Question

What is 25% of 90?

Answer 1

Hint: To find 25% of 90, we have to convert 25% into fractions by dividing 25 by 100. Then we have to multiply the resultant with 90. We have to simplify the answer as much as possible.

Complete step by step solution:
We have to find 25% of 90. We know that a percentage is a number or a ratio represented in the form of fractions of 100. Let us consider a number, say p%. We can convert it into fractions by dividing p by 1000
$p\mathrm{\%}={\displaystyle \frac{p}{100}}$
Similarly, we have to convert 25% into fractions.
$\Rightarrow 25\mathrm{\%}={\displaystyle \frac{25}{100}}$
Now, we have to find 25% of 90. This means we have to multiply ${\displaystyle \frac{25}{100}}$ with 90.
$\Rightarrow {\displaystyle \frac{25}{100}}\times 90$
Let us cancel a zero from 90 in the numerator and 100 in the denominator.
$\Rightarrow {\displaystyle \frac{25}{10}}\times 9$
We can see that 25 and 10 have a common factor of 5. Hence, we can simplify the above result as shown below.
$\Rightarrow {\displaystyle \frac{5}{2}}\times 9$
Now, we have to perform the multiplication.
$\Rightarrow {\displaystyle \frac{45}{2}}$
We can either leave the result in fractional form or convert it into decimals. Let us convert ${\displaystyle \frac{45}{2}}$ into decimals.
$$2\stackrel{22.5}{\overline{)\begin{array}{rl}& 45.0\\ & -4\\ & \mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\\ & 5\\ & -4\\ & \mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\\ & 10\\ & -10\\ & \mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\\ & \begin{array}{cc}& 0\end{array}\end{array}}}$$
Hence 25% of 90 is ${\displaystyle \frac{45}{2}}$ or 22.5.

Note: Students must note that ‘of’ in mathematics means multiplication. They must also note that p% of q is the same as q% of p. For example, let us consider 90% of 25. We can write it as
${\displaystyle \frac{90}{100}}\times 25$
Let us cancel the zeroes.
$\Rightarrow {\displaystyle \frac{9}{10}}\times 25$
Let us cancel the common factors and do the multiplication.
$\Rightarrow {\displaystyle \frac{9}{2}}\times 5={\displaystyle \frac{45}{2}}$