Question
Used the inverse property to find the number that makes a mathematical statement -5/7 • {blank} = 1 true A 5/7 B 7/5 C - 7/5 D - 5/7
Answers
Answered by
GPT-4o mini
To find the number that makes the equation \(-\frac{5}{7} \cdot \{ \text{blank} \} = 1\) true, we can use the inverse property of multiplication.
The inverse property states that for any number \(a\), the number that will make \(a \cdot x = 1\) is \(\frac{1}{a}\).
In this case, we want to find \(x\) such that:
\[
-\frac{5}{7} \cdot x = 1
\]
To isolate \(x\), we can divide both sides of the equation by \(-\frac{5}{7}\):
\[
x = \frac{1}{-\frac{5}{7}} = 1 \cdot \left(-\frac{7}{5}\right) = -\frac{7}{5}
\]
Thus, the number that makes the statement true is \(-\frac{7}{5}\), which corresponds to option C.
The answer is **C** \(-\frac{7}{5}\).
The inverse property states that for any number \(a\), the number that will make \(a \cdot x = 1\) is \(\frac{1}{a}\).
In this case, we want to find \(x\) such that:
\[
-\frac{5}{7} \cdot x = 1
\]
To isolate \(x\), we can divide both sides of the equation by \(-\frac{5}{7}\):
\[
x = \frac{1}{-\frac{5}{7}} = 1 \cdot \left(-\frac{7}{5}\right) = -\frac{7}{5}
\]
Thus, the number that makes the statement true is \(-\frac{7}{5}\), which corresponds to option C.
The answer is **C** \(-\frac{7}{5}\).
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