Fraction Calculator

Use this fraction calculator to instantly add, subtract, multiply, or divide any two fractions. Just select the type of fraction (simple fraction or mixed fraction), enter these fractions, select the right operator (+,-,x, or ÷), and click calculate. The calculator will instantly return the correct answer in its simplest form as a proper or mixed fraction. You’ll also see other variations of the answer in decimal, percentage, or improper form.

This tool is useful when you want more than a final answer. It shows the main steps used to solve the problem, including common denominators, reciprocal multiplication for division, simplification, and final answer interpretation.

How to Use the Fraction Calculator

This fraction calculator can perform operations on simple fractions or fractions with whole-number parts. You can use it to add, subtract, multiply, or divide two fractions.

To use the calculator, follow these steps:

1. Choose the fraction type (simple fractions or mixed fractions)
2. Enter the first fraction
3. Choose the operation (+, −, ×, or ÷)
4. Enter the second fraction.
5. Click Calculate.

The calculator will instantly solve the two fractions, provide an accurate answer in its simplest form, and show you how to solve the fractions manually, step-by-step.

Example 1. Operation on Simple Fractions

A simple fraction has only a numerator and a denominator. In other words, simple fractions do not contain a separate whole-number part. Thus, you should use the simple fractions option when working with proper fractions or improper fractions such as $\dfrac{2}{7}$ or $\dfrac{9}{4}$.

Example. solve: $\frac{6}{17} +\frac{13}{15}$

Using the calculator, just follow these steps:

1. Select the Simple fractions option
2. Enter 6 as the numerator and 17 as the denominator for the first fraction.
3. Choose the addition sign +.
4. Enter 13 as the numerator and 15 as the denominator for the second fraction.
5. Click Calculate.

The calculator gives the correct answer as $1\frac{56}{255}$

Example 2. Operation on Mixed Fractions

A mixed fraction has a whole-number part and a fraction part. For example, $3\frac{2}{5}$ is a mixed fraction because it contains the whole number 3 and the fraction $\frac{2}{5}$​.

You should use the Mixed fractions option when one or both values contain a whole-number part.

Example. solve: $3\frac{2}{5} -1\frac{5}{6}$

Using the calculator, follow these steps:

1. Select the Mixed fractions option.
2. For the first value, enter 3 as the whole number, 2 as the numerator, and 5 as the denominator.
3. Choose the subtraction sign −.
4. For the second value, enter 1 as the whole number, 5 as the numerator, and 6 as the denominator.
5. Click Calculate.

The calculator gives the correct answer as: $1\frac{17}{30}$

Want a specialized tool that performs basic arithmetic operations on mixed fractions only? Use our Mixed Fraction Calculator.

Example 3. Operation on a Mixed Fraction and a Simple Fraction

Sometimes, you may need to perform an operation where one value is a mixed fraction, and the other is a simple fraction. In this case, select the Mixed fractions option because one of the values has a whole-number part.

Example. Solve: $2\frac{5}{6}- \frac{3}{7}$

Using the calculator, follow these steps:

1. Select the Mixed fractions option.
2. For the first value, enter 2 as the whole number, 5 as the numerator, and 6 as the denominator.
3. Choose the subtraction sign −.
4. For the second value, leave the whole-number box blank, enter 3 as the numerator, and 7 as the denominator.
5. Click Calculate.

The calculator gives the correct answer as: $2\frac{17}{42}$

What This Fraction Calculator Can Do

This calculator is designed to help you perform basic arithmetic operations (+, -, x, or ÷) on two fractions (either simple or mixed fractions). To help you learn, the calculator provides you with the correct answer, along with a clear, step-by-step explanation of how your fractions can be solved manually.

In other words, this fraction calculator can help you:

• Add two simple or mixed fractions
• Subtract two simple or mixed fractions
• Multiply two simple or mixed fractions
• Divide two simple or mixed fractions
• Do arithmetic operations on fractions involving a combination of mixed fractions and simple fractions.

Fraction Operations

Fractions are easier to work with when you know the rule for each operation. Addition and subtraction usually require a common denominator. However, multiplication and division do not require you to find a common denominator.

The following section shows how to add, subtract, multiply, or divide two fractions by hand.

Adding Fractions

To add fractions, the denominators must be the same. If the denominators are different, you need to find the least common denominator first, rewrite both fractions, and add the numerators.

Therefore, to add two fractions manually, follow these steps:

1. Check the denominators.
2. Find the least common denominator if the denominators are different.
3. Rewrite both fractions using the common denominator.
4. Add the numerators.
5. Keep the denominator the same.
6. Simplify the answer if possible.

Example: Solve $\frac{1}{2} + \frac{1}{3}$

Solution

Step 1: Check the denominators

The denominators are 2 and 3. Since they are different, we need a common denominator.

Step 2: Find the least common denominator

The least common denominator of 2 and 3 is 6. That is, LCD(2,3) = 6

Step 3: Rewrite both fractions using the common denominator

Rewriting these fractions using 6 as the denominator gives:

Rewrite each fraction with denominator 6.$$\frac{1}{2} = \frac{1\times 3}{2\times 3} = \frac{3}{6}$$21​=2×31×3​=63​ $$\frac{1}{3} = \frac{1\times 2}{3\times 2} = \frac{2}{6}$$31​=3×21×2​=62​

Step 4: Add the numerators$$\frac{3}{6}+\frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}$$63​+62​=63+2​=65​

Step 5: Simplify the answer

The fraction is already in simplest form.$$\frac{5}{6}$$65​

Final answer:$$\frac{1}{2}+\frac{1}{3} = \frac{5}{6}$$21​+31​=65​

The answer is 5/6.

Subtracting Fractions

To subtract fractions, make the denominators the same. Then subtract the numerators and keep the denominator.

Steps for Subtracting Fractions

To subtract two fractions:

1. Check the denominators.
2. Find the least common denominator if the denominators are different.
3. Rewrite both fractions using the common denominator.
4. Subtract the numerators.
5. Keep the denominator the same.
6. Simplify the answer if possible.

Example: Subtract Two Fractions

Problem: Subtract the following fractions.$$\frac{3}{4}-\frac{1}{6}$$43​−61​

Step 1: Check the denominators

The denominators are 4 and 6. Since they are different, we need a common denominator.

Step 2: Find the least common denominator

The least common denominator of 4 and 6 is 12.$$LCD(4,6)=12$$LCD(4,6)=12

Step 3: Rewrite both fractions

Rewrite each fraction with denominator 12.$$\frac{3}{4} = \frac{3\times 3}{4\times 3} = \frac{9}{12}$$43​=4×33×3​=129​ $$\frac{1}{6} = \frac{1\times 2}{6\times 2} = \frac{2}{12}$$61​=6×21×2​=122​

Step 4: Subtract the numerators$$\frac{9}{12}-\frac{2}{12} = \frac{9-2}{12} = \frac{7}{12}$$129​−122​=129−2​=127​

Step 5: Simplify the answer

The fraction is already in simplest form.$$\frac{7}{12}$$127​

Final answer:$$\frac{3}{4}-\frac{1}{6} = \frac{7}{12}$$43​−61​=127​

The answer is 7/12.

Multiplying Fractions

To multiply fractions, multiply the numerators together and multiply the denominators together. You do not need a common denominator.

Steps for Multiplying Fractions

To multiply two fractions:

1. Multiply the numerators.
2. Multiply the denominators.
3. Write the result as a fraction.
4. Simplify the answer if possible.

Example: Multiply Two Fractions

Problem: Multiply the following fractions.$$\frac{2}{5}\times\frac{3}{4}$$52​×43​

Step 1: Multiply the numerators$$2\times 3=6$$2×3=6

Step 2: Multiply the denominators$$5\times 4=20$$5×4=20

Step 3: Write the result as a fraction$$\frac{2}{5}\times\frac{3}{4} = \frac{6}{20}$$52​×43​=206​

Step 4: Simplify the answer

The greatest common factor of 6 and 20 is 2.$$\frac{6}{20} = \frac{6\div 2}{20\div 2} = \frac{3}{10}$$206​=20÷26÷2​=103​

Final answer:$$\frac{2}{5}\times\frac{3}{4} = \frac{3}{10}$$52​×43​=103​

The answer is 3/10.

Dividing Fractions

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal is found by flipping the numerator and denominator.

Steps for Dividing Fractions

To divide two fractions:

1. Keep the first fraction.
2. Change the division sign to multiplication.
3. Flip the second fraction.
4. Multiply the numerators.
5. Multiply the denominators.
6. Simplify the answer if possible.
7. Write the answer as a mixed number if it is improper.

Example: Divide Two Fractions

Problem: Divide the following fractions.$$\frac{5}{6}\div\frac{2}{3}$$65​÷32​

Step 1: Keep the first fraction$$\frac{5}{6}$$65​

Step 2: Change division to multiplication$$\div \quad \text{becomes} \quad \times$$÷becomes×

Step 3: Flip the second fraction

The reciprocal of:$$\frac{2}{3}$$32​

is:$$\frac{3}{2}$$23​

So,$$\frac{5}{6}\div\frac{2}{3} = \frac{5}{6}\times\frac{3}{2}$$65​÷32​=65​×23​

Step 4: Multiply the numerators$$5\times 3=15$$5×3=15

Step 5: Multiply the denominators$$6\times 2=12$$6×2=12

So,$$\frac{5}{6}\times\frac{3}{2} = \frac{15}{12}$$65​×23​=1215​

Step 6: Simplify the answer

The greatest common factor of 15 and 12 is 3.$$\frac{15}{12} = \frac{15\div 3}{12\div 3} = \frac{5}{4}$$1215​=12÷315÷3​=45​

Step 7: Write as a mixed number

Since 5/4 is an improper fraction, it can be written as:$$1\frac{1}{4}$$141​

Final answer:$$\frac{5}{6}\div\frac{2}{3} = \frac{5}{4} = 1\frac{1}{4}$$65​÷32​=45​=141​

The answer is 5/4, or 1 1/4 in mixed-number form.

Working with Fractions That Include Whole Numbers

Some fractions include a whole-number part. For example:$$2\frac{1}{3}$$231​

Before calculating, rewrite this value as an improper fraction.$$2\frac{1}{3} = \frac{2\times 3+1}{3} = \frac{7}{3}$$231​=32×3+1​=37​

The calculator does this automatically when you choose the option for fractions with whole numbers. After converting, it performs the selected operation using the same fraction rules shown above.

For a page focused only on this type of problem, use the Mixed Fraction Calculator.

Example: Add Fractions with Whole-Number Parts

Problem: Add the following values.$$2\frac{1}{3}+1\frac{3}{4}$$231​+143​

Step 1: Convert the first value$$2\frac{1}{3} = \frac{2\times 3+1}{3} = \frac{7}{3}$$231​=32×3+1​=37​

Step 2: Convert the second value$$1\frac{3}{4} = \frac{1\times 4+3}{4} = \frac{7}{4}$$143​=41×4+3​=47​

Step 3: Rewrite the problem$$2\frac{1}{3}+1\frac{3}{4} = \frac{7}{3}+\frac{7}{4}$$231​+143​=37​+47​

Step 4: Find the least common denominator

The denominators are 3 and 4.$$LCD(3,4)=12$$LCD(3,4)=12

Step 5: Rewrite both fractions$$\frac{7}{3} = \frac{7\times 4}{3\times 4} = \frac{28}{12}$$37​=3×47×4​=1228​ $$\frac{7}{4} = \frac{7\times 3}{4\times 3} = \frac{21}{12}$$47​=4×37×3​=1221​

Step 6: Add the numerators$$\frac{28}{12}+\frac{21}{12} = \frac{28+21}{12} = \frac{49}{12}$$1228​+1221​=1228+21​=1249​

Step 7: Write as a mixed number$$\frac{49}{12} = 4\frac{1}{12}$$1249​=4121​

Final answer:$$2\frac{1}{3}+1\frac{3}{4} = \frac{49}{12} = 4\frac{1}{12}$$231​+143​=1249​=4121​

The answer is 49/12, or 4 1/12 in mixed-number form.

Simple Fractions vs Fractions with Whole Numbers

A simple fraction has a numerator and denominator only.

Example:$$\frac{3}{8}$$83​

A fraction with a whole-number part has a whole number and a fraction.

Example:$$2\frac{1}{3}$$231​

This means:$$2+\frac{1}{3}$$2+31​

In the calculator, choose Simple fractions when both values only have numerators and denominators. Choose Fractions with whole numbers if either value has a whole-number part.

If one value is simple and the other has a whole-number part, choose Fractions with whole numbers and leave the whole-number box blank for the simple fraction.

How the Fraction Calculator Works

The calculator uses standard fraction rules. The rule depends on the operation selected.

For addition and subtraction, the calculator finds a common denominator. For multiplication, it multiplies across. For division, it multiplies by the reciprocal of the second fraction.

If a value includes a whole-number part, the calculator first rewrites it as an improper fraction. Then it performs the operation and simplifies the result.

Addition and Subtraction

For addition and subtraction, fractions must have the same denominator.

For example:$$\frac{a}{b}+\frac{c}{d}$$ba​+dc​

can be rewritten using a common denominator before adding.

The same idea applies to subtraction. The calculator finds the least common denominator, rewrites both fractions, adds or subtracts the numerators, and simplifies the answer.

Multiplication

For multiplication, the calculator multiplies the numerators and denominators.$$\frac{a}{b}\times\frac{c}{d} = \frac{a\times c}{b\times d}$$ba​×dc​=b×da×c​

Then it simplifies the result.

Division

For division, the calculator uses the reciprocal of the second fraction.$$\frac{a}{b}\div\frac{c}{d} = \frac{a}{b}\times\frac{d}{c}$$ba​÷dc​=ba​×cd​

The calculator then multiplies and simplifies the final answer.

Simplification

After the operation is complete, the calculator reduces the answer to lowest terms.

For example:$$\frac{6}{20} = \frac{3}{10}$$206​=103​

A fraction is in simplest form when the numerator and denominator have no common factor other than 1.

For a tool focused only on reducing fractions, use the Simplifying Fractions Calculator.

Types of Fraction Answers

The calculator may show the answer in different forms. Each form represents the same value.

Simplified Fraction

A simplified fraction is reduced to lowest terms.

Example:$$\frac{6}{20} = \frac{3}{10}$$206​=103​

The calculator always tries to return the fraction in simplest form.

Proper Fraction

A proper fraction has a numerator smaller than the denominator.

Example:$$\frac{7}{12}$$127​

This type of answer is already less than 1, so it should not be written as a mixed number.

Improper Fraction

An improper fraction has a numerator greater than or equal to the denominator.

Example:$$\frac{13}{12}$$1213​

This value is greater than 1, so it can be written in mixed-number form.

If you want a tool focused on improper fractions, use the Improper Fraction Calculator.

Mixed-Number Form

An improper fraction can be rewritten using a whole number and a fraction.

Example:$$\frac{13}{12} = 1\frac{1}{12}$$1213​=1121​

The calculator shows mixed-number form only when the final answer is improper.

To convert only between these forms, use the Improper Fraction to Mixed Number Calculator or the Mixed Number to Improper Fraction Calculator.

Decimal and Percent Forms

The calculator also shows decimal and percent forms.

Example:$$\frac{1}{2}=0.5=50\%$$21​=0.5=50%

These forms are useful when comparing values or using the result in real-life problems.

For dedicated conversion tools, use the Fraction to Decimal Calculator or the Fraction to Percent Calculator.

Common Fraction Rules

The calculator follows these rules:

• A denominator cannot be zero.
• You cannot divide by a fraction equal to zero.
• Addition and subtraction require a common denominator.
• Multiplication does not require a common denominator.
• Division uses the reciprocal of the second fraction.
• Values with whole-number parts are rewritten as improper fractions before calculation.
• The final answer should be simplified.
• Proper fractions should remain proper fractions.
• Improper fractions can be written in mixed-number form.

These rules help the calculator return a correct and simplified 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:

• Adding two fractions
• Subtracting two fractions
• Multiplying two fractions
• Dividing two fractions
• Checking homework answers
• Learning the steps behind fraction operations
• Simplifying the final answer
• Writing an improper answer in mixed-number form
• Seeing decimal and percent equivalents

This calculator is best for two-fraction problems. If your expression has three or more fractions, use a dedicated calculator for longer fraction expressions.

Need a More Specific Fraction Tool?

This calculator is designed for adding, subtracting, multiplying, or dividing two fractions. If you need a more specific tool, try one of the calculators below.

Simplify and Rewrite Fractions

• Simplifying Fractions Calculator
• Improper Fraction Calculator
• Improper Fraction to Mixed Number Calculator
• Mixed Number to Improper Fraction Calculator

Work with Values That Have Whole-Number Parts

• Mixed Fraction Calculator

Convert Fractions

• Fraction to Decimal Calculator
• Fraction to Percent Calculator

When available, you can also use a dedicated 3 fractions calculator for expressions with three fractions or more.

Frequently Asked Questions

What is a fraction calculator?

A fraction calculator is a tool that adds, subtracts, multiplies, or divides fractions. It gives the final answer in simplified form and shows the steps used to solve the problem.

Does this calculator show steps?

Yes. The calculator shows the main steps, such as finding a common denominator, multiplying by the reciprocal, simplifying the answer, and writing the final result.

Can I use fractions with whole-number parts?

Yes. Choose the option for fractions with whole-number parts, then enter the whole number, numerator, and denominator separately.

Can I enter a simple fraction in that mode?

Yes. If one value is a simple fraction, leave the whole-number box blank and enter only the numerator and denominator.

How do you add fractions with different denominators?

Find a common denominator, rewrite both fractions with that denominator, add the numerators, and simplify the result.

How do you subtract fractions with different denominators?

Find a common denominator, rewrite both fractions, subtract the numerators, and simplify the answer.

How do you multiply fractions?

Multiply the numerators together and multiply the denominators together. Then simplify the result.

How do you divide fractions?

Keep the first fraction, change division to multiplication, flip the second fraction, then multiply and simplify.

Does the calculator simplify the answer?

Yes. The calculator reduces the final fraction to lowest terms whenever possible.

Why is my answer shown in mixed-number form?

The calculator shows mixed-number form when the final answer is an improper fraction.

Can a denominator be zero?

No. A denominator cannot be zero because division by zero is undefined.

Can this calculator solve three fractions?

This calculator is designed for two fractions. For three fractions or longer expressions, use a dedicated calculator for multiple fractions.