Fraction Calculator
Add, subtract, multiply, or divide two fractions and instantly see the simplified result, the mixed number form, and the decimal equivalent — built for homework, cooking measurements, and everyday math.
Calculate With Fractions
Enter both fractions and choose an operation — the result updates instantly.
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How Fraction Arithmetic Works
A fraction represents a part of a whole, written as a numerator over a denominator (like 3/4). Adding, subtracting, multiplying, and dividing fractions each follow their own rule, and the result is usually simplified to its lowest terms so it's as easy to read as possible. Fractions show up constantly in cooking measurements, construction and woodworking, financial splits, and math homework at every level.
Unlike whole numbers, fractions can't always be combined directly — adding or subtracting requires a shared denominator first, while multiplying and dividing can be done straight across. Once the raw result is found, it's simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
The Four Fraction Operations
Each operation on two fractions (a/b and c/d) follows a fixed rule.
Addition & Subtraction
a/b ± c/d = (a×d ± c×b) / (b×d)
Find a common denominator by cross-multiplying, combine the numerators, then simplify.
Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
Multiplication & Division
a/b × c/d = (a×c) / (b×d)
Multiply straight across for multiplication; for division, multiply by the reciprocal of the second fraction instead.
Example: 2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9
Common Fraction to Decimal Table
A ready reference for fractions that come up often in everyday measurements and recipes.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.6667 | 66.67% |
| 3/4 | 0.75 | 75% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
For a fraction not listed here, the calculator at the top of this page computes the exact decimal and percentage instantly.
Worked Examples: Step by Step
Example 1: Add 3/4 and 1/6
- Common denominator: 4 × 6 = 24
- Convert: 3/4 = 18/24, 1/6 = 4/24
- Add: 18/24 + 4/24 = 22/24
- Simplify (GCD of 22 and 24 is 2): 22/24 = 11/12
- Answer: 3/4 + 1/6 = 11/12
Example 2: Subtract 2/5 from 7/10
- Common denominator: 10 (already shared)
- Convert: 2/5 = 4/10
- Subtract: 7/10 − 4/10 = 3/10
- Answer: 7/10 − 2/5 = 3/10 (already in lowest terms)
Example 3: Multiply 5/6 by 3/10, then check the answer as a decimal
- Multiply straight across: (5×3) / (6×10) = 15/60
- Simplify (GCD of 15 and 60 is 15): 15/60 = 1/4
- Decimal check: 1/4 = 0.25, and 5/6 × 3/10 = 0.8333 × 0.3 = 0.25 ✓
- Answer: 5/6 × 3/10 = 1/4
Where Fraction Math Comes Up
Cooking and Baking
Scaling a recipe up or down, or combining measurements like 3/4 cup and 1/3 cup, requires adding and multiplying fractions accurately to avoid ruining a dish.
Construction and Woodworking
Measurements on a tape measure are often given in fractions of an inch, and adding or subtracting cut lengths (like 5/8" and 1/4") relies on fraction arithmetic to get an exact fit.
Homework and Test Prep
Fraction operations are a core part of elementary and middle school math curricula, and checking work against a calculator helps confirm the simplification and common-denominator steps were done correctly.
Financial Splits and Ratios
Splitting a bill, dividing ownership shares, or calculating a discount expressed as a fraction all rely on the same addition, subtraction, and multiplication rules.
Sewing and Fabric Cutting
Pattern measurements are frequently given in fractional inches, and combining multiple pattern pieces means adding fractions together precisely before cutting fabric.
Common Mistakes When Working With Fractions
- Adding or subtracting numerators and denominators separately. 1/2 + 1/3 is NOT 2/5 — fractions must share a common denominator before the numerators can be combined.
- Forgetting to flip the second fraction when dividing. Dividing by a fraction means multiplying by its reciprocal; skipping this step (or flipping the wrong fraction) gives an incorrect result.
- Leaving the answer unsimplified. A fraction like 8/12 is mathematically correct but should be reduced to 2/3 by dividing both terms by their GCD for a clear, standard answer.
- Mixing up mixed numbers and improper fractions during multiplication. A mixed number like 1 1/2 must first be converted to an improper fraction (3/2) before multiplying or dividing — multiplying the whole number and fraction parts separately gives the wrong answer.
Cheat Sheet: The Four Operations
| Operation | Rule |
|---|---|
| Add | a/b + c/d = (a×d + c×b) / (b×d) |
| Subtract | a/b − c/d = (a×d − c×b) / (b×d) |
| Multiply | a/b × c/d = (a×c) / (b×d) |
| Divide | a/b ÷ c/d = a/b × d/c = (a×d) / (b×c) |
Frequently Asked Questions
How do I add two fractions with different denominators?
Cross-multiply to find a common denominator, combine the numerators, then simplify. For example, 1/4 + 2/5 = (1×5 + 2×4) / (4×5) = 13/20.
How do I divide fractions?
Multiply the first fraction by the reciprocal (flipped version) of the second. For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD). For example, 12/18 has a GCD of 6, so it simplifies to 2/3.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 5/8 = 5 ÷ 8 = 0.625.
What's the difference between a proper fraction, an improper fraction, and a mixed number?
A proper fraction has a numerator smaller than its denominator (like 3/4). An improper fraction has a numerator equal to or larger than its denominator (like 7/4). A mixed number combines a whole number with a proper fraction (like 1 3/4), and it's equivalent to the improper fraction form.
Can this calculator handle negative fractions?
Yes. Enter a negative number in either the numerator or denominator field and the calculator will apply the correct sign to the simplified result, mixed number, and decimal.
Does this calculator simplify the result automatically?
Yes. Every result is reduced to its lowest terms using the greatest common divisor, and it's also shown as a mixed number, a decimal, and a percentage.