Question

Write the opposite numbers for the following numbers.

Number	+47	+52	-33	-21
Opposite number

Answer 1

Hint: We solve this problem by using the definition of opposite number. The opposite number is nothing but additive inverse of a given number. A number \['x'\] is said to be the additive inverse of a number \['n'\] if and only if
\[n+x=0\]
By using the above definition we find the opposite numbers of given numbers.

Complete step by step answer:
We are asked to find the opposite numbers of a few numbers.
We know that the opposite number is nothing but the additive inverse of a given number.
Let us find the additive inverse of given numbers one by one.
(i) +47
Let us assume that the given number as
\[\Rightarrow {{n}_{1}}=+47\]
Let us assume that the additive inverse of +47 as \['{{k}_{1}}'\]
We know that number \['x'\] is said to be the additive inverse of a number \['n'\] if and only if
\[n+x=0\]
By using the above formula we get
\[\Rightarrow {{n}_{1}}+{{k}_{1}}=0\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow +47+{{k}_{1}}=0 \\
 & \Rightarrow {{k}_{1}}=-47 \\
\end{align}\]
Therefore, we can say that the opposite number of +47 is -47.
(ii) +52
Let us assume that the given number as
\[\Rightarrow {{n}_{2}}=+52\]
Let us assume that the additive inverse of +52 as \['{{k}_{2}}'\]
By using the additive inverse definition we get
\[\Rightarrow {{n}_{2}}+{{k}_{2}}=0\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow +52+{{k}_{2}}=0 \\
 & \Rightarrow {{k}_{2}}=-52 \\
\end{align}\]
Therefore, we can say that the opposite number of +52 is -52.
(iii) -33
Let us assume that the given number as
\[\Rightarrow {{n}_{3}}=-33\]
Let us assume that the additive inverse of -33 as \['{{k}_{3}}'\]
By using the additive inverse definition we get
\[\Rightarrow {{n}_{3}}+{{k}_{3}}=0\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow -33+{{k}_{3}}=0 \\
 & \Rightarrow {{k}_{3}}=+33 \\
\end{align}\]
Therefore, we can say that the opposite number of -33is +33.
(iv) -21
Let us assume that the given number as
\[\Rightarrow {{n}_{4}}=-21\]
Let us assume that the additive inverse of -21 as \['{{k}_{4}}'\]
By using the additive inverse definition we get
\[\Rightarrow {{n}_{4}}+{{k}_{4}}=0\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow -21+{{k}_{4}}=0 \\
 & \Rightarrow {{k}_{4}}=+21 \\
\end{align}\]
Therefore, we can say that the opposite number of -21 is +21.

Now, by writing the opposite numbers in the given table we get

Number	+47	+52	-33	-21
Opposite number	-47	-52	+33	+21

.

Note: Students may make mistakes in finding the opposite number of a number.
The opposite number of any number is given as additive inverse.
A number \['x'\] is said to be the additive inverse of a number \['n'\] if and only if
\[n+x=0\]
But, students may make mistakes and take the opposite number of a number as multiplicative inverse.
A number \['x'\] is said to be the multiplicative inverse of a number \['n'\] if and only if
\[n\times x=1\]
This gives the wrong answer as reciprocal.
The opposite number is additive inverse and the reciprocal is multiplicative inverse.