Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, and convert fractions, with full working shown, a visual size comparison, and a recipe-scaling mode most fraction calculators don't offer.
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Most fraction calculators handle the same core list: add, subtract, multiply, divide, simplify, and convert. This one does all of that, plus two things you won't find on most competitor tools: a visual bar that shows the actual size of a fraction, and a scaling mode built specifically for adjusting recipe quantities, since "how much is 3/4 cup times 2.5" is one of the most common real reasons people search for a fraction calculator in the first place.
Related Calculators
How Each Mode Works
1. Add, Subtract, Multiply, Divide
Adding and subtracting fractions requires a common denominator first. Multiplying is more direct: multiply numerators together and denominators together. Dividing flips the second fraction and multiplies.
Multiply: (a/b) × (c/d) = ac / bd
Divide: (a/b) ÷ (c/d) = ad / bc
1/2 + 1/3 = (1×3 + 2×1) / (2×3) = 5/6
2. Simplify a Fraction
A fraction is in simplest form when the numerator and denominator share no common factor other than 1. Finding the greatest common divisor (GCD) and dividing both numbers by it does this in one step.
18/24: the GCD of 18 and 24 is 6, so 18/24 simplifies to 3/4.
3. Mixed Number to Improper Fraction
A mixed number like 2 3/4 combines a whole number and a fraction. Converting it to a single improper fraction makes it usable in the arithmetic modes above.
2 3/4 becomes (2×4 + 3)/4 = 11/4.
4. Compare Fractions
Cross-multiplying is the fastest way to compare two fractions without converting either one to a decimal first.
2/3 vs 3/5: 2×5=10 and 3×3=9, so 2/3 is larger.
5. Fraction to Decimal or Percent
Dividing the numerator by the denominator gives the decimal form directly. Multiplying that by 100 gives the percentage.
Percent = decimal × 100
5/8 = 0.625 = 62.5%.
6. Visualize and Scale (Recipe Mode)
This mode is built for a specific, very common situation: you have a recipe measurement as a fraction and need to scale it up or down. Enter the fraction (say, 3/4 cup per serving) and a scale factor (say, 2.5 for two and a half times the recipe), and it shows both the resulting fraction and a visual bar so you can see the size at a glance rather than just reading a number.
Where Fractions Actually Come Up
Cooking and Recipes
Recipes are one of the most common places fractions show up outside a classroom. A recipe that calls for 2/3 cup of flour per batch needs a different amount entirely if you're making one and a half batches for a larger group, and doing that mental maths under time pressure in a kitchen is where mistakes happen. Multiplying 2/3 by 1.5 gives exactly 1 cup, which is a much easier number to measure than a stray fraction. The scale mode above exists specifically for this, since "double this fraction" or "make three-quarters of this recipe" are questions people run into constantly and rarely have a quick way to check.
Construction and DIY Measurements
Tape measures are marked in fractions of an inch, not decimals, so anyone cutting wood, laying tile, or measuring a wall is working in fractions whether they think of it that way or not. Adding two measurements like 3/8 inch and 5/16 inch requires a common denominator before they can be combined, and getting that wrong by even a small amount compounds across multiple cuts.
School and Homework
Fractions appear early in maths education and stay relevant well beyond it, showing up again in algebra, probability, and unit conversion. Checking homework against a calculator that shows the common denominator or the cross-multiplication step (rather than just the final answer) tends to catch a different kind of mistake than checking the answer alone, since it's usually the method that goes wrong before the arithmetic does.
Everyday Comparisons
Working out which of two fractions is larger comes up more often than it might seem: comparing serving sizes on packaging, splitting a workload between two people unevenly, or figuring out whether 3/8 of a tank of fuel will get you further than 2/5. Cross-multiplying avoids the extra step of converting either fraction to a decimal first.
Fraction Formulas at a Glance
| Operation | Formula | Example |
|---|---|---|
| Add / Subtract | (ad ± bc) / bd | 1/2 + 1/3 = 5/6 |
| Multiply | ac / bd | 2/3 × 3/4 = 1/2 |
| Divide | ad / bc | 1/2 ÷ 1/4 = 2 |
| Simplify | n/GCD over d/GCD | 18/24 = 3/4 |
| Mixed to improper | (w×d + n) / d | 2 3/4 = 11/4 |
| Compare | a×d vs b×c | 2/3 > 3/5 |
Common Mistakes
Frequently Asked Questions
How do I add two fractions with different denominators?
Convert both fractions to a common denominator first, usually the least common multiple of the two denominators, then add the numerators. Use the "Add / Subtract / Multiply / Divide" mode above and it will show the working.
What does it mean to simplify a fraction?
Simplifying means dividing the numerator and denominator by their greatest common divisor so the fraction is expressed with the smallest possible numbers while keeping the same value.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place that total over the original denominator. The "Mixed Number ↔ Improper" mode above does this instantly.
How can I tell which of two fractions is bigger without a calculator?
Cross-multiply: multiply the first numerator by the second denominator, and the second numerator by the first denominator, then compare the two results. The larger result belongs to the larger fraction.
Can this calculator help me scale a recipe up or down?
Yes. Use the "Visualize & Scale" mode, enter the fraction from your recipe and the multiplier you need (for example, 2 for doubling), and it shows the new amount along with a visual bar for a quick sanity check.