Question

The reciprocal of 8/9 is -8/9 . (true or false)​

Answer 1

It is False that the reciprocal of 8/9 is - 8/9

Given :

The statement : The reciprocal of 8/9 is - 8/9

To find :

True/ False the statement

Solution :

Step 1 of 3 :

Define reciprocal of a number

We know that a number m is said to be reciprocal of n if m × n = 1

More precisely

$\displaystyle \sf{ The \: reciprocal \: of \: n \: is \: \: \frac{1}{n} }$

Step 2 of 3 :

Find the reciprocal of 8/9

$\displaystyle \sf{Here \: the \: given \: number \: is \: \frac{8}{9} }$

$\displaystyle \sf{ Let \: \: n \: is \: \: reciprocal \: of \: \: \frac{8}{9} }$

So by the given condition

$\displaystyle \sf{ n \times \bigg(\frac{8}{9}\bigg) = 1 }$

$\displaystyle \sf{ \implies \: n = \frac{9}{8} }$

$\displaystyle \sf{ The \: reciprocal \: of \: \: \frac{8}{9} } \: \: is \: \: \frac{9}{8}$

Step 3 of 3 :

Check True/ False the statement

Here the given statement is "The reciprocal of 8/9 is - 8/9 "

But we have found that reciprocal of 8/9 is 9/8

Hence the statement "The reciprocal of 8/9 is - 8/9" is False

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