Use this fraction calculator to add, subtract, multiply, or divide two, three, or longer fractions in one place. The tool supports simple fractions, mixed numbers, negative fractions, and operations involving a mix of mixed numbers and simple fractions.
To use the tool, just enter the fractions you want to operate on, select the operator (+, -, x, or ÷), and click calculate. The calculator will instantly return the final answer as a simplified fraction, a mixed number, a decimal, and a percentage equivalent. It also provides a clear, step-by-step solution, showing exactly how to solve your fractions.
Fraction Calculator with step-by-step explanation
+ − × ÷Add, subtract, multiply, or divide fractions and get a simplified answer with steps.
Step-by-step solution
Want to add, subtract, multiply, or divide mixed numbers only? Use our mixed fraction calculator.
How to Use the Fraction Calculator
This fraction calculator can perform operations on simple fractions, mixed fractions, whole numbers, negative fractions, or a mix of these values. You can use it to add, subtract, multiply, or divide two fractions, three fractions, or more.
To use the calculator, follow these steps:
- Choose the fraction type. Select simple fractions, mixed fractions, or a mix of both.
- Enter the fractions. The calculator starts with two fractions by default.
- Add more fractions if needed. Click Add another if you want to solve 3 fractions, 4 fractions, or a longer fraction expression.
- Choose the operation. Select the correct operator between the fractions: +, −, ×, or ÷.
- Click Calculate.
The calculator will return the final answer in simplest form, either as a proper fraction, mixed number, decimal, or percent equivalent. It will also show a clear, step-by-step explanation of how the answer was obtained.
What This Fraction Calculator Can Solve
This calculator is not limited to two fractions. You can use it for basic fraction operations and longer fraction expressions.
The table below shows examples of fraction operations you can solve using our fraction calculator.
| You can solve | Example |
|---|---|
| Two fractions | |
| Three fractions | |
| More than three fractions | |
| Mixed fractions | |
| Three mixed fractions | |
| Whole numbers and fractions | |
| Negative fractions | |
| Fraction division |
If the final answer can be reduced, the calculator simplifies it automatically. However, if the answer is an improper fraction, it can also show the equivalent mixed number.
Want a tool that operates on improper fractions only? Use the improper fraction calculator. However, if your aim is just to simplify a fraction, our simplifying fractions calculator can come in handy.
Fraction Operations with Step-by-Step Examples
Working with fractions can feel confusing, especially when denominators are different or when the problem includes more than two fractions. However, each operation follows a clear rule.
In this section, we explain how to perform fraction operations manually. You will see examples for operations on two fractions, three or more fractions, and mixed fractions. You can also enter the same values in the fraction calculator above to compare your answer with the calculator’s step-by-step solution.
Operations on Two Fractions
Most fraction problems start with two fractions. The method you use depends on the operator between the fractions.
1. Adding Two Fractions
To add two fractions, the denominators must be the same. If the denominators are different, find the least common denominator first.
Here’s how to manually add two fractions:
- Find the least common denominator.
- Rewrite both fractions with the common denominator.
- Add the numerators.
- Keep the denominator the same.
- Simplify the final answer if possible.
Example 1: Add Two Fractions
Problem: Add the following fractions:
Solution
The denominators are 2 and 3. The least common denominator is 6.
Rewrite each fraction with denominator 6:
Now add the numerators:
Final answer:
The answer is 5/6. This is already in the simplest form.
Subtracting Two Fractions
To subtract two fractions, make the denominators the same. Then subtract the numerators and keep the denominator.
Steps for Subtracting Two Fractions
- Find the least common denominator.
- Rewrite both fractions with the common denominator.
- Subtract the numerators.
- Keep the denominator the same.
- Simplify the final answer if possible.
Example 2: Subtract Two Fractions
Problem: Subtract the following fractions:43−61
Solution
The denominators are 4 and 6. The least common denominator is 12.
Rewrite each fraction with denominator 12:43=129 61=122
Now subtract the numerators:129−122=129−2=127
Final answer:43−61=127
The answer is 7/12. This fraction is already in simplest form.
Multiplying Two Fractions
Multiplying fractions is usually easier than adding or subtracting fractions because you do not need a common denominator.
Steps for Multiplying Two Fractions
- Multiply the numerators.
- Multiply the denominators.
- Write the result as a fraction.
- Simplify the final answer if possible.
Example 3: Multiply Two Fractions
Problem: Multiply the following fractions:52×43
Solution
Multiply the numerators:2×3=6
Multiply the denominators:5×4=20
So,52×43=206
Simplify:206=103
Final answer:52×43=103
The answer is 3/10.
Dividing Two Fractions
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal is made by flipping the numerator and denominator.
Steps for Dividing Two Fractions
- Keep the first fraction.
- Change the division sign to multiplication.
- Flip the second fraction.
- Multiply the numerators.
- Multiply the denominators.
- Simplify the final answer if possible.
Example 4: Divide Two Fractions
Problem: Divide the following fractions:65÷32
Solution
Keep the first fraction:65
Change division to multiplication and flip the second fraction:32→23
Now multiply:65÷32=65×23
Multiply the numerators and denominators:6×25×3=1215
Simplify:1215=45
Convert to a mixed number:45=141
Final answer:65÷32=45=141
The answer is 5/4, or 1 1/4 as a mixed number.
Operations on Three or More Fractions
Some fraction problems include three or more fractions. The method is the same, but you apply the rule to all the fractions in the expression.
When you add or subtract three or more fractions, find a common denominator for all fractions involved. When you multiply or divide several fractions, work from left to right unless multiplication and division appear with addition or subtraction. In that case, follow the order of operations.
The calculator above is useful for these problems because you can click Add another and solve longer fraction expressions in one place.
Steps for Solving Three or More Fractions
- Enter all the fractions in the expression.
- Follow the order of operations.
- Perform multiplication and division first, from left to right.
- Perform addition and subtraction after that.
- Use a common denominator where addition or subtraction is needed.
- Simplify the final answer.
Example 5: Add Three Fractions
Problem: Add the following three fractions:21+31+41
Solution
The denominators are 2, 3, and 4. The least common denominator is 12.
Rewrite each fraction with denominator 12:21=126 31=124 41=123
Now add the numerators:126+124+123=126+4+3=1213
Convert to a mixed number:1213=1121
Final answer:21+31+41=1213=1121
The answer is 13/12, or 1 1/12 as a mixed number.
Example 6: Solve Three Fractions with Mixed Operations
Problem: Solve the following expression:21+32×43
Solution
This expression includes addition and multiplication. According to the order of operations, multiply first.32×43=3×42×3=126=21
Now add:21+21=22=1
Final answer:21+32×43=1
The answer is 1.
This example shows why order of operations matters when solving longer fraction expressions.
Operations on Mixed Fractions
A mixed fraction has a whole-number part and a fraction part. For example:231
Before performing operations on mixed fractions, convert them to improper fractions. After solving, you can convert an improper answer back to a mixed number if needed.
Steps for Solving Mixed Fractions
- Convert each mixed fraction to an improper fraction.
- Perform the operation shown in the problem.
- Use a common denominator if adding or subtracting.
- Multiply by the reciprocal if dividing.
- Simplify the final answer.
- Convert the answer to a mixed number if it is improper.
Example 7: Solve Mixed Fractions
Problem: Solve the following mixed-fraction expression:121+231−341
Solution
Convert each mixed fraction to an improper fraction:121=23 231=37 341=413
Now solve:23+37−413
The denominators are 2, 3, and 4. The least common denominator is 12.
Rewrite each fraction with denominator 12:23=1218 37=1228 413=1239
Now add and subtract the numerators:1218+1228−1239=1218+28−39=127
Final answer:121+231−341=127
The answer is 7/12. This is a proper fraction, so it does not need to be written as a mixed number.
Frequently Asked Questions
A fraction calculator is an online tool that helps you quickly add, subtract, multiply, and divide fractions. Our calculator also gives a step-by-step solution, making it useful for learning and practice.
To add fractions with different denominators, enter both fractions in the calculator and choose addition. The adding fractions calculator with steps will automatically find the common denominator and show you the full working process.
Yes. You can use it as a subtract fractions calculator. Just enter the fractions, choose subtraction, and click calculate. The tool will give you the final simplified answer and the step-by-step working.
When you use it as a multiply fractions calculator, it multiplies the numerators together and the denominators together. The tool then simplifies the result and shows each step clearly.
To divide fractions manually, multiply the first fraction by the reciprocal of the second. With our divide fractions calculator, you only need to enter the numbers. The calculator shows the final answer and explains the steps in detail.
Yes. After solving, the calculator gives the answer in its simplest form and also shows the working that led to the simplified result.
Steps for Solving Fractions
Before looking at the examples, it helps to understand the basic steps used by the calculator. The exact steps depend on the operation you choose.
Steps for Adding Fractions
To add fractions:
- Check the denominators.
- If the denominators are different, find the least common denominator.
- Rewrite each fraction using the common denominator.
- Add the numerators.
- Keep the denominator.
- Simplify the result.
For example:ba+dc
can be rewritten using a common denominator before adding.
When adding three or more fractions, the calculator finds a common denominator for all the fractions involved in the addition part of the expression.
Steps for Subtracting Fractions
To subtract fractions:
- Check the denominators.
- Find a common denominator if the denominators are different.
- Rewrite each fraction using the common denominator.
- Subtract the numerators.
- Keep the denominator.
- Simplify the answer.
The process is almost the same as addition. The main difference is that you subtract the numerators instead of adding them.
Steps for Multiplying Fractions
To multiply fractions:
- Multiply the numerators.
- Multiply the denominators.
- Simplify the result.
The general rule is:ba×dc=b×da×c
For three or more multiplied fractions, multiply all the numerators together and all the denominators together. Then reduce the final fraction.
Steps for Dividing Fractions
To divide fractions:
- Keep the first fraction.
- Change division to multiplication.
- Flip the second fraction.
- Multiply the numerators.
- Multiply the denominators.
- Simplify the result.
The general rule is:ba÷dc=ba×cd
The flipped fraction is called the reciprocal.
Steps for Solving Mixed Fractions
To solve mixed fractions:
- Convert each mixed number to an improper fraction.
- Perform the required operation.
- Simplify the result.
- Convert the final improper fraction to a mixed number if needed.
For example:231=37
Fraction Calculator Examples
The examples below apply the steps explained above. Each example is written in an exam-style format, then solved step by step.
Example 1: Add Two Fractions
Problem:
A student is asked to add the following fractions:72+83
Solution
Step 1: Find the least common denominator
The denominators are 7 and 8.LCM(7,8)=56
Step 2: Rewrite each fraction with denominator 5672=7×82×8=5616 83=8×73×7=5621
Step 3: Add the numerators5616+5621=5616+21=5637
Answer72+83=5637
The answer is 37/56. This is a proper fraction because the numerator is smaller than the denominator.
Example 2: Add Three Fractions
Problem:
Find the sum of the three fractions below:21+31+41
Solution
Step 1: Find the least common denominator
The denominators are 2, 3, and 4.LCM(2,3,4)=12
Step 2: Rewrite each fraction with denominator 1221=126 31=124 41=123
Step 3: Add the numerators126+124+123=126+4+3=1213
Answer21+31+41=1213
The answer is 13/12, or 1 1/12 as a mixed number.
Example 3: Subtract Fractions
Problem:
Subtract the second fraction from the first fraction:65−41
Solution
Step 1: Find the least common denominator
The denominators are 6 and 4.LCM(6,4)=12
Step 2: Rewrite both fractions65=1210 41=123
Step 3: Subtract the numerators1210−123=1210−3=127
Answer65−41=127
The answer is 7/12. It is already in simplest form.
Example 4: Multiply and Divide Fractions
Problem:
Solve the following fraction expression:32×109÷53
Solution
Since multiplication and division have the same priority, work from left to right.
Step 1: Multiply the first two fractions32×109=3×102×9=3018
Simplify:3018=53
Step 2: Divide by the third fraction53÷53
To divide by a fraction, multiply by its reciprocal.53÷53=53×35 =5×33×5=1515=1
Answer32×109÷53=1
The answer is 1.
Example 5: Add Mixed Fractions
Problem:
A student wants to add the following mixed fractions:231+143
Solution
Step 1: Convert each mixed number to an improper fraction231=32×3+1=37 143=41×4+3=47
Step 2: Find the least common denominator
The denominators are 3 and 4.LCM(3,4)=12
Step 3: Rewrite both fractions37=1228 47=1221
Step 4: Add the numerators1228+1221=1249
Answer231+143=1249
The answer is 49/12, or 4 1/12 as a mixed number.
Example 6: Add Three Mixed Fractions
Problem:
Solve the expression:121+231−341
Solution
Step 1: Convert each mixed number to an improper fraction121=23 231=37 341=413
Step 2: Find the least common denominator
The denominators are 2, 3, and 4.LCM(2,3,4)=12
Step 3: Rewrite each fraction23=1218 37=1228 413=1239
Step 4: Add and subtract the numerators1218+1228−1239=1218+28−39=127
Answer121+231−341=127
The answer is 7/12. This is a proper fraction.
Two Fractions vs Three Fractions vs Multiple Fractions
Some fraction calculators only solve two fractions at a time. This calculator can solve two fractions, three fractions, or longer expressions.
A two-fraction problem looks like this:21+31
A three-fraction problem looks like this:21+31+41
A multiple-fraction expression may include different operations:21+31−41×52
When the expression has mixed operations, the calculator follows the order of operations. It works out multiplication and division first, then handles addition and subtraction.
This is helpful when your problem has more than one operation and you want one clean final answer.
Types of Fractions This Calculator Supports
This calculator supports the most common types of fractions used in school, exams, recipes, measurements, and everyday math.
Proper Fractions
A proper fraction has a numerator smaller than the denominator.
Example:83
Since 3 is smaller than 8, 3/8 is a proper fraction.
If your final answer is a proper fraction, the calculator keeps it as a fraction. It does not call it a mixed number because there is no whole-number part.
Improper Fractions
An improper fraction has a numerator greater than or equal to the denominator.
Example:49
Since 9 is greater than 4, 9/4 is an improper fraction.
Improper fractions can be changed into mixed numbers.49=241
Mixed Fractions or Mixed Numbers
A mixed fraction, also called a mixed number, has a whole-number part and a fraction part.
Example:231
This means:2+31
You can use this calculator to solve one mixed fraction, two mixed fractions, three mixed fractions, or a longer expression with mixed numbers.
For negative mixed numbers, place the negative sign on the whole-number part.
Example:−243
Negative Fractions
The calculator supports negative fractions.
Example:−53+21
A negative fraction can appear in the numerator or as part of a mixed number. For mixed numbers, use the whole-number box for the negative sign.
For example, enter:−243
as whole number -2, numerator 3, and denominator 4.
Whole Numbers with Fractions
You can also solve problems that include whole numbers and fractions.
Example:3+21
The calculator treats a whole number as a fraction with denominator 1.3=13
This allows whole numbers, simple fractions, and mixed numbers to be solved in the same expression.
Fraction Answers Explained
The calculator may show the answer in more than one form. These forms represent the same value.
Simplified Fraction
A simplified fraction is reduced to lowest terms.
Example:206=103
The calculator simplifies the final answer by dividing the numerator and denominator by their greatest common factor.
Proper Fraction
A proper fraction has a numerator smaller than the denominator.
Example:127
This type of answer does not need to be converted to a mixed number because it is already less than 1.
Improper Fraction
An improper fraction has a numerator greater than or equal to the denominator.
Example:1213
This fraction is greater than 1, so it can be written as a mixed number:1213=1121
The calculator shows the mixed-number form when the answer is improper.
Mixed Number
A mixed number combines a whole number and a proper fraction.
Example:1121
Mixed numbers are often easier to read in measurement problems, recipes, and school answers. However, improper fractions are often easier to use during calculation.
That is why the calculator may use improper fractions in the steps and show a mixed number in the final answer.
Decimal and Percent Forms
The calculator also shows decimal and percent forms.
Example:21=0.5=50%
These forms are useful when you want to compare values or use the answer in a real-life setting.
For example:43=0.75=75%
Common Fraction Rules Used by the Calculator
The calculator follows these fraction rules:
- A denominator cannot be zero.
- You cannot divide by a fraction equal to zero.
- To add fractions, use a common denominator.
- To subtract fractions, use a common denominator.
- To multiply fractions, multiply numerators and denominators.
- To divide fractions, multiply by the reciprocal.
- Mixed fractions are converted to improper fractions before calculation.
- The final answer should be simplified.
- Improper fractions can be rewritten as mixed numbers.
- Proper fractions should remain proper fractions.
These rules help the calculator produce a simplified and mathematically correct answer.
When to Use This Fraction Calculator
Use this calculator when you need to solve a fraction problem quickly and see the steps.
It can help with:
- Solving homework fraction problems
- Checking answers for two-fraction problems
- Adding or subtracting three fractions
- Solving three mixed fractions
- Working with recipes and measurements
- Checking improper fraction to mixed number answers
- Converting fraction answers to decimals or percents
- Learning each step instead of only getting the answer
The calculator is especially useful when your problem has more than two fractions or when mixed numbers make the calculation harder to do by hand.
Frequently Asked Questions
What is a fraction calculator?
A fraction calculator is a tool that solves fraction problems. It can add, subtract, multiply, and divide fractions. It can also simplify the answer and show the steps used to get the result.
Can this calculator solve three fractions?
Yes. You can click Add another and solve expressions such as:21+31+41
The calculator will find the answer and show the steps.
Can this calculator solve more than three fractions?
Yes. The calculator can solve longer fraction expressions. You can add more fractions and choose the operation between each one.
Can this calculator solve three mixed fractions?
Yes. Choose the mixed-number option and enter each whole-number part, numerator, and denominator. The calculator will convert the mixed numbers to improper fractions, solve the expression, and simplify the answer.
Does the calculator show step-by-step explanations?
Yes. The calculator shows the main steps, including mixed-number conversion, common denominators, reciprocal multiplication for division, simplification, and final answer interpretation.
How do you add three fractions?
To add three fractions, find a common denominator for all three fractions. Rewrite each fraction using that denominator. Then add the numerators and simplify the result.
How do you subtract mixed fractions?
To subtract mixed fractions, first convert each mixed number to an improper fraction. Then find a common denominator, subtract the numerators, and simplify the answer.
How do you divide fractions?
To divide fractions, keep the first fraction, change division to multiplication, and flip the second fraction. Then multiply and simplify.
Why does the calculator convert mixed numbers to improper fractions?
Mixed numbers are easier to calculate after converting them to improper fractions. After the calculation, an improper answer can be converted back to a mixed number.
Can a denominator be zero?
No. A denominator cannot be zero because division by zero is undefined. The calculator will show an error if any denominator is zero.