Answer :
To estimate 50% of 65, we start by calculating 50% of 65 directly:
- 50% of 65 is calculated as [tex]\( 0.5 \times 65 = 32.5 \)[/tex].
Next, we evaluate each given option to see which is the most accurate estimate:
1. Option A: [tex]\(\frac{1}{3} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{3} \times 66 = 22.0 \)[/tex]
2. Option B: [tex]\(\frac{2}{3} \times 66\)[/tex]
- Calculate: [tex]\( \frac{2}{3} \times 66 = 44.0 \)[/tex]
3. Option C: [tex]\(\frac{1}{4} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{4} \times 66 = 16.5 \)[/tex]
4. Option D: [tex]\(\frac{1}{2} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{2} \times 66 = 33.0 \)[/tex]
Now let's determine which option is closest to 32.5:
- Difference between 32.5 and Option A: [tex]\( |32.5 - 22.0| = 10.5 \)[/tex]
- Difference between 32.5 and Option B: [tex]\( |32.5 - 44.0| = 11.5 \)[/tex]
- Difference between 32.5 and Option C: [tex]\( |32.5 - 16.5| = 16.0 \)[/tex]
- Difference between 32.5 and Option D: [tex]\( |32.5 - 33.0| = 0.5 \)[/tex]
The smallest difference is 0.5, occurring with Option D: [tex]\(\frac{1}{2} \times 66\)[/tex].
Therefore, the most accurate way to estimate 50% of 65 from the given options is [tex]\(\frac{1}{2} \times 66\)[/tex], which gives us 33.0.
- 50% of 65 is calculated as [tex]\( 0.5 \times 65 = 32.5 \)[/tex].
Next, we evaluate each given option to see which is the most accurate estimate:
1. Option A: [tex]\(\frac{1}{3} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{3} \times 66 = 22.0 \)[/tex]
2. Option B: [tex]\(\frac{2}{3} \times 66\)[/tex]
- Calculate: [tex]\( \frac{2}{3} \times 66 = 44.0 \)[/tex]
3. Option C: [tex]\(\frac{1}{4} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{4} \times 66 = 16.5 \)[/tex]
4. Option D: [tex]\(\frac{1}{2} \times 66\)[/tex]
- Calculate: [tex]\( \frac{1}{2} \times 66 = 33.0 \)[/tex]
Now let's determine which option is closest to 32.5:
- Difference between 32.5 and Option A: [tex]\( |32.5 - 22.0| = 10.5 \)[/tex]
- Difference between 32.5 and Option B: [tex]\( |32.5 - 44.0| = 11.5 \)[/tex]
- Difference between 32.5 and Option C: [tex]\( |32.5 - 16.5| = 16.0 \)[/tex]
- Difference between 32.5 and Option D: [tex]\( |32.5 - 33.0| = 0.5 \)[/tex]
The smallest difference is 0.5, occurring with Option D: [tex]\(\frac{1}{2} \times 66\)[/tex].
Therefore, the most accurate way to estimate 50% of 65 from the given options is [tex]\(\frac{1}{2} \times 66\)[/tex], which gives us 33.0.
