# Percent to fraction

Here you will learn about converting percents to fractions.

Students will first learn about converting fractions to percentages in 6th grade math as part of their work with ratios and proportional relationships and will expand that knowledge to solving problems such as finding the whole given a part and the percent or finding the part given the whole and the percent.

This will later be used to find percent increase/decrease in 7th grade.

## What is percent to fraction?

Converting a percent to a fraction is representing the percentage as a fraction without changing its value.

The word “percent” means one part out of one hundred, and you can use this information to express a percent as a fraction.

For example,

\begin{aligned} 25\% &=\cfrac{1}{4} \\\\ 45\% &=\cfrac{9}{20} \\\\ 33.3\% &=\cfrac{1}{3} \\\\ 80\% &=\cfrac{4}{5} \end{aligned}

## Common Core State Standards

How does this apply to 6th grade math?

• Ratios and Proportional Relationships (6.RP.A.3a)
Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

## How to convert percentages to fractions

In order to convert from a percentage to a fraction you need to:

1. Divide the percentage by \bf{100} .
2. Write in fraction form.
3. Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.
4. Simplify the fraction to lowest terms.
5. Clearly state the answer showing ‘percentage’ = ‘fraction’.

## Converting percentages to fractions examples

### Example 1: converting a simple percentage to a fraction

Convert 7\% to a fraction.

1. Divide the percentage by \bf{100} .

7 \div 100

2Write in fraction form.

7 \div 100=\cfrac{7}{100}

3Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

The numerator is not a decimal number and therefore already an integer, so you do not need to multiply the numerator and denominator by a multiple of 10.

4Simplify the fraction to lowest terms.

This fraction cannot be simplified because the only factor 7 and 100 share is 1.

5Clearly state the answer showing ‘percentage’ = ‘fraction’.

7\%=\cfrac{7}{100}

You can read this as ‘ 7 hundredths’ or ‘ 7 out of 100 ’.

This is a decimal as the denominator is a power of 10.

### Example 2: converting a percentage to a fraction (with simplifying)

Convert 40\% to a fraction, give your answer in its simplest form.

Divide the percentage by \bf{100} .

Write in fraction form.

Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

Simplify the fraction to lowest terms.

Clearly state the answer showing ‘percentage’ = ‘fraction’.

### Example 3: converting a percentage to a fraction where the percentage contains a decimal

Convert 60.2\% to a fraction.

Divide the percentage by \bf{100} .

Write in fraction form.

Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

Simplify the fraction to lowest terms.

Clearly state the answer showing ‘percentage’ = ‘fraction’.

### Example 4: converting a percentage to a fraction (where the answer will be an improper fraction)

Convert 120\% to a fraction. Give your answer as an improper fraction.

Divide the percentage by \bf{100} .

Write in fraction form.

Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

Simplify the fraction to lowest terms.

Clearly state the answer showing ‘percentage’ = ‘fraction’.

### Example 5: converting a percentage to a fraction (where the answer will be a mixed number)

Convert 150\% to a fraction. Give your answer as a mixed number.

Divide the percentage by \bf{100} .

Write in fraction form.

Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

Simplify the fraction to lowest terms.

Clearly state the answer showing ‘percentage’ = ‘fraction’.

### Example 6: converting a percentage to a fraction

Convert 0.008\% to a fraction, give your answer in its simplest form.

Divide the percentage by \bf{100} .

Write in fraction form.

Convert the numerator to an integer by multiplying by a power of \bf{10} , for example, \bf{10, 100, 1000} . You need to do the same to the denominator to create an equivalent fraction.

Simplify the fraction to lowest terms.

Clearly state the answer showing ‘percentage’ = ‘fraction’.

### Teaching tips for percent to fraction

• Use visual models such as hundreds grids or pie charts to illustrate the equivalence of percents and fractions and to demonstrate how both forms are ways to represent a part of a whole or a rate.

• Use real world contexts to demonstrate how percentages can be thought of as fractions.

• Worksheets for converting percentages to fractions have their place, but make sure that students have a conceptual understanding of the relationship between percentages and fractions.

### Easy mistakes to make

• Multiplying by an incorrect multiple of \bf{10}
You must multiply by a power 10 (for example, 10, 100 or 1000 ) that results in the numerator being an integer (a whole number). Use your knowledge of place value to help decide which multiple of 10 to multiply by.

For example,
0.003 \times 10 = 0.03. This is not an integer.
0.003 \times 1000 = 3. This is an integer.

• Simplifying the fraction to lowest terms
Often questions will say “give your answer in simplest form.” Always take a moment to see if the fraction can be simplified. To simplify a fraction, you need to divide the numerator and the denominator by a common factor.

To simplify a fraction to the lowest terms, you must divide the numerator and the denominator by the greatest common factor.

• Not multiplying the denominator by the same number as the numerator
When you multiply the numerator by a multiple of 10 you must do the same for the denominator otherwise you are changing the value of the fraction.

• Converting between a mixed number and an improper fraction
Not correctly converting between numbers in different forms, for example, mixed numbers and improper fractions.

### Practice percent to fractions questions

1. Convert 10\% to a fraction in its simplest form.

\cfrac{10}{100}

\cfrac{1}{10}

\cfrac{0.1}{1}

\cfrac{0.01}{100}

Start by writing the percent number as a fraction over 100.

\cfrac{10}{100}

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 10, the GCF of 10 and 100.

This gives you \, \cfrac{1}{10} \, .

2. Convert 20\% to a fraction in its simplest form.

\cfrac{20}{100}

\cfrac{2}{10}

\cfrac{1}{5}

\cfrac{0.4}{1}

Start by writing the percent number as a fraction over 100.

\cfrac{20}{100}

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 20, the GCF of 20 and 100.

This gives you \, \cfrac{1}{5} \, .

3. Convert 130\% to a fraction in its simplest form.

\cfrac{1.3}{1}

\cfrac{13}{10}

\cfrac{130}{100}

\cfrac{3}{10}

Start by writing the percent number as a fraction over 100.

\cfrac{130}{100}

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 10, the GCF of 130 and 100.

This gives you \, \cfrac{13}{10} \, .

4. Convert 0.6\% to a fraction in its simplest form.

\cfrac{0.6}{100}

\cfrac{6}{100}

\cfrac{6}{1000}

\cfrac{3}{500}

Start by writing the percent number as a fraction over 100.

\cfrac{0.6}{100}

Make sure that the numerator is an integer by multiplying it by a power of 10.

In this case, you can make 0.6 an integer by multiplying it by 10.

Multiply the denominator by 10 as well to make an equivalent fraction!

Now you have \, \cfrac{6}{1000}.

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 2, the GCF of 6 and 1000.

This gives you \, \cfrac{3}{500} \, .

5. Convert 3005\% to a fraction in its simplest form.

\cfrac{601}{20}

\cfrac{1}{20}

3005

\cfrac{3005}{100}

Start by writing the percent number as a fraction over 100.

\cfrac{3005}{100}

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 5, the GCF of 3005 and 100.

This gives you \, \cfrac{601}{20} \, .

6. Which of the below is the fractional equivalent of 12\%?

\cfrac{3}{25}

\cfrac{12}{100}

\cfrac{6}{50}

\cfrac{12}{10}

Start by writing the percent number as a fraction over 100.

\cfrac{12}{100}

Then simplify the fraction to lowest terms by dividing the numerator and denominator by 4, the GCF of 12 and 100.

This gives you \, \cfrac{3}{25} \, .

## Percent to fraction FAQs

Are there instances where it will be necessary to not simplify the fraction?

In some cases, yes. For instance, if you wanted to express a rate per 100 in fraction form, sometimes this may be easiest to represent with the denominator as 100 given the context, even if it is not in simplest form.

What is the difference between a multiple of \bf{10} and a power of \bf{10} ?

Multiples of 10 are the products of 10 with any other integer. Powers of 10 are also multiples of 10, but more specifically the multiples that can be expressed as 10 to the power of another number, indicating the number of times to multiply 10 to itself.

Should I represent an improper fraction as a mixed number every time?

No. Either the improper fraction or the mixed number answer will be correct. Most often, answers are preferred as improper fractions to represent the rate more clearly.

## Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.