Fraction Calculator

Add, subtract, multiply, and divide fractions. Simplifies results to the lowest terms automatically.

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What Is a Fraction Calculator?

This fraction calculator performs addition, subtraction, multiplication, and division on any two fractions. Enter the numerators and denominators, pick an operation, and get the simplified result instantly.

Fractions represent parts of a whole. The number above the line (numerator) counts the parts. The number below the line (denominator) sets how many equal parts make the whole. Operations on fractions follow fixed rules that this tool applies automatically.

Results are reduced to lowest terms using the greatest common divisor. Mixed numbers and improper fractions are both supported. Use this calculator for homework, recipes, woodworking measurements, or any task that involves parts of a whole.

How Do You Use This Fraction Calculator?

Enter two fractions using the numerator and denominator fields, select the operation (add, subtract, multiply, or divide), and click Calculate. The result is automatically simplified.

Enter the numerator and denominator of the first fraction.
Select the operation: add, subtract, multiply, or divide.
Enter the numerator and denominator of the second fraction.
Click Calculate to see the result.
Read the simplified fraction displayed below.
Review the step-by-step working if shown.
Click Reset to perform another calculation.

How Does the Fraction Calculator Formula Work?

The formula used: a/b + c/d = (ad + bc) / bd. a/b × c/d = ac / bd. a/b ÷ c/d = ad / bc

Add or subtract fractions by finding a common denominator. Multiply each numerator by the other fraction's denominator, then add or subtract the adjusted numerators.

a/b + c/d = (ad + bc) / bd

a/b - c/d = (ad - bc) / bd

Multiply fractions by multiplying numerators together and denominators together.

a/b × c/d = ac / bd

Divide fractions by flipping the second fraction and multiplying.

a/b ÷ c/d = a/b × d/c = ad / bc

Simplify the result by dividing both parts by their greatest common divisor (GCD).

What Are Some Example Calculations?

1/3 + 1/4 = 4/12 + 3/12 = 7/12. 2/3 × 3/5 = 6/15 = 2/5. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.

A recipe calls for 2/3 cup of flour and you want to add 1/4 cup more.

2/3 + 1/4 = (2×4 + 1×3) / (3×4) = (8 + 3) / 12 = 11/12.

You need 11/12 cup of flour in total.

A board is 7/8 metre long. Cut it into 2 equal pieces.

7/8 ÷ 2 = 7/8 ÷ 2/1 = 7/8 × 1/2 = 7/16.

Each piece measures 7/16 metre.

A tank is 3/5 full. You use 1/4 of the total capacity.

3/5 - 1/4 = (3×4 - 1×5) / (5×4) = (12 - 5) / 20 = 7/20.

The tank is 7/20 full after use.

When Should You Use a Fraction Calculator?

Use this calculator when working with values expressed as fractions rather than decimals. Common situations include doubling or halving recipe quantities, calculating dimensions in woodworking or sewing, and solving maths homework problems.

Fractions appear in financial contexts too — stock prices, interest-rate splits, and proportional ownership. Enter your two fractions above and the calculator handles common denominators, cross-multiplication, and simplification automatically.

What Do These Terms Mean?

Numerator

The top number in a fraction. It counts how many parts are taken from the whole.

Denominator

The bottom number in a fraction. It states how many equal parts the whole is divided into.

Improper fraction

A fraction where the numerator is larger than the denominator. Example: 7/4 equals 1 and 3/4.

Mixed number

A whole number combined with a proper fraction. Example: 2 and 1/3.

Greatest common divisor (GCD)

The largest number that divides evenly into both the numerator and denominator.

Reciprocal

A fraction flipped upside down. The reciprocal of 3/4 is 4/3. Used when dividing fractions.

How Do the Options Compare?

Operation	Rule	Example
Addition	Find common denominator, add numerators	1/3 + 1/4 = 4/12 + 3/12 = 7/12
Subtraction	Find common denominator, subtract numerators	3/4 - 1/3 = 9/12 - 4/12 = 5/12
Multiplication	Multiply numerators, multiply denominators	2/3 × 3/5 = 6/15 = 2/5
Division	Flip second fraction, then multiply	3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2
Simplification	Divide both parts by GCD	8/12 → GCD is 4 → 2/3
Mixed to improper	Whole × denominator + numerator	2 1/3 = (2×3+1)/3 = 7/3

What Are the Best Tips to Know?

Convert mixed numbers to improper fractions first. Multiply the whole number by the denominator, add the numerator.
Simplify before multiplying to keep numbers smaller. Cancel common factors across numerators and denominators.
Check your answer by converting the result to a decimal and comparing with a decimal calculation.
Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Use the GCD to reduce the answer. If both numbers are even, divide by 2 as a quick first step.

What Mistakes Should You Avoid?

Adding numerators and denominators directly. 1/3 + 1/4 is not 2/7. Find a common denominator first.
Forgetting to flip the second fraction when dividing. Multiply by the reciprocal instead.
Not simplifying the final answer. Always reduce to lowest terms using the GCD.
Cross-multiplying when multiplying fractions. Cross-multiplication applies to addition and subtraction only.
Ignoring negative signs on numerators or denominators, leading to incorrect positive results.

Frequently Asked Questions

How do I add fractions with different denominators?

Find a common denominator by multiplying the denominators. Then adjust each numerator accordingly. For example, 1/3 + 1/4: common denominator is 12, so 4/12 + 3/12 = 7/12.

How do I simplify a fraction?

Divide both the numerator and denominator by their greatest common divisor (GCD). For example, 6/15: the GCD of 6 and 15 is 3, so 6/15 simplifies to 2/5.

How do I divide fractions?

Flip the second fraction (take its reciprocal) and multiply. For example, 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator and add the numerator. Place the result over the original denominator. For example, 3 2/5 = (3×5 + 2)/5 = 17/5.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375. Some fractions produce repeating decimals: 1/3 = 0.3333 recurring.

What is the least common denominator (LCD)?

The LCD is the smallest number that both denominators divide into evenly. For 1/6 and 1/4, the LCD is 12. Using the LCD keeps numbers smaller than using the product of the denominators.

How do I subtract fractions from a whole number?

Write the whole number as a fraction with denominator 1. Then find a common denominator and subtract. For example, 3 - 2/5 = 15/5 - 2/5 = 13/5 = 2 3/5.

Can I multiply a fraction by a whole number?

Yes. Write the whole number as a fraction over 1 and multiply. For example, 3/4 × 6 = 3/4 × 6/1 = 18/4 = 9/2 = 4 1/2.

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