Fraction Calculator
How do you add fractions with different denominators?
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. Pairs well with the LCM and HCF Calculator and the Percentage Calculator.
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.
How does fraction calculator: practical work?
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 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
LCM method for adding and subtracting fractions
To add fractions with different denominators, find the LCM of the denominators. Example: 1/4 + 1/6. LCM(4,6) = 12. Convert: 3/12 + 2/12 = 5/12. Why LCM? It gives the smallest common denominator, keeping numbers manageable. For 2/5 + 3/7: LCM(5,7) = 35. Convert: 14/35 + 15/35 = 29/35. Shortcut for two fractions: denominator = product of denominators ÷ GCD. This gives the LCD without computing LCM separately.
Fractions in everyday India: cooking, medicine, and carpentry
Fractions appear constantly in practical Indian contexts. Cooking: a recipe for 4 calls for 2½ cups of rice — scaling to 6 people requires multiplying by 6/4 = 3/2, giving 3¾ cups. Medicine: a 500 mg tablet cut in half (1/2) gives 250 mg. A 0.5 mL dose from a 2 mL vial = ¼ of the vial. Carpentry: lumber sold in standard lengths often requires cutting 3/8-inch, 5/16-inch, or 7/32-inch dimensions. Understanding fractions prevents dosing errors and material waste.
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). — see also: LCM and HCF calculator
Common fraction, decimal, and percentage equivalents
| Fraction | Decimal | Percentage | Notes |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half |
| 1/3 | 0.333... | 33.33% | Repeating decimal |
| 2/3 | 0.666... | 66.67% | Repeating decimal |
| 1/4 | 0.25 | 25% | Quarter |
| 3/4 | 0.75 | 75% | Three quarters |
| 1/5 | 0.2 | 20% | |
| 1/6 | 0.1666... | 16.67% | Repeating decimal |
| 1/7 | 0.142857... | 14.29% | 6-digit repeating |
| 1/8 | 0.125 | 12.5% | One eighth |
| 1/10 | 0.1 | 10% | |
| 1/12 | 0.0833... | 8.33% | One twelfth |
| 1/16 | 0.0625 | 6.25% | Used in cooking (US) |
| 1/20 | 0.05 | 5% | |
| 1/100 | 0.01 | 1% | One percent |
Sources & References
Sources: Common Core State Standards for Mathematics (CCSS.MATH.CONTENT.4.NF); Euclid's algorithm for GCD — Elements, Book VII.
Related calculators
Where do fractions show up in everyday Indian life?
Indian kitchens still run on fractional measures — half katori of dal, quarter kilo of paneer, three-fourths cup of rice — and scaling a 4-person recipe to 6 means multiplying every fraction by 3/2, exactly the operation this calculator performs. Market maths leans the same way: sabzi vendors price by quarter kilo (pao), and gold by fractions of a tola (11.66 g), where 3/4 tola at ₹74,000 per tola is a 55,500-rupee fraction problem.
Land records keep older fractional traditions alive: agricultural holdings are often described in fractional bigha or acre shares among heirs — a 5/8 share of 2.4 acres is 1.5 acres — and partition deeds regularly require exactly the common-denominator addition this tool demonstrates. Construction follows suit, with plumbing and hardware sized in fractional inches (1/2", 3/4") despite metric officialdom.
For students, fractions are the gateway skill the CBSE curriculum builds ratios, percentages, and probability upon. The visual bars above show why denominators must match before adding — the single concept that, once internalised, removes most fraction errors. Convert any result to a percentage with the percentage calculator or to a decimal for calculator-friendly arithmetic.