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What is the additive inverse of $\frac{a}{b}$ ?

see full answer

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\frac{- a}{b}

\frac{b}{a}

\frac{- b}{a}

\frac{a}{b}

answer is A.

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Detailed Solution

The given expression is

\frac{a}{b}

.
The additive inverse of a number is what you add to a number to create the sum of zero.
So, in other words, the additive inverse of

x

is another number,

y

, as long as the sum of

x + y

equals zero.
The additive inverse of

x

is equal and opposite in sign to it (so,

y = - x

or vice versa).
Let the additive inverse of

\frac{a}{b}

z

. Then,

\Rightarrow \frac{a}{b} + z = 0

\Rightarrow z = - \frac{a}{b}

Therefore, the additive inverse of

\frac{a}{b}

- \frac{a}{b} .

Hence, option 1 is correct.

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