Question

What is the multiplicative inverse of -27 and what is the multiplicative inverse for 7/9 and -9/16

Answer 1

The multiplicative inverse of a number is the number when you multiply it, it gives you the product of 1.

So for - 27, what number will give us 1 when we multiply it by -27

-27 * -1/27 = 1

So the multiplicative inverse of -27 = -1/27

7/9 * 9/7 = 1

-9/16 * -16/9 = 1

So in essence, just take the number and flip it

-27 = -1 / 27

7/9 = 9/7

-9/16 = -16/9

Answer 2

❁ Question -:

Find the multiplicative inverse of -27 and 7/9.

❁ Explanation -:

To solve this problem first we need to understand what does multiplicative inverse mean.

What does multiplicative inverse mean ?

Multiplicative inverse means the reciprocal of any number. Multiplicative inverse of a number is a value which when multiplied by the original number results in 1.

Example :

Find the multiplicative inverse of 5.

$\small\sf{The \: multiplicative \: inverse \: of  \: 5 \: is \: \dfrac{1}{5}. }$

Let us check whether the multiplicative inverse is correct or not.

$\small\rm{ \cancel5 \times \dfrac{1}{ \cancel{5}} = 1 }$

We get the identity number 1. So the answer is correct.

Now let us solve the above questions.

1) Find the multiplicative inverse of -27

$\small\sf {The \: multiplicative \: inverse \: of \: -27 \: is \: - { \dfrac{ 1}{3}. } }$

Let us check.

$\small \cancel{-27 }× \cancel-\dfrac{1}{ \cancel{27}} = 1$

2) Find the multiplicative inverse of 7/9.

$\small\sf {The \: multiplicative \: inverse \: of \: \dfrac {7}{9} \: is \: \dfrac{9}{7}.}$

Let us check.

$\small\dfrac{\cancel{7} \: 1}{\cancel{9} \:1 }×\dfrac{\cancel{9} \:1 }{\cancel{7} \:1 } = 1$