Add, subtract, multiply, or divide two fractions and get a simplified result plus the decimal value.
Addition and subtraction find a common denominator before combining the numerators. Multiplication multiplies straight across, and division multiplies by the reciprocal of the second fraction. The result is automatically simplified to its lowest terms using the greatest common divisor.
Enter the numerator (top number) and denominator (bottom number) for your first fraction, then do the same for the second fraction. Choose an operation — addition, subtraction, multiplication, or division — from the dropdown between the two fractions, then click Calculate. The tool returns the answer as a simplified fraction and as a decimal, so you can use whichever format your homework, recipe, or project needs. Negative numbers are supported in either the numerator or denominator, and the calculator automatically moves any negative sign to the numerator and simplifies the fraction to its lowest terms.
Fractions can only be added or subtracted directly when they share the same denominator. If the denominators are different, the calculator finds a common denominator by multiplying the two denominators together, then adjusts each numerator to match. For example, adding 1/2 and 1/3: the common denominator is 2 × 3 = 6. That turns 1/2 into 3/6 and 1/3 into 2/6, so the sum is 3/6 + 2/6 = 5/6. Subtraction works the same way — 1/2 − 1/3 becomes 3/6 − 2/6 = 1/6. This method always works, even though it doesn't always produce the smallest possible common denominator (the "least common denominator"), which is why the final step is always to simplify.
Multiplication is the simplest fraction operation: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. So 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2. Division works by flipping the second fraction upside down (finding its reciprocal) and then multiplying. Dividing 2/3 by 3/4 becomes 2/3 × 4/3 = 8/9. This "flip and multiply" rule is often taught as "keep, change, flip" — keep the first fraction as it is, change division to multiplication, and flip the second fraction.
A fraction is in its lowest terms when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 8/12 has a GCD of 4, so dividing both numbers by 4 gives 2/3 — the simplified form. This calculator performs that step automatically after every calculation, so you never need to simplify the result by hand.
Any fraction can be converted to a decimal by dividing the numerator by the denominator. For instance, 3/4 = 3 ÷ 4 = 0.75, and 1/3 = 0.333... (a repeating decimal). Some fractions, like 1/3 or 1/7, never terminate as a decimal — they repeat forever, and the calculator rounds these to six decimal places for readability. Knowing both the fraction and decimal form is useful in different situations: fractions are common in cooking, construction, and math class, while decimals are more common in finance, science, and anywhere a calculator or spreadsheet is involved.
The most frequent error is adding or subtracting numerators and denominators separately without finding a common denominator first — for example, incorrectly calculating 1/2 + 1/3 as 2/5. This shortcut only works for multiplication, never for addition or subtraction. Another common mistake is forgetting to simplify the final answer, which can make a correct result look "wrong" if a textbook or answer key expects the reduced form. Finally, when dividing fractions, a common slip is flipping the first fraction instead of the second — remember, only the fraction you're dividing *by* gets flipped.
Fractions aren't just a classroom exercise. Cooking and baking recipes are written in fractions of a cup, teaspoon, or tablespoon, and doubling or halving a recipe means multiplying every fraction by 2 or by 1/2. Carpentry and construction rely on fractional measurements down to sixteenths of an inch on a tape measure. Financial contexts like interest rates, stock splits, and ownership shares are frequently expressed as fractions before being converted to percentages. Even time is fractional — a quarter hour is 1/4 of 60 minutes, and understanding that relationship makes mental math with schedules much faster.
Fractions, ratios, and percentages all describe parts of a whole, but they're used differently depending on context. A fraction like 3/4 shows a portion out of a total. A ratio like 3:4 compares two separate quantities to each other rather than a part to a whole. A percentage converts any fraction to a value out of 100 — 3/4 becomes 75%. Being comfortable converting between all three is genuinely useful: a recipe might use fractions (3/4 cup), a mixing instruction might use a ratio (3 parts water to 4 parts concentrate), and a discount might be shown as a percentage (75% off). This calculator focuses on fraction arithmetic, but converting your fraction result to a percentage is as simple as multiplying the decimal output by 100.
Try these by hand, then check your work with the calculator above. Addition: 2/5 + 1/4 — common denominator 20, so 8/20 + 5/20 = 13/20 (already in lowest terms). Subtraction: 5/6 − 1/4 — common denominator 12, so 10/12 − 3/12 = 7/12. Multiplication: 3/5 × 2/7 = 6/35. Division: 5/8 ÷ 2/3 = 5/8 × 3/2 = 15/16. Working through a handful of examples like these by hand is the fastest way to build confidence before relying on a calculator for speed.
Can this calculator handle mixed numbers, like 1 and 1/2? Enter mixed numbers as improper fractions first — for example, 1 and 1/2 becomes 3/2 (multiply the whole number by the denominator, then add the numerator). A future update may add direct mixed-number input.
What happens if I enter 0 as a denominator? The calculator will show an error, since division by zero is mathematically undefined. Double-check your denominator values if you see this message.
Why does my answer look different from my textbook's answer? If the numeric value matches but the fraction looks different, your textbook may not have simplified fully, or may be expressing the result as a mixed number instead of an improper fraction. Convert and compare the decimal values to confirm they match.
Is the simplified result always the smallest possible fraction? Yes — the calculator divides by the greatest common divisor, which guarantees the lowest possible terms every time.
Can I use this to compare which of two fractions is larger? Yes — subtract one from the other. If the result is positive, the first fraction is larger; if negative, the second is larger; if zero, they're equal.
Last reviewed by Mehmed on July 11, 2026.