Question

The multiplicative inverse of -p/q

Answer 1

The multiplicative inverse of - p/q is - q/p

Given :

The number - p/q

To find :

The multiplicative inverse of - p/q

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 - p/q

Let N be the multiplicative inverse of - p/q

$\displaystyle \sf{ N \times \bigg( - \frac{p}{q} \bigg) = 1 }$

$\displaystyle \sf{ \implies N = \frac{1}{\bigg( - \frac{p}{q} \bigg)} }$

$\displaystyle \sf{ \implies N = \frac{1}{ \frac{ - p}{q} } }$

$\displaystyle \sf{ \implies N = 1 \times \frac{q}{-p} }$

$\displaystyle \sf{ \implies N = - \frac{q}{p} }$

The multiplicative inverse of - p/q is - q/p

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