To determine which of the two calculations is closer to [tex]\(\frac{1}{2}\)[/tex], let's go through each step carefully.
### Calculation A: [tex]\(\frac{2}{15} + \frac{1}{3}\)[/tex]
1. Convert [tex]\(\frac{1}{3}\)[/tex] to a fraction with the common denominator of 15:
[tex]\[
\frac{1}{3} = \frac{5}{15}
\][/tex]
2. Now add [tex]\(\frac{2}{15}\)[/tex] and [tex]\(\frac{5}{15}\)[/tex]:
[tex]\[
\frac{2}{15} + \frac{5}{15} = \frac{7}{15}
\][/tex]
3. Convert [tex]\(\frac{7}{15}\)[/tex] to a decimal:
[tex]\[
\frac{7}{15} \approx 0.4667
\][/tex]
### Calculation B: [tex]\(\frac{6}{7} - \frac{1}{3}\)[/tex]
1. Convert both fractions to a common denominator. The least common multiple of 7 and 3 is 21:
[tex]\[
\frac{6}{7} = \frac{18}{21}\quad \text{and}\quad \frac{1}{3} = \frac{7}{21}
\][/tex]
2. Now subtract [tex]\(\frac{7}{21}\)[/tex] from [tex]\(\frac{18}{21}\)[/tex]:
[tex]\[
\frac{18}{21} - \frac{7}{21} = \frac{11}{21}
\][/tex]
3. Convert [tex]\(\frac{11}{21}\)[/tex] to a decimal:
[tex]\[
\frac{11}{21} \approx 0.5238
\][/tex]
### Comparing to [tex]\(\frac{1}{2}\)[/tex] (which is 0.5 in decimal)
1. Find the absolute difference between Calculation A and [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\left| 0.4667 - 0.5 \right| = 0.0333
\][/tex]
2. Find the absolute difference between Calculation B and [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\left| 0.5238 - 0.5 \right| = 0.0238
\][/tex]
### Conclusion
Since the absolute difference for Calculation B (0.0238) is smaller than that for Calculation A (0.0333), Calculation B is closer to [tex]\(\frac{1}{2}\)[/tex].
Therefore, the answer is B.
