Fraction Calculator
Fraction Calculator
Choose a calculation type below. For a mixed number like 1¾, enter it as an improper fraction: 7/4.
Full Breakdown
How to Use the Fraction Calculator
Our Fraction Calculator combines three tools in one: add, subtract, multiply or divide two fractions; simplify a single fraction to its lowest terms; or convert a decimal number into a fraction. Every result is shown as a simplified fraction, a mixed number, and a decimal, so you can use whichever form suits you.
- Choose a calculation type using the buttons at the top: “Add / Subtract / Multiply / Divide”, “Simplify A Fraction”, or “Decimal To Fraction”.
- For fraction operations: enter Fraction A and Fraction B as numerator and denominator, and choose an operation (+, −, ×, ÷).
- For simplifying: enter a numerator and denominator to reduce to lowest terms.
- For decimal to fraction: type a decimal number, such as 0.75 or -3.2.
- Results update automatically as you type, or click Calculate to refresh manually.
- Use Copy Results to copy a plain-text summary, or Print for a printable version.
How Fraction Arithmetic Works
| Operation | Method | Example |
|---|---|---|
| Add / Subtract | Convert to a common denominator, then add or subtract the numerators | 1/2 + 1/3 = 5/6 |
| Multiply | Multiply the numerators together and the denominators together | 1/2 × 1/3 = 1/6 |
| Divide | Multiply by the reciprocal of the second fraction | 1/2 ÷ 1/3 = 3/2 |
| Simplify | Divide numerator and denominator by their greatest common divisor | 18/24 = 3/4 |
Entering Mixed Numbers
This calculator works with numerator/denominator pairs rather than a separate whole-number field, so a mixed number needs to be entered as an improper fraction first. To convert, multiply the whole number by the denominator and add the numerator: for example, 1¾ becomes (1 × 4) + 3 = 7, so you’d enter 7/4. Every result is also shown back in mixed-number form for readability.
Converting Between Decimals and Fractions
To convert a decimal to a fraction, this calculator reads the decimal’s digits directly rather than relying on floating-point division, so terminating decimals like 0.75 or 0.125 convert exactly rather than picking up tiny rounding errors. The digits after the decimal point become the numerator over a matching power of 10 (for example, 0.75 becomes 75/100), which is then simplified to lowest terms (3/4).
Common Uses for a Fraction Calculator
- Cooking and baking: Combine or scale ingredient measurements given as fractions, such as 3/4 cup plus 1/3 cup.
- DIY and construction: Add or subtract measurements given in fractions of an inch.
- Homework and study: Check working for fraction arithmetic, simplification, and decimal conversions.
- Recipes and ratios: Simplify ratios or proportions down to their simplest whole-number form.
Important Assumptions
- Numerators and denominators must be whole numbers; a warning is shown if a decimal is entered into these fields instead.
- A denominator must be a whole number of 1 or greater; negative or zero denominators are rejected. Put any minus sign on the numerator instead, e.g. -1/2 rather than 1/-2.
- Numerators and denominators are limited to 15 digits each as a sensible input cap. The underlying arithmetic uses exact whole-number (BigInt) calculations rather than standard floating-point maths, so results stay precise even when intermediate numbers, such as a common denominator, grow much larger than the inputs themselves.
- Mixed numbers should be entered as improper fractions (see above); the calculator does not have a separate whole-number input field.
- Decimal-to-fraction conversion supports up to 12 decimal places and works from the typed digits directly, avoiding floating-point rounding errors for terminating decimals.
- Decimal results elsewhere in the calculator are rounded to 6 decimal places for display.
Frequently Asked Questions
How do I add or subtract fractions with different denominators?
Find a common denominator by multiplying the two denominators together, convert each fraction to that common denominator, then add or subtract the numerators. This calculator does that automatically and simplifies the result.
How do I multiply and divide fractions?
To multiply fractions, multiply the numerators together and the denominators together. To divide fractions, multiply the first fraction by the reciprocal of the second (flip the second fraction’s numerator and denominator, then multiply).
How do I simplify a fraction to its lowest terms?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 18/24 has a GCD of 6, so it simplifies to 3/4.
How do I enter a mixed number like 1 3/4?
Enter it as an improper fraction instead: 1 3/4 becomes 7/4 (multiply the whole number by the denominator, then add the numerator). The calculator’s results also show a mixed-number form automatically.
How do I convert a decimal to a fraction?
Write the decimal’s digits as the numerator over a power of 10 matching the number of decimal places, then simplify. For example, 0.75 becomes 75/100, which simplifies to 3/4.
Why can’t a fraction have a denominator of 0?
A fraction’s denominator represents the number of equal parts something is divided into, and dividing by 0 parts is mathematically undefined, so this calculator does not allow a denominator of 0.