In order to convert between fractions and percentages and vice versa, it's important to remember that one percent - .
If you remember this principle, the calculations are simple.
In order to convert between fractions and percentages and vice versa, it's important to remember that one percent - .
If you remember this principle, the calculations are simple.
In the numerator, we write the given percentage number (without the percentage sign)
and in the denominator, we always write the number .
We reduce the fraction that we obtained as much as possible in order to achieve the final answer.
We expand or reduce the fraction so that the number 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.
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 through expansion or reduction.
Convert the fraction into a percentage:
\( \frac{24}{100}=\text{?} \)
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.
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 .
For example:
will be written as .
Although we have succeeded in converting it to a fraction, this is not the final answer and we must continue to 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 .
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 .
Convert the fraction into a percentage:
\( \frac{56}{100}=\text{?} \)
Convert the fraction into a percentage:
\( \frac{2}{100}=\text{?} \)
Write the percentage 87% as a fraction with a denominator of 100.
Convert to a fraction
Solution:
According to the first step, we write the percentage number in the numerator and write in the denominator.
We obtain the following
According to the second step, we reduce the fraction as much as possible.
We divide by and obtain:
The final answer is .
Another exercise:
Convert to a fraction
Solution:
We'll write in the numerator and in the denominator
We obtain the following:
is a prime number - divisible only by itself and and is not divisible by .
Therefore, we cannot reduce the fraction and the final result remains .
Additional exercise:
Convert to a fraction
Solution:
Let's write in the numerator and in the denominator.
Note - don't get confused. Even if the number is large/small, we always write in the denominator.
We obtain the following:
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 .
We obtain the following:
Notice that we can reduce the fraction even more. Let's reduce it again by and we obtain:
Let's convert our result to a mixed number as follows:
The final result is .
We will expand or reduce the fraction so that its denominator will be the number .
We will make sure to perform the expansion / reduction operation on both the numerator and denominator.
For example-
If we have the fraction we will expand it by and obtain -
After we obtain a fraction with a denominator of , we can write the numerator as a percentage and that will be the final answer!
For example –
After expanding we obtained the fraction .
The final answer will be .
Pay attention!! Not every fraction can be converted to percentages (without a calculator). Not every given denominator can be converted to through expansion or reduction.
Write the percentage 66% as a fraction with a denominator of 100.
Write the percentage 201% as a fraction with a denominator of 100.
Write the percentage 33% as a fraction with a denominator of 100.
Convert the fraction to a percentage
Solution:
According to the first step, the denominator must be . To do this, we will expand the fraction by .
We obtain the following
According to the second step, the final answer is .
Convert the fraction to a percentage
Solution:
We cannot convert the denominator from to without the aid of a calculator.
Convert the fraction to a percentage
Solution:
We expand by
We obtain the following
The answer is .
Convert to a simple fraction.
Solution:
Let's perform a simple division and obtain: .
Convert the fraction to a percentage.
Solution:
We'll expand the denominator to : .
Let's convert the fractions to percentages.
Solution:
In each case we'll multiply by as follows:
Let's convert from percentages to fractions
Solution:
In each case we divide by as follows:
Write the percentage 118% as a fraction with a denominator of 100.
Write the percentage 75% as a fraction with a denominator of 100.
Write the percentage 54% as a fraction with a denominator of 100.
Convert the fraction into a percentage.
The fraction:
is actually x percent.
Therefore we use the formula:
7%
Write the percentage 201% as a fraction with a denominator of 100.
We use the formula:
Write the percentage 87% as a fraction with a denominator of 100.
We use the formula:
Convert the following fraction into a percentage:
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%.
75%
Write the percentage 7.5% as a fraction with denominator 100.
We use the formula: