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Fraction Calculator

Add, subtract, multiply, and divide fractions. Get simplified results, mixed numbers, and step-by-step working.

numerator

denominator

+

numerator

denominator

=

5
6

Result

5/6

= 0.83333333

Simplified Fraction

5/6

Mixed Number

5/6

Decimal

0.83333333

How it's calculated

(1/2) + (1/3)

= (1×3 + 1×2) / (2×3)

= 5 / 6

= 5/6 (simplified)

About the Fraction Calculator

Fractions appear in mathematics, cooking, engineering tolerances, and financial calculations. While decimal approximations work for many purposes, exact fraction arithmetic avoids rounding errors in calculations where precision matters - like determining that 1/3 + 1/6 = 1/2 exactly, not 0.4999... The step-by-step working shown by this calculator helps students understand the process, not just the answer.

Fraction Operations

Add/Subtract: find LCD, convert, operate on numerators · Multiply: numerators × numerators, denominators × denominators · Divide: multiply by reciprocal

LCD = Least Common Denominator = LCM of denominators · GCD used to simplify result · Mixed number: whole part + proper fraction · Improper fraction: numerator > denominator

Worked Example

Recipe uses 2/3 cup sugar and 3/4 cup butter - total cups of ingredients

Sugar:2/3 cup
Butter:3/4 cup
Operation:Addition

LCD(3,4) = 12 · 2/3 = 8/12 · 3/4 = 9/12 · Sum = 17/12 = 1 5/12 cups

Tips & Insights

  • 1

    Always simplify your final answer by dividing numerator and denominator by their GCD.

  • 2

    To compare fractions, convert to the same denominator or convert both to decimals.

  • 3

    For division: 'keep, change, flip' - keep the first fraction, change ÷ to ×, flip the second fraction.

Why this matters for you

Fraction arithmetic is a foundational skill that many students find confusing precisely because they were taught mechanical rules without understanding. Clear, step-by-step fraction calculation builds the intuition needed for algebra, proportional reasoning, and any quantitative field. From school homework to engineering tolerances, fractions are inescapable.

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