Question

Write the multiplicative inverse of each of the following rational numbers: $7$; $-11$; $\dfrac{2}{5}$; $\dfrac{-7}{15}$ ?

Answer 1

Hint: A multiplicative inverse of a number is a number which when multiplied with the original number produces 1. So to find the multiplicative inverse, you need to divide 1 by the number for which you want to find the multiplicative inverse. In other words, you should find the reciprocal of the number to find the multiplicative inverse.

Complete step by step solution:
Here is the step wise solution.
The first step to do is to divide 1 by each of the numbers, that is we need to find the reciprocal of the numbers to find the multiplicative inverse, as multiplicative inverse of a number returns 1 when multiplied by the number.
Therefore, the multiplicative inverse of 7 is $\dfrac{1}{7}$
The multiplicative inverse of -11 is $\dfrac{-1}{11}$
The multiplicative inverse of $\dfrac{2}{5}$ is $\dfrac{1}{\dfrac{2}{5}} = \dfrac{5}{2}$
The multiplicative inverse of $\dfrac{-7}{15}$ is $\dfrac{1}{\dfrac{-7}{15}} = \dfrac{-15}{7}$
Therefore, we get the final answer of the question, write the multiplicative inverse of each of the following rational numbers: $7$; $-11$; $\dfrac{2}{5}$; $\dfrac{-7}{15}$ as $\dfrac{1}{7}$ , $\dfrac{-1}{11}$ , $\dfrac{5}{2}$ , $\dfrac{-15}{7}$ .

Note: You need to remember what the multiplicative inverse. Also the multiplicative inverse of a multiplicative inverse if a numbers gives back the number. You can also consider multiplicative inverse as the number to the power of -1. You also have another inverse called the additive inverse. Additive inverse is a number which added to the original number gives 0. So additive inverse is just the negative or the opposite of the number.