Use this free Fraction Calculator to add, subtract, multiply and divide fractions and mixed numbers. Enter your fractions, choose the operation you want to perform, and get a simplified answer instantly.
The calculator shows the result as a simplified fraction, mixed number and decimal. It also provides a step-by-step calculation so you can see how the answer was obtained.
Whether you are working with simple fractions such as 1/2 and 3/4 or mixed numbers such as 1 1/2 and 2 1/4, this calculator makes fraction calculations quick and easy.
🧮 Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers. Get a simplified answer with a step-by-step explanation.
First Fraction
Second Fraction
Results are calculated exactly and simplified to their lowest terms. Decimal and mixed-number results are also shown where applicable.
What Is a Fraction?
A fraction represents a part of a whole and is written using two numbers: a numerator and a denominator. The numerator is the number above the fraction line, while the denominator is the number below it.
For example, in the fraction 3/4, the number 3 is the numerator and 4 is the denominator. This means that a whole has been divided into four equal parts and three of those parts are being considered.
Fractions can represent values smaller than one, greater than one, or whole numbers. They are commonly used in mathematics, measurements, percentages, ratios, and everyday calculations.
Numerator and Denominator
Every fraction has two main parts:
- Numerator – the top number, which tells you how many parts are being used.
- Denominator – the bottom number, which tells you how many equal parts make up the whole.
For example:
5/8
Here, 5 is the numerator and 8 is the denominator. The fraction means five out of eight equal parts.
The denominator cannot be zero because division by zero is undefined.
Proper and Improper Fractions
A proper fraction has a numerator that is smaller than its denominator. For example, 3/5 and 7/10 are proper fractions.
An improper fraction has a numerator that is equal to or larger than its denominator. Examples include 7/4 and 9/3.
An improper fraction can also be written as a mixed number. For example:
7/4 = 1 3/4
Understanding these different forms is useful when adding, subtracting, multiplying, or dividing fractions.
How to Calculate Fractions
Fractions can be added, subtracted, multiplied, and divided. The method depends on the type of operation being performed.
Adding Fractions
To add fractions with the same denominator, add the numerators and keep the denominator unchanged.
For example:
2/7 + 3/7 = 5/7
When the denominators are different, they first need to be converted to a common denominator.
For example:
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Subtracting Fractions
Subtracting fractions works in a similar way. When the denominators are the same, subtract the numerators and keep the denominator.
For example:
5/8 − 2/8 = 3/8
For different denominators, convert the fractions to equivalent fractions with a common denominator before subtracting.
Multiplying Fractions
To multiply two fractions, multiply the numerators together and the denominators together.
For example:
2/3 × 4/5 = 8/15
Unlike addition and subtraction, you do not need to find a common denominator when multiplying fractions.
Dividing Fractions
To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction.
For example:
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
The reciprocal of a fraction is found by switching its numerator and denominator.
Simplifying Fractions
After performing a calculation, the result can often be simplified.
For example:
8/12 = 2/3
Both 8 and 12 can be divided by 4, giving the equivalent fraction 2/3.
A simplified fraction has no common factor greater than 1 between its numerator and denominator.
Equivalent Fractions
Equivalent fractions are fractions that have different numerators and denominators but represent the same value.
For example:
1/2 = 2/4 = 3/6 = 4/8
All of these fractions represent one half.
To create an equivalent fraction, multiply or divide both the numerator and denominator by the same non-zero number.
For example:
2/3 × 2/2 = 4/6
Therefore:
2/3 = 4/6
Finding a Common Denominator
A common denominator is especially useful when adding or subtracting fractions with different denominators.
For example:
1/4 + 2/3
The denominators are 4 and 3. A common denominator is 12.
Convert both fractions:
1/4 = 3/12
2/3 = 8/12
Now the fractions can be added:
3/12 + 8/12 = 11/12
Finding the least common denominator can make fraction calculations easier and can help keep the final answer as simple as possible.
Simplifying a Fraction
A fraction can be simplified by dividing the numerator and denominator by their greatest common factor.
For example:
12/18
The greatest common factor of 12 and 18 is 6:
12 ÷ 6 / 18 ÷ 6 = 2/3
Therefore:
12/18 = 2/3
The fraction calculator can help you perform these calculations and provide the resulting fraction in simplified form.
Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are different ways of representing the same value. Being able to convert between them is useful in mathematics, measurements, finance, and everyday calculations.
Converting a Fraction to a Decimal
To convert a fraction to a decimal, divide the numerator by the denominator.
For example:
3/4 = 3 ÷ 4 = 0.75
Another example:
1/5 = 1 ÷ 5 = 0.2
Some fractions produce repeating decimals. For example:
1/3 = 0.333…
Converting a Fraction to a Percentage
To convert a fraction to a percentage, first convert the fraction to a decimal and then multiply by 100.
For example:
3/4 = 0.75
0.75 × 100 = 75%
Therefore:
3/4 = 75%
Converting a Decimal to a Fraction
A decimal can often be converted into a fraction by writing it over the appropriate power of 10 and then simplifying.
For example:
0.75 = 75/100 = 3/4
Similarly:
0.2 = 2/10 = 1/5
Converting a Percentage to a Fraction
To convert a percentage to a fraction, write the percentage over 100 and simplify.
For example:
25% = 25/100 = 1/4
Another example:
60% = 60/100 = 3/5
These conversions show that a fraction, decimal, and percentage can all represent exactly the same value.
Fraction, Decimal, and Percentage Conversion Table
The table below shows some common fractions and their equivalent decimal and percentage values.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33…% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.166… | 16.67…% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
| 1/25 | 0.04 | 4% |
| 1/50 | 0.02 | 2% |
| 1/100 | 0.01 | 1% |
| 2/3 | 0.666… | 66.67…% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.8 | 80% |
| 5/6 | 0.833… | 83.33…% |
| 7/8 | 0.875 | 87.5% |
| 9/10 | 0.9 | 90% |
For repeating decimals, the values in the table are shown with an ellipsis (...) to indicate that the decimal continues indefinitely.
Fraction Calculation Examples
Working through examples is one of the easiest ways to understand how fraction calculations work. Here are some common examples of adding, subtracting, multiplying, dividing, and simplifying fractions.
Example 1: Adding Fractions
Calculate:
1/4 + 2/3
First, find a common denominator. The least common denominator of 4 and 3 is 12.
Convert the fractions:
1/4 = 3/12
2/3 = 8/12
Now add the numerators:
3/12 + 8/12 = 11/12
The answer is:
11/12
Example 2: Subtracting Fractions
Calculate:
5/6 − 1/4
The least common denominator is 12.
Convert the fractions:
5/6 = 10/12
1/4 = 3/12
Subtract:
10/12 − 3/12 = 7/12
The answer is:
7/12
Example 3: Multiplying Fractions
Calculate:
2/5 × 3/4
Multiply the numerators and denominators:
2 × 3 / 5 × 4 = 6/20
Simplify the result:
6/20 = 3/10
The answer is:
3/10
Example 4: Dividing Fractions
Calculate:
3/4 ÷ 2/5
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
3/4 × 5/2 = 15/8
The result is an improper fraction:
15/8 = 1 7/8
Therefore:
3/4 ÷ 2/5 = 1 7/8
Example 5: Simplifying a Fraction
Simplify:
18/24
The greatest common factor of 18 and 24 is 6.
Divide both numbers by 6:
18 ÷ 6 = 3
24 ÷ 6 = 4
Therefore:
18/24 = 3/4
The simplified fraction is 3/4.
These examples demonstrate the basic steps used by a fraction calculator when working with common fraction operations.
Mixed Numbers and Improper Fractions
Fractions can be written as either proper fractions, improper fractions, or mixed numbers. Knowing how to convert between these forms makes fraction calculations easier.
What Is a Mixed Number?
A mixed number consists of a whole number and a proper fraction.
For example:
2 1/3
This means two whole units plus one third.
Mixed numbers are often used when a value is greater than one but is easier to understand when written as a whole number and a fraction.
Converting a Mixed Number to an Improper Fraction
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.
For example:
2 1/3
Multiply the whole number by the denominator:
2 × 3 = 6
Add the numerator:
6 + 1 = 7
Keep the denominator:
2 1/3 = 7/3
Converting an Improper Fraction to a Mixed Number
To convert an improper fraction into a mixed number, divide the numerator by the denominator.
For example:
7/3
Divide 7 by 3:
7 ÷ 3 = 2 remainder 1
The whole number is 2 and the remainder becomes the numerator:
7/3 = 2 1/3
Calculating with Mixed Numbers
Mixed numbers can be converted to improper fractions before performing calculations.
For example:
1 1/2 + 2 1/3
Convert both mixed numbers:
1 1/2 = 3/2
2 1/3 = 7/3
Find a common denominator:
3/2 = 9/6
7/3 = 14/6
Add:
9/6 + 14/6 = 23/6
Convert the result back to a mixed number:
23/6 = 3 5/6
Therefore:
1 1/2 + 2 1/3 = 3 5/6
Greatest Common Factor and Least Common Denominator
The greatest common factor (GCF) and least common denominator (LCD) are useful when working with fractions. They are especially important when simplifying fractions or adding and subtracting fractions with different denominators.
Greatest Common Factor (GCF)
The greatest common factor is the largest number that divides two or more numbers without leaving a remainder.
For example, consider 12 and 18.
The factors of 12 include:
1, 2, 3, 4, 6, 12
The factors of 18 include:
1, 2, 3, 6, 9, 18
The largest factor they have in common is 6.
Therefore:
GCF(12, 18) = 6
The GCF can be used to simplify fractions. For example:
12/18 = 2/3
because both the numerator and denominator can be divided by 6.
Least Common Denominator (LCD)
The least common denominator is the smallest positive number that can be used as a common denominator for two or more fractions.
For example:
1/4 + 1/6
The denominators are 4 and 6. Their least common multiple is 12, so 12 is the least common denominator.
Convert both fractions:
1/4 = 3/12
1/6 = 2/12
Now they can be added:
3/12 + 2/12 = 5/12
Finding the LCD is particularly useful when adding or subtracting fractions with different denominators.
GCF vs. LCD
The GCF is mainly used to simplify fractions, while the LCD is used to convert fractions to a common denominator before adding or subtracting them.
Using the correct method makes fraction calculations easier and helps produce a simplified final answer.
Fractions on a Number Line
A number line can be used to visualize the value of a fraction and understand where it is located relative to whole numbers.
For example, the fraction 1/2 is located halfway between 0 and 1.
Similarly:
1/4 is one quarter of the distance from 0 to 1.
3/4 is three quarters of the distance from 0 to 1.
5/4 is greater than 1 and is located between 1 and 2.
Understanding the Denominator
The denominator tells you how many equal sections the distance between whole numbers is divided into.
For example, when working with 1/4, the distance from 0 to 1 is divided into four equal parts.
The numerator tells you how many of those parts you move from zero.
For 3/4, you move three of the four equal sections:
0 → 1/4 → 2/4 → 3/4 → 4/4
Since 4/4 = 1, the fraction 3/4 is just before 1.
Fractions Greater Than One
Fractions with a numerator larger than the denominator have a value greater than one.
For example:
5/4 = 1 1/4
On a number line, 5/4 is located between 1 and 2.
Using a number line makes it easier to compare fractions and understand their relative values. It also shows why equivalent fractions such as 1/2, 2/4, and 4/8 all represent the same point on the number line.
Common Fraction Mistakes
Fractions can be easy to calculate once the basic rules are understood, but some common mistakes can lead to incorrect answers.
Adding the Denominators
When adding fractions, do not add the denominators together.
For example:
1/4 + 1/4 = 2/4 = 1/2
The denominator remains 4 because the fractions already have the same denominator.
Forgetting to Find a Common Denominator
When adding or subtracting fractions with different denominators, they must first be converted to equivalent fractions with a common denominator.
For example:
1/2 + 1/3
You cannot simply add the numerators and denominators. Instead, use a common denominator:
1/2 = 3/6
1/3 = 2/6
Therefore:
3/6 + 2/6 = 5/6
Forgetting to Simplify
A fraction may be correct but not fully simplified.
For example:
8/12
can be simplified to:
2/3
Whenever possible, reduce the final fraction to its simplest form.
Dividing Fractions Incorrectly
When dividing fractions, the second fraction must be inverted before multiplying.
For example:
2/3 ÷ 4/5
becomes:
2/3 × 5/4 = 10/12 = 5/6
Only the second fraction is flipped.
Dividing by Zero
A denominator can never be zero. Division by zero is undefined, so a fraction such as 5/0 does not represent a valid numerical value.
Check the Final Answer
After completing a fraction calculation, check that the result is simplified and that the operation was performed correctly. Converting the answer to a decimal can also provide a quick way to check whether the result is reasonable.
Frequently Asked Questions About Fractions
What is a fraction?
A fraction represents a part of a whole and consists of a numerator and a denominator. The numerator is the top number and the denominator is the bottom number. For example, in 3/4, 3 is the numerator and 4 is the denominator.
How do you add fractions?
To add fractions with the same denominator, add the numerators and keep the denominator unchanged. For fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators.
How do you subtract fractions?
To subtract fractions with the same denominator, subtract the second numerator from the first while keeping the denominator unchanged. If the denominators are different, first convert the fractions to equivalent fractions with a common denominator.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and multiply the denominators together. For example, 2/3 × 4/5 = 8/15. The result should then be simplified if possible.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6.
How do you simplify a fraction?
To simplify a fraction, divide the numerator and denominator by their greatest common factor. For example, 12/18 can be divided by 6, giving 2/3.
What is an improper fraction?
An improper fraction has a numerator that is equal to or greater than its denominator. For example, 7/4 is an improper fraction. It can also be written as the mixed number 1 3/4.
What is a mixed number?
A mixed number contains a whole number and a proper fraction, such as 2 1/3. Mixed numbers can be converted to improper fractions for calculations. For example, 2 1/3 = 7/3.
How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
How do you convert a fraction to a percentage?
To convert a fraction to a percentage, divide the numerator by the denominator and multiply the result by 100. For example, 3/4 = 0.75, and 0.75 × 100 = 75%.
What is a numerator and denominator?
The numerator is the number above the fraction line and represents how many parts are being considered. The denominator is the number below the fraction line and represents how many equal parts make up the whole.
Can a denominator be zero?
No. A denominator cannot be zero because division by zero is undefined. A fraction such as 5/0 therefore does not represent a valid numerical value.
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