Fraction Calculator

Calculate fraction addition, subtraction, multiplication, division, mixed numbers, and decimals.

Decimal number

Result

What is the Online Fraction Calculator?

The free online Fraction Calculator solves fraction arithmetic quickly in your web browser and shows the steps to simplify results. It handles addition, subtraction, multiplication, and division for proper fractions, improper fractions, and mixed numbers. Each calculation automatically reduces the answer to its simplest form (irreducible fraction) while displaying common denominators, step-by-step workings, and exact decimal conversions to help verify schoolwork or recipes.

Beyond standard arithmetic, it provides simultaneous conversion between fractions and decimals, displays least common denominators (LCD), and breaks down improper fractions into mixed numbers. With memory keys (MC, MR, M+, M−, MS), you can chain multi-step fraction equations for carpentry, baking, and engineering.

Step-by-Step Guide: How to Calculate Fractions

Select Operation: Choose + (Add), − (Subtract), × (Multiply), or ÷ (Divide).
Enter Numerators and Denominators:
- Proper / Improper Fractions: Enter the top numerator and bottom denominator for both fractions.
- Mixed Numbers: Enter the whole integer alongside the numerator and denominator (e.g., 2 3/4).
Click Calculate and Review Output:
- Reduced Fraction (Simplest Form): The exact fraction reduced by its greatest common divisor.
- Mixed Number Form: Proper representation showing whole integer and remainder.
- Decimal Equivalent: Floating-point decimal representation (e.g., 3/4 = 0.75).
- Step-by-Step Solution: Common denominator finding and intermediate cross-multiplication.
Store Values in Memory: Retain fraction totals using MS and M+ for subsequent project measurements.

Core Fraction Formulas & Rules

Addition: a/b + c/d = (a·d + b·c) / (b·d) (Find common denominator, add numerators)
Subtraction: a/b − c/d = (a·d − b·c) / (b·d) (Find common denominator, subtract numerators)
Multiplication: a/b × c/d = (a·c) / (b·d) (Multiply numerators together, multiply denominators together)
Division (Invert & Multiply): a/b ÷ c/d = a/b × d/c = (a·d) / (b·c)
Simplifying (Reducing): Divide numerator and denominator by their Greatest Common Divisor: GCD(numerator, denominator).

Practical Real-World Calculation Examples

Adding Unlike Fractions (Baking / Recipes): 1/3 cup + 1/4 cup = 4/12 + 3/12 = 7/12 cup ≈ 0.5833.
Dividing Fractions (Carpentry Measurements): 3/4 inch ÷ 1/8 inch = 3/4 × 8/1 = 24/4 = 6 cuts.
Multiplying Mixed Numbers: 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4.

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Frequently Asked Questions (FAQ)

How do you add or subtract fractions with different denominators?

Find the Least Common Denominator (LCD), convert each fraction to an equivalent fraction with that common denominator, then add or subtract the numerators while keeping the denominator the same (e.g., 1/2 + 1/3 = 3/6 + 2/6 = 5/6).

How do you multiply fractions?

Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator, then reduce to simplest form (e.g., 2/3 × 4/5 = 8/15).

Why do you invert and multiply when dividing fractions?

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal (the inverted fraction). For example, 3/4 ÷ 2/3 becomes 3/4 × 3/2 = 9/8.

What does simplifying or reducing a fraction mean?

Simplifying means dividing both the numerator and denominator by their Greatest Common Divisor (GCD) until they cannot be divided any further (e.g., 8/12 reduces to 2/3).

What is the difference between an improper fraction and a mixed number?

An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/3), while a mixed number represents the same value as a whole number and a proper fraction combined (e.g., 2 1/3).

How do you convert a fraction into a decimal?

Divide the numerator by the denominator using standard division (e.g., 3/4 = 3 ÷ 4 = 0.75). Our calculator displays both the exact fraction and decimal approximation.

Can you convert a decimal into a fraction?

Yes, write the decimal over its place value (such as 0.75 = 75/100) and reduce it by dividing numerator and denominator by their GCD (25) to get 3/4.

What happens if the denominator is zero?

Division by zero is mathematically undefined. A fraction cannot have a denominator of 0, and the calculator will prompt you to enter a non-zero denominator.

How do I calculate mixed numbers on this tool?

Enter the whole number in the integer box, and enter the remaining fractional part in the numerator/denominator boxes (e.g., 1 1/2 + 2 1/4 = 3 3/4).

Is this fraction calculator free on smartphones and tablets?

Yes, it is 100% free with no registration required and is fully optimized for touch controls on iOS and Android devices.

Can this fraction calculator be used for baking and woodworking?

Yes, it is widely used for scaling recipe ingredients (like 1/3 cup + 1/2 cup) and calculating fractional lumber dimensions.