Question

\[45\] is what percent of \[90\] ?

Answer 1

Hint:In this question, we need to find that \[45\] is what percent of \[90\] . That is we need to find what percentage is \[45\] of \[90\] . Percentage is nothing but it is a number or a ratio expressed in the fraction of \[100\] . It is a dimensionless number and has no unit of measurement. In other words, the percentage is a fraction with \[100\] as a denominator. The symbol used to represent percentage is \[\%\] .

Complete step by step solution:
Let us consider the percentage as \[x\%\]
We need to find the percentage.
Given, \[45\] is \[x\%\] of \[90\]
\[\Rightarrow\ 45 = \dfrac{x}{100} \times 90\]
On simplifying ,
\[\Rightarrow \ 45 = \dfrac{x}{10} \times 9\]
On cross multiplying,
We get,
\[\Rightarrow \dfrac{45 \times 10}{9} = x\]
On further simplifying,
\[x = 50\]
Thus we get percentage is \[50\%\]
\[45\] is \[50\%\] of \[90\]

Note:
Alternative Method
We can also find the percentage in another method.
Here we need to know what percent is \[45\] of \[90\] .
\[45\] of \[90\] can be rewritten as \[\dfrac{45}{90}\] ,
To find the percentage, we need to find an equivalent fraction with denominator \[100\] .
By multiplying both numerator & denominator by 100 ,
We get,
\[\Rightarrow \dfrac{45}{90} \times \dfrac{100}{100}\]
We can rewrite this expression as
\[\Rightarrow \ \left( 45 \times \dfrac{100}{90} \right) \times \dfrac{1}{100}\]
Thus by simplifying,
We get,
\[\Rightarrow \ 50 \times \dfrac{1}{100}\]
Therefore the percentage is \[50\%\]