# Name the property under multiplication used in each of the following.(i) $\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}$(ii) $-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}$(iii) $\frac{-19}{29} \times \frac{29}{-19}=1$.

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Given:

(i) $\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}$
(ii) $-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}$
(iii) $\frac{-19}{29} \times \frac{29}{-19}=1$.

To do:

We have to name the property under multiplication used in each case.

Solution:

(i) Multiplicative Identity:

One (1) is the multiplicative identity of rational numbers. When we multiply a rational number with 1, the result will always be the same rational number.

Therefore,

Multiplicative identity is used in the given expression.
(ii) $-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}$ is commutative property of multiplication.

(iii) $\frac{-19}{29} \times \frac{29}{-19}=1$ is multiplicative inverse property.

Updated on 10-Oct-2022 13:47:38