Fraction Calculator
Add, subtract, multiply, and divide fractions. Get simplified results, mixed numbers, and step-by-step working.
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. 12/18 simplifies to 2/3 because GCD(12,18) = 6. Un-simplified fractions in an exam answer often cost marks even when the value is correct.
- 2
To compare fractions, convert to the same denominator or convert both to decimals. 3/7 vs 4/9: cross-multiply to compare - 3×9=27 vs 4×7=28, so 3/7 < 4/9. This avoids the rounding errors that come from decimal conversion of non-terminating fractions.
- 3
For division: 'keep, change, flip' - keep the first fraction, change ÷ to ×, flip the second fraction (reciprocal). (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1 7/8.
- 4
Mixed numbers like 2¾ must be converted to improper fractions (11/4) before any arithmetic. Perform the operation in improper form, then convert back - skipping this step causes systematic errors in multi-step problems.
- 5
In baking, fractions are exact - 3/4 cup means exactly that, not 0.75 rounded. When scaling a recipe that calls for 2/3 cup by 1.5x, the result is exactly 1 cup - cleaner to compute in fractions than decimals to avoid measurement errors.
- 6
Engineering drawings and technical specifications often use fractional tolerances: 1/2 inch ± 1/16 inch. Converting to decimals (0.5 ± 0.0625) introduces representation for comparison but the original fraction form is often more precise in communicating the specification intent.
- 7
For adding three or more fractions, find the LCM of all denominators at once, not sequentially. 1/2 + 1/3 + 1/4: LCM(2,3,4) = 12, so 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12. Sequential LCD-finding risks introducing unnecessary intermediate fractions.
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 why they work. Clear step-by-step calculation builds the intuition needed for algebra, proportional reasoning, and any quantitative field.
In India's school curriculum (CBSE, ICSE), fractions appear from Class 4 through Class 10 in progressively complex forms - from basic addition to complex algebraic fractions. Parents and students who understand the step-by-step process can work through homework independently, without waiting for tuition sessions. The worked example format this calculator provides is directly aligned with how NCERT textbooks present fraction solutions.
Beyond school, fractions appear in remarkably practical contexts: cooking (scaling recipes), carpentry (material measurements), pharmacy (drug dosing in mg/kg expressed as fractions of body weight), and financial ratios. Professionals who can confidently manipulate exact fractions avoid the accumulated rounding errors that come from repeated decimal conversions - especially important in multi-step calculations where each approximation compounds.
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