Question

What is the opposite and reciprocal of \[\dfrac{1}{3}\]?

Answer 1

Hint: The opposite number is also known as the additive inverse. The opposite is the number we have to add to get an answer equal to \[0\]. The reciprocal is also known as the multiplicative inverse. The reciprocal is the number that we have to multiply to get an answer equal to \[1\].

Complete step by step answer:
From the question it is clear that we have to find the opposite and reciprocal of \[\dfrac{1}{3}\].
From the basic concepts of mathematics, the opposite is the number that we have to add to get an answer equal to \[0\].
The opposite number is also known as the additive inverse.
So, let us try to solve it mathematically.
From the basic definition of opposite, we know that the opposite is the number that we have to add to get an answer equal to \[0\].
Now let \[x\] be the number that we have to add to get an answer equal to \[0\].
So,
\[\Rightarrow \]\[\dfrac{1}{3}+x=0\]
Now, let us subtract \[\dfrac{1}{3}\]on both sides.
\[\Rightarrow \]\[\dfrac{1}{3}+x-\dfrac{1}{3}=0-\dfrac{1}{3}\]
On simplification we get,
\[\Rightarrow \]\[x=-\dfrac{1}{3}\]
So,\[x=-\dfrac{1}{3}\] is the opposite of \[\dfrac{1}{3}\].
Now we have to find the reciprocal of \[\dfrac{1}{3}\]
From the basic definition of reciprocal, we know that the reciprocal is the number that we have to multiply to get an answer equal to \[1\].
Let us try to solve mathematically,
Let \[x\]be the number that we have to multiply to get an answer equal to \[1\].
So,
\[\Rightarrow \]\[\dfrac{1}{3}\times x=1\]
Now, multiply with \[3\]on both sides
\[\Rightarrow \]\[\dfrac{1}{3}\times x\times 3=1\times 3\]
On simplification, we get
\[\Rightarrow \]\[x=3\].
Now we can conclude that \[-\dfrac{1}{3}\] is the opposite and \[3\] is the reciprocal of the given number.

Note: Students should know the basic concepts of mathematics. Students should have minimum knowledge about additive inverse and multiplicative inverse. In case of any misconception may lead to do this type of question wrong. So, students should focus on concepts to make this kind of question correct.