Converting between fractions and percentages and vice versa

In this article, we will teach you how to convert fractions to percentages and percentages to fractions easily, quickly, and effortlessly.
All you need to do is follow the steps and be proficient in expanding and reducing fractions.

Let's convert from percentage notation to fraction notation.
In the numerator, we write the given percentage number (without the percentage sign)
and in the denominator, we always write the number $100$.
For example:
$45\%$ will be written as $45 \over 100$.
Although we've converted to a fraction, this is not the final answer and we must continue to the second stage.

We will reduce the fraction we received as much as possible and reach the final answer.
For example:
We will reduce the fraction we received by $5$.
$\frac{9}{20}=\frac{45}{100}$
$\frac{9}{20}$ is the final answer.

Reminder - How to Reduce Fractions?
We perform the same division operation on both numerator and denominator - using a number that divides evenly into both the numerator and denominator until we reach a fraction where no number can be found that divides without remainder into both numerator and denominator.

Convert $25\%$ to a fraction

Solution:
According to the first step, we write the percentage number in the numerator and write $100$ in the denominator.
We get $25 \over 100$
According to the second step, we reduce the fraction as much as possible.
We divide by $25$ and get:
$\frac{1}{4}=\frac{25}{100}$

The final answer is $1 \over 4$.

Another exercise:
Convert $67\%$ to a fraction

Solution:
We'll write $67$ in the numerator and $100$ in the denominator
We get:
$67 \over 100$
$67$ is a prime number - divisible only by itself and $1$ and $100$ is not divisible by $67$.
Therefore, we cannot reduce the fraction and the final result remains $67 \over 100$ .

Additional exercise:
Convert $225\%$ to a fraction

Solution:
Let's write $225$ in the numerator and $100$ in the denominator.
Note - don't get confused. Even if the number is large/small, we always write $100$ in the denominator.
We get:
$225 \over 100$
Now let's move to the second step and reduce the fraction as much as possible.
We can reduce in several steps to avoid mistakes.
First, let's reduce by $5$.
We get:
$\frac{225}{100}=\frac{45}{20}$
Notice that we can reduce the fraction even more. Let's reduce it again by $5$ and we get:
$\frac{45}{20}=\frac{9}{5}$
Let's convert our result to a mixed number and we get:
$\frac{9}{4}=2\frac{1}{4}$
The final result is $2\frac{1}{4}$.

We will expand or reduce the fraction so that its denominator will be the number $100$.
We will make sure to perform the expansion / reduction operation on both the numerator and denominator.
For example-
If we have the fraction $3 \over 25$ we will expand it by $4$ and get - $12 \over 100$

After we get a fraction with a denominator of $100$, we'll write what we got in the numerator as a percentage and that will be the final answer!
For example –
After expanding we got the fraction $12 \over 100$.
The final answer will be $12\%$.

Pay attention!! Not every fraction can be converted to percentages (without a calculator). Not every given denominator can reach $100$ through expansion or reduction.

Convert the fraction $4 \over 5$ to percentage

Solution:
According to the first step, we want to reach a denominator of $100$. To do this, we will expand the fraction by $20$.
We get $\frac{80}{100}=\frac{4}{5}$
According to the second step, the final answer is $80\%$.

Convert the fraction $10 \over 11$ to percentage

Solution:
We cannot get from the denominator $11$ to the denominator $100$ without a calculator.

Convert the fraction $60 \over 50$ to percentage

Solution:
We will expand by $2$
We get
$\frac{120}{100}=\frac{60}{50}$
The answer is $120\%$.

Convert $67\%$ to a simple fraction.

Solution:
Let's perform a simple division and get: $67\%=\frac{67}{100}$.

Convert the fraction $7 \over 20$ to a percentage.

Solution:
We'll expand to $100$ for the denominator and get: $\frac{7}{20}=\frac{35}{100}=35\%$.

Let's convert the fractions $\frac {1}{2}, \frac {3}{4}, \frac {5}{20}, \frac {1}{25},$ to percentages.

Solution:
In each case we'll multiply by $100$ and get:

$\frac {1}{2}*100=50\%$

$\frac {3}{4}*100=75\%$

$\frac {5}{20}*100=20\%$

$\frac {1}{25}*100=4\%$

Let's convert from percentages to fractions $2\%, 10\%, 35\%, 70\%,63\%$

Solution:
In each case we divide by $100$ and get:

$2 \% = \frac{2}{100}= \frac{1}{50}$

$10 \% = \frac{10}{100}= \frac{1}{10}$

$35 \% = \frac{35}{100}= \frac{7}{20}$

$70 \% = \frac{70}{100}= \frac{7}{10}$

$63 \% = \frac{63}{100}$