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Here are two calculations:

[tex]\[
\begin{array}{l}
\frac{2}{15} + \frac{1}{3} \quad \text{(A)} \\
\frac{6}{7} - \frac{1}{3} \quad \text{(B)}
\end{array}
\][/tex]

Which of the two calculations is closer in value to [tex]\(\frac{1}{2}\)[/tex]?

You must show your working and state clearly whether the answer is A or B.



Answer :

GinnyAnswer
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.

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