Math & Algebra Tool

Fraction Calculator

Add, Subtract, Multiply, and Divide fractions.

Σ The Formula

a/b + c/d = (ad + bc) / bd | a/b × c/d = ac / bd | a/b ÷ c/d = ad / bc

Real World Examples

Adding Fractions
1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
Multiplying Fractions
2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2
Dividing Fractions
3/4 ÷ 1/2 = (3×2) / (4×1) = 6/4 = 3/2
Subtracting Fractions
5/6 - 1/3 = (5×3 - 1×6) / (6×3) = 9/18 = 1/2

# About This Calculator

Fractions represent parts of a whole and are fundamental to mathematics, cooking, construction, and countless real-world applications. A fraction consists of a numerator (top number) and denominator (bottom number), where the denominator indicates how many equal parts make up the whole.

Performing arithmetic operations with fractions requires understanding common denominators for addition and subtraction, while multiplication and division follow simpler rules. This calculator handles all four basic operations and automatically simplifies results to their lowest terms.

Adding and subtracting fractions requires finding a common denominator - typically the least common multiple (LCM) of both denominators. Multiplying fractions is straightforward: multiply numerators together and denominators together. Division involves flipping the second fraction and multiplying.

Whether you're scaling recipes, calculating measurements in woodworking, solving algebra problems, or working with ratios in business, this tool provides step-by-step solutions showing exactly how the calculation works, helping you learn while getting accurate results.

How To Use

  1. Enter two fractions.
  2. Select operation (+ - × ÷).
  3. Click Calculate.

Frequently Asked Questions

How do I add fractions with different denominators?+

Find a common denominator (usually the LCM of both denominators), convert both fractions to equivalent fractions with that denominator, then add the numerators. For example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Why do I flip the second fraction when dividing?+

Dividing by a fraction is the same as multiplying by its reciprocal (flipped version). For example, dividing by 1/2 is the same as multiplying by 2/1. This is because division asks 'how many times does this fit?' and the reciprocal gives that answer.

Do I need a common denominator for multiplication?+

No! When multiplying fractions, simply multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c)/(b×d). Then simplify the result if possible.

How do I simplify a fraction?+

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 6/12 has GCD of 6, so 6÷6 / 12÷6 = 1/2.

Can I add a whole number to a fraction?+

Yes! Convert the whole number to a fraction with denominator 1, then proceed normally. For example: 3 + 1/4 = 3/1 + 1/4 = 12/4 + 1/4 = 13/4 = 3 1/4.

Is Fraction Calculator free to use?+

Yes, Fraction Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Fractions represent parts of a whole and are fundamental to mathematics, cooking, construction, and countless real-world applications. A fraction consists of a numerator (top number) and denominator (bottom number), where the denominator indicates how many equal parts make up the whole.

Performing arithmetic operations with fractions requires understanding common denominators for addition and subtraction, while multiplication and division follow simpler rules. This calculator handles all four basic operations and automatically simplifies results to their lowest terms.

Adding and subtracting fractions requires finding a common denominator - typically the least common multiple (LCM) of both denominators. Multiplying fractions is straightforward: multiply numerators together and denominators together. Division involves flipping the second fraction and multiplying.

Whether you're scaling recipes, calculating measurements in woodworking, solving algebra problems, or working with ratios in business, this tool provides step-by-step solutions showing exactly how the calculation works, helping you learn while getting accurate results.

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