Questions: Decide whether the statement is an example of a commutative, associative, identity or inverse property, or of the distributive property. (left(5/7)right)cdot(left(7/5)right)=1 Choose the correct answer below. A. Associative property B. Commutative property C. Identity property D. Inverse property E. Distributive property

Solution Steps

The given statement \(\left(\frac{5}{7}\right) \cdot\left(\frac{7}{5}\right)=1\) is an example of the inverse property. The inverse property states that for any non-zero number \(a\), there exists a number \(b\) such that \(a \cdot b = 1\). In this case, \(\frac{5}{7}\) and \(\frac{7}{5}\) are multiplicative inverses of each other.

The given statement is \(\left(\frac{5}{7}\right) \cdot \left(\frac{7}{5}\right) = 1\). This expression involves two fractions, \(\frac{5}{7}\) and \(\frac{7}{5}\), which are multiplied together to yield 1.

The inverse property of multiplication states that for any non-zero number \(a\), there exists a number \(b\) such that \(a \cdot b = 1\). Here, we have: \[ a = \frac{5}{7} \approx 0.7143 \] \[ b = \frac{7}{5} = 1.4 \] Multiplying these two numbers: \[ a \cdot b = \frac{5}{7} \cdot \frac{7}{5} = 1 \] This confirms that \(\frac{5}{7}\) and \(\frac{7}{5}\) are multiplicative inverses of each other.

Final Answer