Fraction Calculator

What Is a Fraction Calculator?

A fraction calculator performs arithmetic operations on fractions including addition, subtraction, multiplication, and division. This tool handles proper fractions, improper fractions, and mixed numbers. Results are automatically simplified to lowest terms and can be displayed as both fractions and decimals.

Fraction Operation Formulas

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

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

Multiplication: a/b × c/d = ac / bd

Division: a/b ÷ c/d = ad / bc

Example Calculation

Adding 2/3 + 3/4

Using the formula: (2×4 + 3×3) / (3×4) = (8 + 9) / 12 = 17/12

Result: 17/12 = 1 5/12 ≈ 1.417

Enter Fractions

Enter whole numbers (optional), numerators, and denominators.

Result

When to Use This Calculator

📚

Math Homework

Check your fraction calculations and learn the steps.

🍳

Cooking & Recipes

Adjust ingredient measurements when scaling recipes.

📐

Construction

Calculate measurements in inches and fractions.

💹

Finance

Work with fractional shares and interest rates.

Notes

Denominators cannot be zero.
Results are automatically simplified to lowest terms.
Large numbers may result in precision limitations.

Frequently Asked Questions

To add fractions with different denominators: 1) Find the Least Common Denominator (LCD) of both fractions. 2) Convert each fraction to an equivalent fraction with the LCD. 3) Add the numerators while keeping the denominator. 4) Simplify if possible. Example: 1/4 + 2/3 → LCD is 12 → 3/12 + 8/12 = 11/12. A common mistake is adding denominators—never do this.

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Formula: (a/b) × (c/d) = (a×c)/(b×d). Then simplify the result. Example: 2/3 × 4/5 = 8/15. No common denominator is needed for multiplication. You can also simplify before multiplying by cross-canceling common factors.

To divide fractions, multiply by the reciprocal of the second fraction. Flip the second fraction (swap numerator and denominator) and multiply. Formula: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c). Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Remember: "Keep, Change, Flip" is a helpful mnemonic.

To convert a mixed number (like 2 3/4) to an improper fraction: Multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. Formula: a b/c = (a×c + b)/c. Example: 2 3/4 = (2×4 + 3)/4 = 11/4. This is essential before performing operations with mixed numbers.

To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). Find the largest number that divides both evenly. Example: 24/36 → GCD of 24 and 36 is 12 → 24÷12 / 36÷12 = 2/3. A fraction is fully simplified when the GCD of numerator and denominator is 1.

Yes, this calculator supports mixed numbers. Enter the whole number in the first field and the fractional part in the numerator/denominator fields. The calculator converts mixed numbers to improper fractions for calculation, then can display results as mixed numbers. This makes it easier to work with real-world measurements and recipes.

References

Khan Academy. "Fraction Arithmetic." Khan Academy, 2024.
Wolfram MathWorld. "Fraction." MathWorld, 2024.
National Council of Teachers of Mathematics. "Principles and Standards." NCTM, 2020.
Common Core State Standards Initiative. "Mathematics Standards: Number and Operations—Fractions." CCSSI, 2021.

Inputs Explained

Numerator: The top number of a fraction, representing the parts you have.
Denominator: The bottom number of a fraction, representing the total parts. Cannot be zero.
Whole Number: For mixed numbers, enter the whole number part separately (e.g., 2 in "2 3/4").
Operation: Select addition (+), subtraction (−), multiplication (×), or division (÷).
Simplify Option: When enabled, results are automatically reduced to lowest terms.

Limitations & Notes

Division by zero (denominator = 0) is undefined and will produce an error.
Very large numerators or denominators may cause display issues; use decimal approximations for extreme values.
Negative fractions are supported; the negative sign applies to the entire fraction.
Mixed numbers are converted to improper fractions for calculation, then converted back for display.
Repeating decimals from fraction conversion are truncated; exact fraction form is more precise.
Complex fractions (fractions within fractions) should be simplified step by step.