Question

Name the property under multiplication used in each of the following:
(i) $\frac{2}{3}\times \frac{4}{5}=\frac{4}{5}\times \frac{2}{3}$
(ii) $\left(\frac{-3}{4}\right)\times 1=\frac{-3}{4}=1\times \left(\frac{-3}{4}\right)$
(iii) $\left(\frac{-17}{28}\right)\times \left(\frac{-28}{17}\right)=1$
(iv) $\frac{1}{5}\times (\frac{7}{8}\times \frac{4}{3})=(\frac{1}{5}\times \frac{7}{8})\times \frac{4}{3}$
(v) $\frac{2}{7}\times (\frac{9}{10}+\frac{2}{5})=\frac{2}{7}\times \frac{9}{10}+\frac{2}{7}\times \frac{2}{5}$

Answer 1

(i) Commutative property

When two numbers are multiplied together, the product is the same regardless of the order

of the multiplicands.

(ii) Identity property of multiplication

The product of 1 and any number is that number.

(iii) Inverse Property of Multiplication

Inverse Property of Multiplication says that any number multiplied by its reciprocal is equal

to one.

(iv) Associative property

Changing the grouping of factors does not change the product.

(v) Distributive property

The sum of two numbers times a third number is equal to the sum of each addend times the

third number.