Question

Give the missing number.
(A) \[35\% = \dfrac{{}}{{100}}\]
(B) \[8\% = \dfrac{{}}{{100}}\]

Answer 1

Hint: Here we need to find the missing number in both the parts. The concept of percentage will be used in the question. So, first we will assume the missing term as and then use the formula for finding a specific percentage of a number as: $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $. Then, we will shift the terms in the equation using the transposition method to find the variable.
If we say \[y\% \] it means \[\dfrac{y}{{100}}\]

Complete step-by-step answer:
We know that percentage means a number, or a ratio expressed in the form of fraction of \[100\] or we can say percentage is the relative value that indicates the hundredth part of any quantity.
Now, in the question it is given that
\[35\% = \dfrac{{}}{{100}}{\text{ }} - - - \left( 1 \right)\]
And we have to find the missing term.

A.So, let us assume the missing number to be \[x\]
\[\therefore \] equation \[\left( 1 \right)\] becomes,
\[35\% = \dfrac{x}{{100}}{\text{ }} - - - \left( 2 \right)\]
Now we know that,
If \[y\% \] is written, it means that \[\dfrac{y}{{100}}\]
So, we can write \[35\% \] as \[\dfrac{{35}}{{100}}\]
\[\therefore \] equation \[\left( 2 \right)\] can be written as,
\[\dfrac{{35}}{{100}} = \dfrac{x}{{100}}\]
As denominators are the same, so they get cancelled. \[\left[ {\because \dfrac{a}{b} = \dfrac{c}{b} \Rightarrow a = c} \right]\]
\[\therefore \] we get,
\[x = 35\]
Hence, the missing number is \[35\]

B.Now, similarly we will find the missing number in the second part.
It is given that
\[8\% = \dfrac{{}}{{100}}{\text{ }} - - - \left( 3 \right)\]
And we have to find the missing term.
So, let us assume the missing number to be \[x\]
\[\therefore \] equation \[\left( 3 \right)\] becomes,
\[8\% = \dfrac{x}{{100}}{\text{ }} - - - \left( 4 \right)\]
Now we know that,
If \[y\% \] is written, it means that \[\dfrac{y}{{100}}\]
So, we can write \[8\% \] as \[\dfrac{8}{{100}}\]
\[\therefore \] equation \[\left( 4 \right)\] can be written as,
\[\dfrac{8}{{100}} = \dfrac{x}{{100}}\]
As denominators are the same, so they get cancelled. \[\left[ {\because \dfrac{a}{b} = \dfrac{c}{b} \Rightarrow a = c} \right]\]
\[\therefore \] we get,
\[x = 8\]
Hence, the missing number is \[8\]

Note: The percentage has no dimensions. It means that they are dimensionless numbers. Also, we can do this question by a short trick i.e., just drop the \[\% \] sign and the number will be the missing term. Like in the first part, if we drop the \[\% \] sign, we get the number as \[35\] and hence \[35\] is the missing term. Similarly, in the second part, if we drop the \[\% \] sign, we get the number as \[8\] and hence \[8\] is the missing term.
Because, if we have to write a percentage as a fraction, we just drop the \[\% \] sign and divide by \[100\]
\[\therefore 35\% = \dfrac{{35}}{{100}}{\text{ }}\] and hence \[35\] is the missing term
Similarly, \[\therefore 8\% = \dfrac{8}{{100}}{\text{ }}\] and hence \[8\] is the missing term.