Fraction Calculator
Add, subtract, multiply, and divide fractions. Get simplified results, mixed numbers, and step-by-step working.
numerator
denominator
+
numerator
denominator
=
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
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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