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 $.

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. 

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. 

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Updated on: 10-Oct-2022

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