Question

How do you rewrite $225\mathrm{\%}$ as a mixed number?

Answer 1

Hint: Convert $225\mathrm{\%}$ in term of fraction by dividing $225$ by $100,$ (As when we have to convert percentage in form of fraction then we have to divide it by $100$), then convert the obtained fraction in form of mixed number.
Eg. Like if we have to convert ${\displaystyle \frac{7}{4}}$ in term if mixed number, then we can rewrite ${\displaystyle \frac{7}{4}}$ as ${\displaystyle \frac{(4+3)}{4}}$ that will be equal to $(1+{\displaystyle \frac{3}{4}})$ So, $1\left({\displaystyle \frac{3}{4}}\right)$ will be the mixed number form of ${\displaystyle \frac{7}{4}}.$
Apply this concept to convert the given number in the form of a mixed number.

Complete step by step solution:
As per data given in the question,
As we have to convert $225\mathrm{\%}$ in term of mixed number,
Mixed numbers are such numbers which are a combination of a whole number and a fraction.
Like, $1\left({\displaystyle \frac{2}{3}}\right)$ is a type of mixed number,
Where, $1\left({\displaystyle \frac{2}{3}}\right)=(1+{\displaystyle \frac{2}{3}})={\displaystyle \frac{5}{3}}$
As, we have $225\mathrm{\%}$ given in the question,
First converting the given number in form by fraction,
As the given number is in form of percentage,
So, in order to converting it in form of fraction,
We need to divide it by $100,$
So, we will get,
$225\mathrm{\%}={\displaystyle \frac{225}{100}}$
Now,
Converting the fractions in form of mixed number,
For that,
Lets converting the fraction firstly in its simplest form,
So,
$\Rightarrow 225=5\times 5\times 9$
$\Rightarrow 100=5\times 5\times 4$
So, dividing both numerator and denominator of the fraction by common multiplier i.e. $5\times 5$ i.e. $25$
So,
We will get,
$\Rightarrow {\displaystyle \frac{225}{100}}={\displaystyle \frac{9}{4}}$
Now,
As we know that,
We can write $9$ as $(8+1)$
So,
$\Rightarrow {\displaystyle \frac{9}{4}}=\left({\displaystyle \frac{8}{4}}\right)+\left({\displaystyle \frac{1}{4}}\right)=2+\left({\displaystyle \frac{1}{4}}\right)$
So, splitting the numerators, we will get,
$\Rightarrow {\displaystyle \frac{9}{4}}=\left({\displaystyle \frac{8}{4}}\right)+\left({\displaystyle \frac{1}{4}}\right)=2+\left({\displaystyle \frac{1}{4}}\right)$
As, the obtained number is in form of a whole number and a fraction,
So, for converting it in form of mix number,
We need to add the both the numbers,
So, obtained mixed number will be $=2\left({\displaystyle \frac{1}{4}}\right)$

When $225\mathrm{\%}$ is converted in form of mixed number it will be equal to $2\left({\displaystyle \frac{1}{4}}\right)$

Additional Information:
Mixed numbers are such numbers which are a combination of a whole number and a proper fraction.
As, proper fraction are such fraction in which the value of numerator of fraction is less than the value of denominators of fraction.
Improper fraction are such fraction in which the value of numerator of fraction is more than the value of denominator of fraction.
We can also convert Improper fraction in term of mixed number,
Like, ${\displaystyle \frac{8}{3}}$ is an example of improper fraction,
So, ${\displaystyle \frac{8}{3}}={\displaystyle \frac{(6+2)}{3}}=\left({\displaystyle \frac{6}{3}}\right)+\left({\displaystyle \frac{2}{3}}\right)=2\left({\displaystyle \frac{2}{3}}\right)$
Hence, here $2\left({\displaystyle \frac{2}{3}}\right)$ is a mixed number.

Note: Always remember when we convert any percentage value in form of fraction, we need to divide it by $100.$
While converting the fraction value as a form of mixed number, split the numeration in such a way that the first part is equal to the value of the denominator or the first part of fractional value must be a multiplier of the value of the denominator.
Like, ${\displaystyle \frac{5}{2}}={\displaystyle \frac{(4+1)}{2}}=\left({\displaystyle \frac{4}{2}}\right)+\left({\displaystyle \frac{1}{2}}\right)=2\left({\displaystyle \frac{1}{2}}\right)$