Question

Name the property under multiplication used in the following:$\frac{-13}{17}\times \left(\frac{-2}{7}\right)=\frac{-2}{7}\times \left(\frac{-13}{17}\right)$

Answer 1

Property used in Multiplication.

According to the commutative property of multiplication by changing the order of factors there is no change in the end product.

Here, $\frac{-13}{17}\times \left(\frac{-2}{7}\right)=\frac{-2}{7}\times \left(\frac{-13}{17}\right)$

Solve $\mathrm{LHS}$:

$\begin{array}{c}\mathrm{LHS}=\frac{-13}{17}\times \left(\frac{-2}{7}\right)\\ \Rightarrow \mathrm{LHS}=\frac{-13\times -2}{17\times 7}\\ \Rightarrow \mathrm{LHS}=\frac{26}{119}\end{array}$

Solve $\mathrm{RHS}$:

$\begin{array}{c}\mathrm{RHS}=\frac{-2}{7}\times \frac{-13}{17}\\ \Rightarrow \mathrm{RHS}=\frac{-2\times -13}{7\times 17}\\ \Rightarrow \mathrm{RHS}=\frac{26}{119}\end{array}$

$\mathrm{LHS}=\mathrm{RHS}$

Hence, the property under multiplication used in $\frac{-13}{17}\times \left(\frac{-2}{7}\right)=\frac{-2}{7}\times \left(\frac{-13}{17}\right)$ is the commutative property of multiplication.