Question

The multiplicative inverse of 1/16 ÷ 1/81 +-1/8​

Answer 1

Given :  1/16 ÷ 1/81   +    -1/8

To find :  multiplicative inverse

Solution:

a multiplicative inverse  is basically a reciprocal

Multiplicative inverse of number  is the number which if multiplied by original number result in 1

1/16 ÷ 1/81   +    -1/8

1/16 ÷ 1/81   = 81/16

 +    -1/8  = - 1/8

81/16  - 1/8

= 81/16  - 2/16

= (81 - 2)/16

= 79/16

Multiplicative inverse = 16/79

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Answer 2

Given :-

$\displaystyle{\sf{\frac{1}{16} \div \frac{1}{81}+\frac{-1}{8} }}$

To find :-

The multiplicative inverse of the given expression above.

Solution :-

$\displaystyle{\sf{\frac{1}{16}\times\frac{81}{1}-\frac{1}{8} }}\\\\\\\displaystyle{\sf{=\frac{81}{16}-\frac{1}{8} }}\\\\\textsf{Taking LCM as 16 :}\\\\\\\displaystyle{\sf{=\frac{81-2}{16} }}$

$\displaystyle{\sf{=\frac{79}{16} }}$

We know that, a multiplicative-inverse(or a reciprocal) of a number gives a product of 1 when it is multiplied with the number.

(Number × Reciprocal of the number = 1)

$\displaystyle\textsf{So, we get that, the reciprocal of }{\sf{\frac{79}{16}\ is\ \frac{16}{79}. }}$

$\displaystyle{\bold{(\frac{79}{16}\times\frac{16}{79}=1) }}$

$\bold{\underline{So,\ we\ conclude\ that,\ the\ reciprocal\ of\ \frac{1}{16}\div\frac{1}{81}+\frac{-1}{8}\ is\ \frac{16}{79} .}}$