Fraction Calculator
Add, subtract, multiply, divide fractions
How to Calculate with Fractions
This calculator performs all four basic operations with fractions and automatically simplifies the result. It shows the answer as a fraction, a simplified fraction, a mixed number, and a decimal value.
Adding and Subtracting Fractions
To add or subtract fractions, find a common denominator by multiplying the denominators together, adjust the numerators accordingly, then add or subtract the numerators. For example, 3/4 + 1/2 = 6/8 + 4/8 = 10/8, which simplifies to 5/4 or 1 and 1/4.
Multiplying and Dividing Fractions
To multiply fractions, multiply the numerators together and the denominators together: (3/4) x (1/2) = 3/8. To divide fractions, multiply by the reciprocal of the second fraction: (3/4) / (1/2) = (3/4) x (2/1) = 6/4 = 3/2.
Simplifying Fractions
A fraction is simplified by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). For example, 10/8 simplified: GCD of 10 and 8 is 2, so 10/8 = 5/4. This calculator automatically simplifies all results.
Fraction Calculator: practical guide
The Fraction Calculator is built for people who want a fast answer without losing context. It keeps the calculation simple, shows the result clearly, and helps you understand what the number means before you use it in a real decision.
This tool is built for quick everyday math. It can help with shopping, invoices, schoolwork, reports, and checking manual calculations.
What is the best way to use the Fraction Calculator?
Enter the values carefully, review the units, and use the result as a reliable reference point. The Fraction Calculator is most useful when you compare scenarios or repeat the calculation with consistent inputs.
Is the Fraction Calculator accurate?
The calculator follows standard calculation logic, but accuracy depends on the values you enter and the assumptions behind the formula. For important math decisions, use it as guidance and verify the result with a trusted source.
Understanding fractions
A fraction represents a part of a whole. It consists of a numerator (the top number, representing how many parts) and a denominator (the bottom number, representing how many equal parts the whole is divided into). The fraction 3/4 means 3 parts out of 4 equal parts. Fractions appear in cooking, construction, finance, probability, and anywhere division yields a non-whole result.
Adding and subtracting fractions
To add or subtract fractions, they must have a common denominator. Find the Least Common Denominator (LCD) — the smallest number divisible by both denominators.
Same denominator: 3/8 + 2/8 = (3+2)/8 = 5/8
Different denominators — step by step:
1/3 + 1/4: LCD = 12. Convert: 4/12 + 3/12 = 7/12
5/6 – 2/9: LCD = 18. Convert: 15/18 – 4/18 = 11/18
3/4 + 5/6: LCD = 12. Convert: 9/12 + 10/12 = 19/12 = 1 7/12 (mixed number)
Multiplying fractions
Multiply numerators together and denominators together. Simplify by cancelling common factors before multiplying when possible.
2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5 (simplified by dividing both by 3)
4/7 × 14/9 = (4×14)/(7×9) = cancel 14/7 = 2: (4×2)/9 = 8/9
Multiplying mixed numbers: convert to improper fractions first. 2½ × 1¾ = 5/2 × 7/4 = 35/8 = 4 3/8
Dividing fractions
To divide by a fraction, multiply by its reciprocal (flip the second fraction).
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6
5 ÷ 3/8 = 5/1 × 8/3 = 40/3 = 13 1/3
Simplifying fractions
A fraction is in simplest form when the numerator and denominator share no common factors (GCD = 1). Divide both by their Greatest Common Divisor (GCD).
24/36: GCD = 12. Simplified: 24÷12 / 36÷12 = 2/3
48/64: GCD = 16. Simplified: 48÷16 / 64÷16 = 3/4
Converting between fractions, decimals and percentages
- Fraction → Decimal: Divide numerator by denominator. 3/8 = 3 ÷ 8 = 0.375
- Decimal → Fraction: Write as fraction with power of 10 denominator. 0.75 = 75/100 = 3/4
- Fraction → Percentage: Convert to decimal then multiply by 100. 7/20 = 0.35 = 35%
- Percentage → Fraction: Divide by 100 and simplify. 65% = 65/100 = 13/20
Frequently asked questions about fractions
What is a mixed number? A mixed number combines a whole number and a proper fraction, like 3 2/5. To convert to improper fraction: (3 × 5 + 2)/5 = 17/5. To convert improper fraction to mixed number: 17 ÷ 5 = 3 remainder 2, so 3 2/5.
What is a reciprocal? The reciprocal of a fraction is formed by swapping numerator and denominator. Reciprocal of 2/3 is 3/2. Reciprocal of 5 is 1/5. A number multiplied by its reciprocal always equals 1.
How do fractions appear in everyday life? Cooking recipes (½ cup, ¾ teaspoon), construction measurements (3/8 inch drill bit), probability (1/6 chance on a die), financial ratios (P/E ratio), and time expressions (¼ hour = 15 minutes).