Question

*Which of the following represents the multiplicative inverse of −4/7?*

1) 4/7
2) 7/4
3) −7/4
4) −4/7
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Answer 1

Answer:

Answer ( Correct and Right ) is Option (3) - 7/4

Answer 2

The multiplicative inverse of - 4/7 is - 7/4

Given :

The number - 4/7

To find :

The multiplicative inverse of - 4/7 is

1) 4/7

2) 7/4

3) - 7/4

4) - 4/7

Solution :

Step 1 of 2 :

Define multiplicative inverse of a number

1 is the Multiplicative identity

Let M is the multiplicative inverse of N ( ≠ 0 )

Then M × N = 1 = N × M

⇒ M = 1/N

So 1/N is multiplicative inverse of N

Step 2 of 2 :

Find multiplicative inverse of - 4/7

Let N be the multiplicative inverse of - 4/7

$\displaystyle \sf{ N \times \bigg( -\frac{4}{7}\bigg) = 1 }$

$\displaystyle \sf{ \implies N = \frac{1}{\frac{-4}{7}} }$

$\displaystyle \sf{ \implies N = 1 \times \frac{7}{-4} }$

$\displaystyle \sf{ \implies N = - \frac{7}{4} }$

The multiplicative inverse of - 4/7 is - 7/4

Hence the correct option is 3) - 7/4

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