Fraction Calculator
How to Work with Fractions
Addition & Subtraction
Find a common denominator, then add or subtract numerators:
a/b ± c/d = (a×d ± c×b) / (b×d)
Multiplication
a/b × c/d = (a×c) / (b×d) — then simplify by GCF.
Division
Multiply by the reciprocal: a/b ÷ c/d = (a×d) / (b×c)
Frequently Asked Questions
What is 3/4 + 2/3?
LCD of 4 and 3 = 12. Convert: 9/12 + 8/12 = 17/12 = 1 5/12.
How do I simplify a fraction?
Divide both numerator and denominator by their GCF (Greatest Common Factor). To simplify 18/24: GCF(18,24) = 6. 18÷6 = 3, 24÷6 = 4. Simplified: 3/4.
What is a mixed number?
A mixed number combines a whole number and a proper fraction: 2 3/4 = 2 + 3/4 = 11/4 as an improper fraction. To convert: multiply whole number by denominator, add numerator: 2×4+3 = 11/4.
Simplification
Divide both parts by their GCF. Example: GCF(12,8) = 4 → 12/8 = 3/2.
Quick Reference
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | (a×d + b×c) / (b×d) | 1/2 + 1/3 | 5/6 |
| Subtraction | (a×d − b×c) / (b×d) | 3/4 − 1/4 | 1/2 |
| Multiplication | (a×c) / (b×d) | 2/3 × 3/4 | 1/2 |
| Division | (a×d) / (b×c) | 1/2 ÷ 1/4 | 2 |
Related Calculators
How to Add, Subtract, Multiply, and Divide Fractions
To add or subtract fractions, find a common denominator (the LCM of the denominators), convert each fraction, then add or subtract numerators. 1/3 + 1/4: LCM(3,4)=12, so 4/12 + 3/12 = 7/12. To multiply fractions, multiply numerators together and denominators together, then simplify: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the reciprocal: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.
Always simplify your answer by dividing numerator and denominator by their GCF. For mixed numbers like 2 1/3, convert to an improper fraction first: 2 1/3 = 7/3. Fractions appear constantly in cooking (double a recipe calling for 3/4 cup), carpentry (cutting wood to 5/8 inch), finance (calculating fractional shares), and statistics (probability expressed as m/n). The ability to manipulate fractions mentally is a core numeracy skill.
Fraction Operations Summary
| Operation | Rule | Example |
|---|---|---|
| Addition | Find LCD, add numerators | 1/4+1/6 = 3/12+2/12 = 5/12 |
| Subtraction | Find LCD, subtract numerators | 3/4−1/3 = 9/12−4/12 = 5/12 |
| Multiplication | Multiply top×top, bottom×bottom | 2/3×3/5 = 6/15 = 2/5 |
| Division | Multiply by reciprocal | 3/4÷1/2 = 3/4×2/1 = 6/4 = 3/2 |
Rules for Fraction Arithmetic
Fraction arithmetic follows consistent rules that ensure results remain exact rational numbers without rounding errors. For addition and subtraction, both fractions must have the same denominator (the least common denominator) before combining the numerators. Find the LCD, convert each fraction, then add or subtract the numerators while keeping the denominator. For multiplication, multiply numerators together and denominators together, then simplify. No common denominator is needed. For division, multiply the first fraction by the reciprocal of the second (flip the divisor and multiply). Simplification should always follow: find the greatest common factor of the result's numerator and denominator and divide both by it. Mixed numbers (such as 2 and 3 fourths) should be converted to improper fractions before performing any operation: multiply the whole number by the denominator, add the numerator, and write the result over the original denominator. Working with fractions precisely is important in cooking, pharmacy dosing, engineering tolerances, financial ratios, and any context where exact proportions matter more than decimal approximations.
Fraction Operations Reference Table
| Operation | Rule | Example |
|---|---|---|
| Addition | Common denominator, add numerators | 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 |
| Subtraction | Common denominator, subtract numerators | 3/4 − 1/8 = 6/8 − 1/8 = 5/8 |
| Multiplication | Multiply numerators, multiply denominators | 2/3 × 3/4 = 6/12 = 1/2 |
| Division | Multiply by reciprocal of divisor | 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2 |
