Question

What is $70\%$ of 250?

Answer 1

Hint: To get what is $70\%$ of 250 we will use percentage definition. Firstly we will remove the percentage sign from 70 and divide it by 100 as percentage means a number per hundred. Then we will simplify the fraction obtained by dividing its numerator and denominator by the same number till a pair of coprime is obtained. Then we will multiply the simplified form fraction with 250 and solve it to get the desired answer.

Complete step by step solution:
To obtain $70\%$ of 250 we will convert it in fraction by dividing it by 100 and removing the percent sign as follows:
$70\%=\dfrac{70}{100}$
Now, we will simplify the above value by dividing the numerator and denominator by 5 as,
$\begin{align}
 & = \dfrac{\dfrac{70}{5}}{\dfrac{100}{5}} \\
 & = \dfrac{14}{20} \\
\end{align}$
Next, divide the numerator and denominator by 2 as,
$\begin{align}
 & = \dfrac{\dfrac{14}{2}}{\dfrac{20}{2}} \\
 & = \dfrac{7}{10} \\
\end{align}$
We can’t simplify the above value further because we got co-prime numbers from numerator and denominator.
So we can write
$70\%=\dfrac{7}{10}$
Next, we will multiply 250 by the above value as,
$\begin{align}
 & = \dfrac{7}{10}\times 250 \\
 & = 7\times 25 \\
 & = 175 \\
\end{align}$
Hence $70\%$ of 250 is $175$.

Note: The term percentage used is a dimensionless number as it has no unit of measurement. It is a ratio or we can say a number that is expressed as a fraction of 100. The percentage can be said to increase or decrease as stated in the question. It is used in our daily life like for calculating the increase in percentage of money for sugar. There is another way to solve the above question by using the formula:
$P\%$ Of Number $=X$
Where $X$ is the answer
So we can write:
$70\%$ of $250=X$
On Removing percentage sign and divide 80 by 100 we get,
$\begin{align}
 & = \dfrac{70}{100}\times 250=X \\
 & = \dfrac{7}{10}\times 250=X \\
 & = 175=X \\
\end{align}$
So we get $X=175$ which is the desired answer.