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Fraction Calculator

Add, subtract, multiply, and divide fractions.

Fraction Operations

Add, subtract, multiply, or divide two fractions.

Simplify Fraction

Reduce any fraction to its lowest terms.

Decimal to Fraction

Convert any decimal number into a simplified fraction.

Fraction to Decimal

Convert a fraction numerator and denominator into a decimal value.

Result
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Calculation Breakdown:

Enter values to compute result.

About this topic

Addition & Subtraction Add or subtract fractions by finding a common denominator.

A fraction represents equal parts of a whole. Before adding or subtracting fractions with different denominators, rewrite them so their denominators match; this ensures you are combining parts of the same size. For example, 1/2 can be rewritten as 3/6 and 1/3 as 2/6, so their sum is 5/6. When denominators already match, you can add or subtract the numerators directly and keep the denominator unchanged.

Key formulas & rules

  • •Requires common denominator
  • •Multiply crosswise to find new numerators
  • •Multiply denominators for new base
  • •Simplify final result using GCD
  • •Cannot add numerators and denominators across the board

Examples

Input Output Note
1/2 + 1/3 5/6 Common denominator is 6
3/4 - 1/4 1/2 Subtraction
2/5 + 1/5 3/5 Same denominator
1/2 - 1/4 1/4 Different denominators

Real-world uses

Cooking measurements Woodworking Time calculations
Multiplication & Division Multiply straight across; divide by multiplying the reciprocal.

Fraction multiplication combines the numerators and denominators, while fraction division asks how many times one fraction fits into another. To divide, keep the first fraction, flip the second fraction, and multiply. For example, 2/3 × 3/4 = 6/12 = 1/2, and 1/2 ÷ 1/4 = 1/2 × 4/1 = 2. You can often cancel common factors before multiplying to make the arithmetic easier.

Key formulas & rules

  • •No common denominator needed
  • •Multiply numerators together
  • •Multiply denominators together
  • •Division: multiply by reciprocal
  • •Cross-cancel common factors before multiplying

Examples

Input Output Note
2/3 × 3/4 1/2 Simplifies to 6/12
1/2 ÷ 1/4 2 Multiply by 4/1
2/3 × 3/2 1 Reciprocals
3/4 ÷ 1/2 3/2 Multiply by 2/1

Real-world uses

Batch cooking Scaling recipes Ratio conversions
Simplifying Fractions (GCD) Reduce a fraction to its lowest terms.

Simplifying a fraction means expressing the same value with smaller whole numbers. Find the greatest common divisor (GCD) shared by the numerator and denominator, then divide both by that number. For example, 24/36 becomes 2/3 because both 24 and 36 are divisible by 12. The value does not change; only the way it is written becomes simpler. A fraction is fully simplified when the numerator and denominator have no common factor greater than 1.

Key formulas & rules

  • •Uses Greatest Common Divisor
  • •Keeps the same value
  • •Makes reading easier
  • •Resulting GCD is 1
  • •Required for final answers

Examples

Input Output Note
24/36 2/3 GCD is 12
10/20 1/2 GCD is 10
7/9 7/9 Already simplified
100/250 2/5 GCD is 50

Real-world uses

Standardizing recipes Simplifying ratios Math homework
Decimal ↔ Fraction Conversion Convert between decimal numbers and fractions.

A terminating decimal can be written as a fraction by placing the digits over 10, 100, 1,000, or another power of 10, depending on the number of decimal places, and then simplifying. For example, 0.75 = 75/100 = 3/4. To convert a fraction to a decimal, divide its numerator by its denominator; for example, 3/4 = 0.75. Some fractions, such as 1/3, produce repeating decimals rather than a terminating result.

Key formulas & rules

  • •Count decimal places (n)
  • •Multiply by 10^n
  • •Simplifies using GCD
  • •Repeating decimals not supported
  • •Fraction to decimal is simple division

Examples

Input Output Note
0.75 3/4 2 decimal places
3/4 0.75 Terminating decimal
1/3 0.3333 Repeating decimal
1.25 5/4 Improper fraction

Real-world uses

Converting measurements Precision machining Data conversion

Modes & formulas

1

Fraction Operations

• Add or subtract by finding a common denominator first. • Multiply by multiplying numerators and denominators straight across. • Divide by multiplying by the reciprocal. • The calculator simplifies the result using the Greatest Common Divisor (GCD).
a/b + c/d = (a·d + b·c) / (b·d)

To add or subtract, multiply crosswise for the new numerator, and multiply denominators for the new denominator. For division, flip the second fraction and multiply.

2

Simplify Fraction

• Reduces a fraction to its lowest possible terms. • Enter the numerator and denominator. • The calculator finds the Greatest Common Divisor (GCD) and divides both numbers by it.
a/b ÷ GCD(a,b) = (a/GCD) / (b/GCD)

A fraction is in its simplest form when the only common factor between the numerator and denominator is 1.

3

Decimal to Fraction

• Converts a decimal number into a fraction. • Count the number of decimal places (n). • Multiply by 10^n, then simplify using the GCD.
0.75 = 75 / 100 = 3 / 4

If there are 2 decimal places, multiply by 100/100. If there are 3, multiply by 1000/1000, then reduce the fraction to its lowest terms.

4

Fraction to Decimal

• Converts a fraction into a decimal. • Enter the numerator and denominator. • The calculator divides the numerator by the denominator.
a / b = decimal

This is standard division. Note that fractions with denominators containing prime factors other than 2 and 5 will result in repeating decimals.

How to use it

Select the tab for the operation you need. Input your fractions or decimals. The tool will provide the exact simplified fraction and its decimal approximation.

Frequently asked questions

What is a GCD?
The Greatest Common Divisor is the largest number that divides evenly into both the numerator and denominator.
Why do fractions need a common denominator?
Before you can add or subtract fractions, the denominators must match so the parts being combined are the same size.
What is the Greatest Common Divisor (GCD)?
The largest number that divides evenly into both the numerator and denominator. For 24 and 36, the GCD is 12.
Why do fractions need a common denominator before adding?
Because you can only add parts of the same size. 1/2 and 1/3 cannot be added directly because halves and thirds are different sizes. Converting both to sixths (3/6 and 2/6) lets you add the numerators.
How do I divide fractions?
Keep the first fraction, flip the second fraction (its reciprocal), and multiply. For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
Can a fraction have a negative denominator?
Yes, but the calculator normalises it. A fraction like 3/(−4) is rewritten as −3/4 so the denominator is always positive.

Related calculators

Percentage Calculate percentages, increases, and decreases. Ratio Solve proportions and simplify ratios. Average Find mean, median, and average of a dataset. Exponent & Root Calculate powers and bases. Square Root & N-th Root Find square roots and radical values. Linear Equation Solve equations of the form ax + b = c.
Read the full Fraction guide — examples & 18 FAQs