To calculate the product of \( \frac{4}{7} \left( -\frac{20}{2} \right) \), we first simplify \( -\frac{20}{2} \):
\[ -\frac{20}{2} = -10 \]
Now, we can rewrite the expression as:
\[ \frac{4}{7} \times (-10) \]
To multiply, we treat \(-10\) as \(-\frac{10}{1}\):
\[ \frac{4}{7} \times \left(-\frac{10}{1}\right) = \frac{4 \times -10}{7 \times 1} = \frac{-40}{7} \]
To express this in mixed number form:
\(-40\) divided by \(7\) gives \(-5\) with a remainder of \(5\), so:
\[ \frac{-40}{7} = -5 \frac{5}{7} \]
Thus, the final result is:
\(-5 \frac{5}{7}\)
Among the options listed:
- −5 and 5 sevenths is the same as our result.
So the correct answer is:
\(-5 \frac{5}{7}\)
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