Converting between fractions and percentages and vice versa

🏆Practice converting fractions to percentages and vice versa

Converting between fractions and percentages and vice versa

In order to convert between fractions and percentages and vice versa, it's important to remember that one percent - 1%=11001\% = \frac{1}{100}.
If you remember this principle, the calculations are simple.

Converting Percentages to Fractions

The first stage -

In the numerator, we write the given percentage number (without the percentage sign)
and in the denominator, we always write the number 100100.

The second stage -

We reduce the fraction that we obtained as much as possible in order to achieve the final answer.

Converting Fractions to Percentages

The first stage -

We expand or reduce the fraction so that the number 100100 appears in its denominator.
We will make sure to perform the expansion/reduction operation on both the numerator and denominator to maintain the value of the fraction.

The second stage -

What we obtained in the numerator will be the percentage and that will be the final answer.

Important note - not every fraction can be converted to percentages (without a calculator) since not every given denominator can be converted to 100100 through expansion or reduction.

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Test yourself on converting fractions to percentages and vice versa!

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Convert the fraction into a percentage:

\( \frac{24}{100}=\text{?} \)

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Converting between fractions and percentages and vice versa

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

How do we convert percentages to fractions?

The first stage -

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 100100.
For example:
45%45\% will be written as 4510045 \over 100.
Although we have succeeded in converting it to a fraction, this is not the final answer and we must continue to the second stage.

The Second Stage -

We must reduce the fraction we received as much as possible in order to obtain the final answer.
For example:
We reduce the fraction we received by 55.
920=45100\frac{9}{20}=\frac{45}{100}
920\frac{9}{20} is the final answer.

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

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Now let's practice:

Convert 25%25\% to a fraction

Solution:
According to the first step, we write the percentage number in the numerator and write 100100 in the denominator.
We obtain the following 2510025 \over 100
According to the second step, we reduce the fraction as much as possible.
We divide by 2525 and obtain:
14=25100\frac{1}{4}=\frac{25}{100}

The final answer is 141 \over 4.


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

Solution:
We'll write 6767 in the numerator and 100100 in the denominator
We obtain the following:
6710067 \over 100
6767 is a prime number - divisible only by itself and 11 and 100100 is not divisible by 6767.
Therefore, we cannot reduce the fraction and the final result remains 6710067 \over 100 .

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

Solution:
Let's write 225225 in the numerator and 100100 in the denominator.
Note - don't get confused. Even if the number is large/small, we always write 100100 in the denominator.
We obtain the following:
225100225 \over 100
Now let's move to the second step and reduce the fraction as much as possible.
We can reduce in several steps in order to avoid mistakes.
First, let's reduce by 55.
We obtain the following:
225100=4520\frac{225}{100}=\frac{45}{20}
Notice that we can reduce the fraction even more. Let's reduce it again by 55 and we obtain:
4520=95\frac{45}{20}=\frac{9}{5}
Let's convert our result to a mixed number as follows:
94=214\frac{9}{4}=2\frac{1}{4}
The final result is 2142\frac{1}{4}.

How do we convert fractions to percentages?

The first stage:

We will expand or reduce the fraction so that its denominator will be the number 100100.
We will make sure to perform the expansion / reduction operation on both the numerator and denominator.
For example-
If we have the fraction 3253 \over 25 we will expand it by 44 and obtain - 1210012 \over 100

The second stage:

After we obtain a fraction with a denominator of 100100, we can write the numerator as a percentage and that will be the final answer!
For example –
After expanding we obtained the fraction 1210012 \over 100.
The final answer will be 12%12\%.


Pay attention!! Not every fraction can be converted to percentages (without a calculator). Not every given denominator can be converted to 100100 through expansion or reduction.

Do you know what the answer is?

Exercises:

Convert the fraction 454 \over 5 to a percentage

Solution:
According to the first step, the denominator must be 100100. To do this, we will expand the fraction by 2020.
We obtain the following 80100=45\frac{80}{100}=\frac{4}{5}
According to the second step, the final answer is 80%80\%.

Convert the fraction 101110 \over 11 to a percentage

Solution:
We cannot convert the denominator from 1111 to 100100 without the aid of a calculator.

Convert the fraction 605060 \over 50 to a percentage

Solution:
We expand by 22
We obtain the following
120100=6050\frac{120}{100}=\frac{60}{50}
The answer is 120%120\%.

Convert 67%67\% to a simple fraction.

Solution:
Let's perform a simple division and obtain: 67%=6710067\%=\frac{67}{100}.

Convert the fraction 7207 \over 20 to a percentage.

Solution:
We'll expand the denominator to 100100 : 720=35100=35%\frac{7}{20}=\frac{35}{100}=35\%.

Let's convert the fractions 12,34,520,125,\frac {1}{2}, \frac {3}{4}, \frac {5}{20}, \frac {1}{25}, to percentages.

Solution:
In each case we'll multiply by 100100 as follows:

12100=50%\frac {1}{2}*100=50\%

34100=75%\frac {3}{4}*100=75\%

520100=20%\frac {5}{20}*100=20\%

125100=4%\frac {1}{25}*100=4\%

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

Solution:
In each case we divide by 100100 as follows:

2%=2100=1502 \% = \frac{2}{100}= \frac{1}{50}

10%=10100=11010 \% = \frac{10}{100}= \frac{1}{10}

35%=35100=72035 \% = \frac{35}{100}= \frac{7}{20}

70%=70100=71070 \% = \frac{70}{100}= \frac{7}{10}

63%=6310063 \% = \frac{63}{100}

Check your understanding

Examples with solutions for Converting Fractions to Percentages and Vice Versa

Exercise #1

Convert the fraction 7100 \frac{7}{100} into a percentage.

Video Solution

Step-by-Step Solution

The fraction:

x100 \frac{x}{100} is actually x percent.

Therefore we use the formula:

x100=x% \frac{x}{100}=x\%

7100=7% \frac{7}{100}=7\%

Answer

7%

Exercise #2

Write the percentage 201% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

We use the formula:

x100=x% \frac{x}{100}=x\%

201100=201% \frac{201}{100}=201\%

Answer

201100 \frac{201}{100}

Exercise #3

Write the percentage 87% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

We use the formula:

x100=x% \frac{x}{100}=x\%

87100=87% \frac{87}{100}=87\%

Answer

87100 \frac{87}{100}

Exercise #4

Convert the following fraction into a percentage:

1520=? \frac{15}{20}=\text{?}

Video Solution

Step-by-Step Solution

A percentage is actually a form of fraction, or more precisely, a fraction out of a hundred.

In other words, it is a fraction where the denominator is always 100.

Therefore, in order to convert a fraction into a percentage, we multiply it so that the denominator becomes 100.

20*5=100

15*5=75

Therefore the fraction is 75/100 and the percentage is 75%.

Answer

75%

Exercise #5

Write the percentage 7.5% as a fraction with denominator 100.

Video Solution

Step-by-Step Solution

We use the formula:

x100=x% \frac{x}{100}=x\%

7.5100=7.5% \frac{7.5}{100}=7.5\%

Answer

7.5100 \frac{7.5}{100}

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