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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.
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.