Question

Use the Properties of Identity, Inverse and Zero ,simplify$\frac{13}{15}\times \frac{9}{17}\times \frac{15}{13}$

Short answer

The simplified form of$\frac{13}{15}\times \frac{9}{17}\times \frac{15}{13}is\frac{9}{17}.$

Step-by-step solution

. Given information

Given expression is $\frac{13}{15}\times \frac{9}{17}\times \frac{15}{13}$,

Simplify the given expression Using the Properties of Inverse .

. Description of inverse property multiplication

Inverse property of multiplication: For any real number a,$a\ge 0,a\times \frac{1}{a}=1,\frac{1}{a}isthemultiplicateinverseofa.$

.  Simplification using inverse property of multiplication

We can write the expression like this$$\begin{gathered} \frac{13}{15}\times \frac{9}{17}\times \frac{15}{13}=\frac{13}{15}\times \frac{15}{13}\times \frac{9}{17} \\ =1\times \frac{9}{17} \\ =\frac{9}{17} \end{gathered}$$