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MathFraction Calculator
Free fraction calculator with step-by-step working. Add, subtract, multiply, divide and simplify fractions or mixed numbers, with instant decimal and percent.
Have feedback? Report bugs, suggest features, or share your thoughts — we read them allHow to Calculate Fractions?
Fractions represent parts of a whole number. They consist of a numerator (top number) and a denominator (bottom number). Understanding fraction operations is essential for many mathematical calculations.
Adding Fractions:
- Find a common denominator for both fractions
- Convert both fractions to have the same denominator
- Add the numerators and keep the common denominator
3/4 + 1/2 = (3×2 + 1×4)/(4×2) = 10/8 = 5/4
Multiplying Fractions:
- Multiply the numerators together
- Multiply the denominators together
5/6 × 2/3 = (5×2)/(6×3) = 10/18 = 5/9
Simplifying Fractions:
- Find the greatest common divisor (GCD) of numerator and denominator
- Divide both numerator and denominator by the GCD
12/18 = (12÷6)/(18÷6) = 2/3
Common fraction values
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.666... | 66.67% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.8 | 80% |
About this fraction calculator
Use this calculator for any of the four fraction operations — addition, subtraction, multiplication and division — on either simple fractions like 3/4 or mixed numbers like 1 1/2. Every result is automatically reduced to its lowest terms using the greatest common divisor, and the equivalent decimal value is shown alongside the fraction. The step-by-step box below the result shows exactly which common denominator was used and how each numerator was scaled, so the calculator works as both a fast answer machine and a study aid.
Frequently Asked Questions
You cannot add 1/4 + 1/6 directly because the pieces are different sizes. First find a common denominator — the Least Common Multiple (LCM) of 4 and 6 is 12 — then convert each fraction: 1/4 = 3/12 and 1/6 = 2/12. Now the pieces match, so 3/12 + 2/12 = 5/12. Subtraction works identically: 1/4 - 1/6 = 3/12 - 2/12 = 1/12. The calculator handles this automatically, but understanding the LCM step explains why answers look the way they do. Using any common denominator (like 24) also works, but the LCM gives the simplest intermediate result, reducing the need for later simplification.
Multiplication is far simpler: multiply numerators together and denominators together. 2/3 x 4/5 = (2 x 4) / (3 x 5) = 8/15 — no common denominator needed. Geometrically, this represents taking a fraction of a fraction: 2/3 of 4/5 of a whole. The result is often smaller than either input because you are taking a part of a part. A common student error is to also "find a common denominator" for multiplication, which produces wrong answers. Pro tip: cancel common factors between any numerator and any denominator before multiplying to keep numbers small. For 4/9 x 3/8, cancel 4 and 8 (to 1 and 2), cancel 3 and 9 (to 1 and 3): result 1/6.
Division by a fraction equals multiplication by its reciprocal: a/b divided by c/d = a/b x d/c. So 3/4 divided by 2/5 = 3/4 x 5/2 = 15/8 = 1 7/8. The reciprocal flip works because dividing by c/d is asking "how many groups of c/d fit?", and inverting d/c counts those groups directly. Be careful with mixed numbers: convert 1 1/2 to 3/2 first, then flip. The rule fails for 0: you cannot divide by 0/anything because the reciprocal anything/0 is undefined. Our calculator catches division by zero and returns an error. This same flip-and-multiply pattern extends to algebraic fractions and complex rational expressions.
Mixed number to improper: multiply the whole part by the denominator, add the numerator, keep the denominator. 2 3/4 = (2 x 4 + 3) / 4 = 11/4. Improper to mixed: divide numerator by denominator; quotient is the whole part, remainder is the new numerator, denominator stays. 17/5 = 3 remainder 2 = 3 2/5. Mixed numbers are friendlier for everyday measurement ("2 and 3/4 cups") while improper fractions are easier to compute with. Our calculator accepts both formats — type "2 3/4" with a space, or "11/4" — and lets you choose the output style. For algebraic work, always work in improper form to avoid sign errors with negative mixed numbers.
Divide numerator and denominator by their Greatest Common Factor (GCF). For 84/126, the GCF is 42, so 84/126 = 2/3. You can also peel off shared factors one at a time: 84/126 = 42/63 (divide by 2) = 14/21 (divide by 3) = 2/3 (divide by 7). Either way you reach the same irreducible result, because once GCF = 1 there is no further simplification possible. A fraction in lowest terms is the unique canonical form, which is why standardized tests demand simplified answers. Our calculator simplifies automatically using the Euclidean algorithm and shows both the original and reduced forms so you can verify the work.
These three forms are mathematically identical because a negative sign can sit on the numerator, the denominator, or out front. By convention, the sign always goes with the numerator in display: -2/3 is standard, 2/-3 is acceptable but uncommon, and -(2/3) is the formal grouping. Our calculator normalises results to the standard -2/3 form. The sign rules follow standard arithmetic: negative divided by positive is negative, negative divided by negative is positive. For mixed numbers, the negative applies to the whole quantity: -2 1/4 means -(2 + 1/4) = -9/4, not -2 + 1/4 = -7/4. Many calculator bugs trace to this distinction, so we explicitly compute -2 1/4 as -(2 + 1/4).
Three reliable methods. First, convert to a common denominator: to compare 3/4 and 5/7, use denominator 28 — 21/28 vs 20/28, so 3/4 is bigger. Second, cross-multiply: a/b vs c/d -> compare a x d to b x c. For 3/4 and 5/7: 3 x 7 = 21 vs 4 x 5 = 20, so 3/4 > 5/7. Third, convert to decimals: 0.75 vs 0.714, same conclusion. Cross-multiplication is fastest for two fractions but does not extend cleanly to more. For sorting many fractions, convert to decimals or a shared denominator. Watch out with negatives — cross-multiplication can flip the inequality if you cross with a negative denominator, so take absolute values first or use decimals.
Practical use is one of the strongest reasons fractions persist. Recipes scale by multiplication: doubling 2/3 cup gives 4/3 = 1 1/3 cups. Halving gives 1/3 cup. Woodworking measurements like 5/16" plus 3/8" require common denominators: 5/16 + 6/16 = 11/16". Imperial-to-metric conversion: 5/8" x 25.4 mm/inch = 15.875 mm — our calculator outputs both fractional and decimal forms so you can pick the precision your tools support. For a 2 1/2" hole saw on a 3/4" plywood scrap, the conversions all reduce to ordinary fraction arithmetic. The same logic underlies stock-market tick sizes (formerly 1/8 dollar), camera apertures, and gear ratios.
A fraction gives a terminating decimal only when its reduced denominator has no prime factors other than 2 and 5. So 3/4 = 0.75 exactly, but 1/3 = 0.333…, 2/7 = 0.285714…, and 5/6 = 0.8333… repeat forever. When the result repeats, the calculator rounds to six decimal places and appends an ellipsis (…) so you know the value is truncated, not exact. The percentage column uses the same rule (1/3 = 33.3333…%, 3/8 = 37.5%). The fraction and step-by-step boxes always stay exact — only the decimal and percent are rounded — so for measurement-grade work (machining, finance, dosing) keep the fractional form and round the decimal only at the very end to avoid stacking rounding error.
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