Question

The multiplicative inverse of a number is also called ____ of that number.
a) identity
b) reciprocal
c) additive inverse
d) multiplicative identity

Answer 1

Hint: The expression ‘inverse’ denotes something that is opposite in effect. So, the reciprocal of any number multiplied with the number gives the result 1.

Complete step by step answer:
Multiplicative inverse of a number is also called reciprocals, because for finding a reciprocal we flip a fraction, or swap the numerator and denominator. For example-
Reciprocal of $\dfrac{2}{3}$ is $\dfrac{3}{2}$, 2 is $\dfrac{1}{2}$. So when we multiply them together, we get 1.
\[\Rightarrow \dfrac{2}{3}\times \dfrac{3}{2}=1\]
\[\Rightarrow \dfrac{1}{2}\times 2=1\]
As we know that an identity is an equality between two expressions. So we can’t say multiplicative inverse as the identity of a number.
Additive inverse is a number which when added with a given number then the result equals to zero. So multiplicative inverse can’t be additive inverse.
Multiplicative identity is 1 because when it is multiplied with a given number then the answer is 1. So multiplicative inverse can’t be a multiplicative identity.
Hence option b is correct.

Note: While answering this question we have to be careful with multiplicative identity because the multiplicative inverse final answer should be 1 and multiplicative identity of any number is 1.