Q59. - Algebra 2

Question

Name the property illustrated by each equation.

 

59. $\frac{7}{9}.\frac{9}{7}=1$

Step-by-Step Solution

Answer

The property illustrated by the equation $\frac{7}{9}·\frac{9}{7}=1$ is inverse property of multiplication.

Step 1 - Define inverse property of multiplication

The inverse property of multiplication is if $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$ where $\frac{1}{a}$ is the multiplicative inverse if a and vice versa.

Step 2 - State an example

Give an example to illustrate the inverse property of multiplication. Let $\mathrm{\pi }$, then $\frac{1}{a}$ will be the multiplicative inverse since $a\ne 0$.

$\begin{array}{c}a\cdot \frac{1}{a}=1\\ \frac{4}{3}\cdot \frac{1}{a}=1\\ \frac{1}{a}=\frac{3}{4}\end{array}$

Therefore, $\frac{4}{3}·\frac{3}{4}=1=\frac{3}{4}·\frac{4}{3}$.

Step 3 - State the conclusion

Since it is given that $\frac{7}{9}·\frac{9}{7}=1$, therefore, as per the definition of inverse property of multiplication, $\frac{7}{9}$ and $\frac{9}{7}$ are multiplicative inverses of each other.