QUESTION

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

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.

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.