Question

Name the property indicated in the following:
$\frac{3}{4}\cdot \frac{9}{5}=\frac{27}{20}$

Answer 1

We know that for some rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, if $\frac{a}{b}\times \frac{c}{d}$ is also a rational number then the set of rational numbers is said to be closed under the operation of multiplication.

Here, both $\frac{3}{4}$ and $\frac{9}{5}$ are rational numbers. Also, the multiplication of $\frac{3}{4}$ and $\frac{9}{5}$ is $\frac{27}{20}$ which is also a rational number.

Hence, $\frac{3}{4}\times \frac{9}{5}=\frac{27}{20}$ satisfies the closure property of multiplication.