Question

How do you find the additive and multiplicative inverse of $ - 8 $ ?

Answer 1

Hint: In this question we need to determine additive and multiplicative inverse of $ - 8 $ . We know that when a number is added with its additive inverse, the result will be zero i.e., $ b + a = 0 \Rightarrow a = - b $ . By substituting $ b = - 8 $ , and determining the value of $ a $ , we will get the additive inverse of $ - 8 $ . Now, to determine the multiplicative inverse we know that when a number is multiplied to its multiplicative inverse, the result is one i.e., \[b \times a = 1 \Rightarrow a = \dfrac{1}{b}\]. Again, by substituting $ b = - 8 $ , and determining the value of $ a $ , we will get the multiplicative inverse of $ - 8 $ .

Complete step-by-step answer:
When a number is added with its additive inverse, the result will be zero i.e., $ b + a = 0 \Rightarrow a = - b $ . Now, the inverse of $ - 8 $ in the additive operation is that element $ \left( a \right) $ that added to $ - 8 $ gives zero.
 $ - 8 + a = 0 $
 $ a = 8 $
Hence, the additive inverse of $ - 8 $ is $ 8 $ .
So, the correct answer is “The additive inverse of $ - 8 $ is $ 8 $ ”.

When a number is multiplied to its multiplicative inverse, the result is one i.e., \[b \times a = 1 \Rightarrow a = \dfrac{1}{b}\].
Now, the inverse of $ - 8 $ in the multiplicative operation is that element $ \left( a \right) $ that multiplied to $ - 8 $ gives one.
 $ - 8 \times a = 1 $
 $ a = - \dfrac{1}{8} $
Hence, the multiplicative inverse of $ - 8 $ is $ - \dfrac{1}{8} $ .
So, the correct answer is “The multiplicative inverse of $ - 8 $ is $ - \dfrac{1}{8} $”.

Note: The additive inverse is the action that undergoes addition. Therefore, adding a negative value undergoes adding the positive value. If we take the negative of a number, we are taking its additive inverse. Zero is the additive inverse of itself. This is equivalent to subtracting the value. This number is also known as opposite, sign change and negation. For a real number, it reverses its sign.
The multiplicative inverse is the action that undergoes multiplication. It is also known as reciprocal for a number. For the multiplicative inverse of a real number, divide one by the number.