Free Fraction Calculator
Add, subtract, multiply, and divide fractions with automatic simplification. Shows decimal equivalents and step-by-step results.
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0.833333
Formula
Addition: a/b + c/d = (ad + bc) / bd — Multiplication: a/b × c/d = ac / bd — then simplify by GCDHow the Fraction Calculator Works
This calculator performs all four arithmetic operations on fractions: addition, subtraction, multiplication, and division. Enter two fractions, select an operation, and get the result instantly — already simplified to its lowest terms using the Greatest Common Divisor (GCD) algorithm.
The decimal equivalent is shown below the fraction result, making it easy to understand the value in both formats.
Fraction Operations Step by Step
- Addition (a/b + c/d): Cross multiply and add: result = (ad + bc) / bd. Then simplify.
- Subtraction (a/b − c/d): Cross multiply and subtract: result = (ad − bc) / bd. Then simplify.
- Multiplication (a/b × c/d): Multiply straight across: result = (a×c) / (b×d). Then simplify.
- Division (a/b ÷ c/d): Flip the second fraction and multiply: result = (a×d) / (b×c). Then simplify.
Common Fraction-Decimal Equivalents
Memorizing these common conversions speeds up mental math:
- 1/2 = 0.5 | 1/3 ≈ 0.333 | 1/4 = 0.25 | 1/5 = 0.2
- 1/6 ≈ 0.167 | 1/8 = 0.125 | 1/10 = 0.1 | 1/12 ≈ 0.083
- 2/3 ≈ 0.667 | 3/4 = 0.75 | 3/8 = 0.375 | 5/8 = 0.625
Tips for Working with Fractions
- Always simplify — reducing fractions makes them easier to compare and work with
- Find the LCD — when adding or subtracting, using the Least Common Denominator (instead of just multiplying denominators) keeps numbers manageable
- Cross-cancel before multiplying — simplify diagonally before multiplying to avoid large numbers
- Check with decimals — convert your answer to a decimal to verify it makes sense
- Watch for negative signs — a negative in the numerator, denominator, or in front of the fraction all mean the same thing
Where Fractions Are Used
Fractions appear constantly in everyday life: cooking (1/2 cup, 3/4 teaspoon), construction (3/8 inch drill bit), music (whole notes, half notes, quarter notes), finance (stock prices historically quoted in fractions), and probability (1 in 6 chance = 1/6). Understanding fraction arithmetic makes all of these easier.
Frequently Asked Questions
How do you add fractions with different denominators?
To add fractions with different denominators, find a common denominator by multiplying the denominators together (or using the LCD). Then convert each fraction: a/b + c/d = (a×d + c×b) / (b×d). For example, 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6.
How do you simplify a fraction?
To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: the GCD of 12 and 18 is 6, so 12/18 = 2/3. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.
How do you multiply fractions?
Multiply the numerators together and the denominators together: a/b × c/d = (a×c)/(b×d). For example, 2/3 × 3/4 = 6/12 = 1/2. Tip: you can cross-cancel before multiplying to keep numbers smaller.
How do you divide fractions?
To divide fractions, multiply by the reciprocal (flip the second fraction). So a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). For example, 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1.5. Remember: dividing by a fraction makes the result larger.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals: 1/3 = 0.333... and 1/7 = 0.142857142857... This calculator shows the decimal equivalent automatically.