To find an expression that represents another method of computing \( 5 \frac{2}{3} \times 7 \), let's first convert \( 5 \frac{2}{3} \) into an improper fraction.
We have:
\[ 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \]
Thus, we want to compute \( \frac{17}{3} \times 7 \), which is the same as:
\[ \frac{17 \times 7}{3} = \frac{119}{3} \]
Now, let's analyze each of the given options:
A. \( (- 5 \times 7) + (- \frac{2}{3} \times 7) \)
This simplifies to \( -35 - \frac{14}{3} \), which does not equal \( \frac{119}{3} \).
B. \( (- 5(- 7)) + (- \frac{2}{3} \times (- 7)) \)
This simplifies to \( 35 + \frac{14}{3} \), which does equal \( \frac{119}{3} \). This is possible since \( 35 = \frac{105}{3} \) and combining gives \( \frac{105 + 14}{3} = \frac{119}{3} \).
C. \( (- 5 \frac{2}{3})(- 7) \)
This equals \( \frac{17}{3} \times (-7) = -\frac{119}{3} \), which does not equal \( \frac{119}{3} \).
D. \( (- 1)(5 - \frac{2}{3})(7) \)
This simplifies to \( - (5 - \frac{2}{3}) \times 7 \); since \( 5 - \frac{2}{3} = \frac{15}{3} - \frac{2}{3} = \frac{13}{3} \) thus becomes \( - \frac{13}{3} \times 7 = -\frac{91}{3} \), which does not equal \( \frac{119}{3} \).
After evaluating all options, the correct expression that computes \( 5 \frac{2}{3} \times 7 \) is:
B. \( (- 5(- 7)) + (- \frac{2}{3} \times (- 7)) \)
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