Question

How do you find the additive and multiplicative inverse of 3?

Answer 1

Hint: We start solving the problem by recalling the definition of additive inverse of a number as if d is called as an additive inverse of a number a, then it needs to satisfy the rule $ a+d=0 $ . We then assume variables for additive inverse and then make use of the definition to get the required value of the additive inverse of 3. We then recall the definition of multiplicative inverse of a number as if d is called as a multiplicative inverse of a number a, then it needs to satisfy the rule $ a\times d=1 $. We then assume variables for multiplicative inverse and then make use of the definition to get the required value of the multiplicative inverse of 3.

Complete step by step answer:
According to the problem, we are asked to find the additive and multiplicative inverse of 3.
Let us recall the definition of additive inverse of a number a.
We know that if d is called as an additive inverse of a number a, then it needs to satisfy the rule $ a+d=0 $.
Now, let us assume a be the additive inverse of 3, then we have $ a+3=0\Leftrightarrow a=-3 $.
Now, let us recall the definition of multiplicative inverse of a number a.
We know that if d is called as a multiplicative inverse of a number a, then it needs to satisfy the rule $ a\times d=1 $.
Now, let us assume m be the multiplicative inverse of 3, then we have $ m\times 3=1\Leftrightarrow m=\dfrac{1}{3} $.
 $ \, therefore, $ The additive and multiplicative inverse of 3 are –3 and $ \dfrac{1}{3} $ .

Note:
 Whenever we get this type of problem, we first recall the required definition and then assume a variable following the definition to get the required answer. We should not confuse additive and multiplicative inverses with additive and multiplicative identities as these is the most common mistakes done by students. Similarly, we can expect problems to find the additive and multiplicative identities of 3.