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

Step 1:Given information

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

Simplify the given expression using inverse property of multiplication.

Step 2:Decription 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$$\begin{gathered} \frac{13}{15}\times \frac{9}{17}\times \frac{15}{13}=\frac{13}{15}\times \frac{15}{13}\times \frac{9}{17} \\ =1\times \frac{9}{17} \\ =\frac{9}{17} \end{gathered}$$$$\begin{gathered} \frac{13}{15}.\frac{9}{17}.\frac{15}{13}=\frac{13}{15}.\frac{15}{13}.\frac{9}{17} \\ =1.\frac{9}{17} \\ =\frac{9}{17} \end{gathered}$$

Since the first and third terms

are reciprocals, so use the Commutative Property of multiplication to re-order the factors.