]\( \frac{1}{2} \times 66 \)[/tex].
1. Calculate the actual value:
- The actual calculation for 48% of 67 is [tex]\( 0.48 \times 67 \)[/tex].
- This results in 32.16.
2. Evaluate each estimation option:
- Option 1: [tex]\( \frac{1}{2} \times 66 \)[/tex]
- Calculate this: [tex]\( 0.5 \times 66 = 33 \)[/tex].
- Option 2: [tex]\( \frac{2}{3} \times 69 \)[/tex]
- Calculate this: [tex]\( \frac{2}{3} \times 69 = 46 \)[/tex].
- Option 3: [tex]\( \frac{1}{2} \times 69 \)[/tex]
- Calculate this: [tex]\( 0.5 \times 69 = 34.5 \)[/tex].
- Option 4: [tex]\( \frac{2}{3} \times 66 \)[/tex]
- Calculate this: [tex]\( \frac{2}{3} \times 66 = 44 \)[/tex].
3. Find the absolute difference between the actual value and each estimate:
- Difference for Option 1:
- [tex]\( |32.16 - 33| = 0.84 \)[/tex].
- Difference for Option 2:
- [tex]\( |32.16 - 46| = 13.84 \)[/tex].
- Difference for Option 3:
- [tex]\( |32.16 - 34.5| = 2.34 \)[/tex].
- Difference for Option 4:
- [tex]\( |32.16 - 44| = 11.84 \)[/tex].
4. Determine the most accurate option:
- The smallest difference indicates the most accurate option.
- Comparing these differences, [tex]\( 0.84 \)[/tex] is the smallest.
Therefore, the most accurate way to estimate 48% of 67 is Option 1: [tex]\( \frac{1}{2} \times 66 \)[/tex].
