Question

Find the sum of additive inverse and multiplicative inverse of 7.

Answer 1

Additive inverse of 7 = -7
Multiplicative inverse of 7 = 1/7
sum of additive and multiplicative inverse of 7 = -7+1/7
                                                                     = -49+1/7 
                                                                     = -48/7.

Answer 2

The sum of additive inverse and multiplicative inverse of 7 is - 48/7

Given :

The number 7

To find :

The sum of additive inverse and multiplicative inverse of 7

Solution :

Step 1 of 3 :

Find additive inverse of 7

Let m is the additive inverse of 7

Then we have ,

$\displaystyle \sf{ m + 7 = 0}$

$\displaystyle \sf{ \implies m = - 7}$

So additive inverse of 7 is - 7

Step 2 of 3 :

Find multiplicative inverse of 7

Let n is the multiplicative inverse of 7

Then we have ,

$\displaystyle \sf{n \times 7 = 1 }$

$\displaystyle \sf{ \implies n = \frac{1}{7} }$

So multiplicative inverse of 2 is 1/7

Step 3 of 3 :

Find sum of additive inverse and multiplicative inverse of 2

Hence the required sum of additive inverse and multiplicative inverse of 7

$\displaystyle \sf{ = - 7 + \frac{1}{7} }$

$\displaystyle \sf{ = \frac{ - 49 + 1}{7} }$

$\displaystyle \sf{ = \frac{ - 48}{7} }$

$\displaystyle \sf{ = - \frac{48}{7} }$

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