Question

What is the multiplicative inverse of – 7?
(a). 7
(b). \[\dfrac{1}{7}\]
(c). – 7
(d). \[ - \dfrac{1}{7}\]

Answer 1

Hint: Multiplicative inverse is when one of the pairs of the numbers when multiplied with another, gives 1. Use this definition to find the multiplicative inverse of – 7.

Complete step-by-step answer:
The multiplicative inverse is an inverse of a number. Inverse means something opposite in effect. It is one of a pair of numbers which when multiplied with another number equals 1, which is the multiplicative identity. For example, the multiplicative inverse of 2 is \[\dfrac{1}{2}\].

In this problem, we need to find the multiplicative inverse of – 7. In other words, we need to find a
number, which when multiplied with – 7, we get the result as 1.
Let the other number be x.
Hence, we have the following equation:
\[ - 7 \times x = 1\]
We divide both the left-hand side and the right-hand side of the above equation by 7. Then, we get
as follows:
\[\dfrac{{ - 7 \times x}}{7} = \dfrac{1}{7}\]
Canceling the common terms in the numerator and denominator in the left-hand side of the above
equation, we have:
\[ - 1 \times x = \dfrac{1}{7}\]
Next, we multiply both the left-hand side and the right-hand side of the equation with – 1 to get as
follows:
\[ - 1 \times - 1 \times x = - 1 \times \dfrac{1}{7}\]
When two negative numbers are multiplied we get a positive number and when one negative and
one positive number is multiplied we get a negative number, so we get:
\[1 \times x = - \dfrac{1}{7}\]
The number 1 is the multiplicative identity, hence, 1 multiplied with any number is the number itself.
\[x = - \dfrac{1}{7}\]
Hence, the multiplicative inverse of – 7 is \[ - \dfrac{1}{7}\].
Hence, the correct answer is option (d).

Note: You might confuse with additive inverse and choose the number 7 as the correct answer but it
is wrong. The multiplicative inverse is when one of the pair of the numbers when multiplied with
another, gives 1.