Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions. Convert between mixed numbers and improper fractions, and see decimal equivalents. All calculations happen locally — nothing leaves your browser.
How do you calculate with fractions? To add or subtract, rewrite both fractions over a common denominator and combine the numerators; to multiply, multiply numerators and denominators straight across; to divide, multiply by the reciprocal of the second fraction. Every answer is then reduced by dividing the numerator and denominator by their greatest common divisor, so 20/24 becomes 5/6.
How to Use the Fraction Calculator
- Enter the first fraction — Type the numerator in the top box and the denominator underneath. The small line below the inputs shows the decimal value, which is a quick sanity check that you typed what you meant.
- Enter the second fraction — Do the same in the second panel. Denominators must be whole numbers of 1 or more — a denominator of zero is undefined and is treated as 1.
- Choose the operation — Tap +, −, × or ÷. The result recalculates immediately, so you can try all four on the same pair of fractions.
- Read the result three ways — The answer appears as a simplified fraction, as a decimal, and — after tapping Show as Mixed Number — as a whole number plus a proper fraction.
- Follow the step-by-step working — The steps panel lists the common denominator it chose, the converted fractions, the raw result before reducing, and the GCD used to simplify it — the same working you would show on paper.
How Fraction Arithmetic Works
A fraction is a division written out: the numerator is how many parts you have and the denominator is how many equal parts make one whole. Because the denominator sets the size of each part, you cannot combine two fractions until both are cut into parts of the same size — which is the entire reason addition and subtraction need a common denominator while multiplication and division do not.
For addition and subtraction the calculator uses the least common denominator, derived from the greatest common divisor of the two denominators:
LCD(a, b) = (a × b) ÷ GCD(a, b)
Using the LCD rather than simply multiplying the denominators keeps the numbers small: for 1/6 and 1/8, a×b gives 48 but the LCD is 24. Each fraction is then scaled to that denominator, the numerators are added or subtracted, and the answer is reduced. Multiplication needs no such setup — numerators multiply, denominators multiply. Division is multiplication in disguise: dividing by 3/4 is the same as multiplying by 4/3, because the reciprocal undoes the division.
Every result then passes through the same reduction step. The greatest common divisor of the numerator and denominator is found with the Euclidean algorithm — repeatedly replace the larger number by its remainder when divided by the smaller until the remainder is zero — and both parts are divided by it. GCD(20, 24) = 4, so 20/24 reduces to 5/6. That guarantees the answer is in lowest terms rather than merely correct.
The Four Operations at a Glance
| Operation | Method | Worked example |
|---|---|---|
| Add | Convert to the LCD, add numerators | 1/3 + 1/4 = 4/12 + 3/12 = 7/12 |
| Subtract | Convert to the LCD, subtract numerators | 3/4 − 1/3 = 9/12 − 4/12 = 5/12 |
| Multiply | Numerator × numerator, denominator × denominator | 2/3 × 4/5 = 8/15 |
| Divide | Multiply by the reciprocal of the second fraction | 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8 |
Worked Examples
Adding 2/3 + 1/6. GCD(3, 6) = 3, so the LCD is (3×6)÷3 = 6. Only the first fraction needs rescaling: 2/3 becomes 4/6. Adding numerators gives 4 + 1 = 5, so the answer is 5/6, already in lowest terms because GCD(5, 6) = 1.
Multiplying 3/5 × 2/7. Multiply straight across: 3×2 = 6 over 5×7 = 35. The answer 6/35 cannot be reduced, since 6 and 35 share no factor.
Dividing 5/8 ÷ 3/4. Flip the second fraction to 4/3 and multiply: 20/24. The greatest common divisor is 4, which reduces the answer to 5/6 — a case where skipping the reduction step would leave a technically correct but unfinished answer.
Mixed Numbers, Improper Fractions and Decimals
An improper fraction has a numerator at least as large as its denominator, such as 7/4. A mixed number writes the same quantity as a whole part plus a proper fraction: 1 3/4. Neither is more correct; improper fractions are easier to calculate with, mixed numbers are easier to picture, so the calculator shows both. Converting is arithmetic on the numerator alone: divide it by the denominator, the quotient is the whole part and the remainder becomes the new numerator.
The decimal reading is simply the division carried out. It is exact only when the reduced denominator has no prime factors besides 2 and 5 — 3/8 is exactly 0.375, but 1/3 is 0.333… forever. The tool rounds the decimal for display while keeping the fraction exact, so when the two appear to disagree in the last digit, the fraction is the one to trust.
Frequently Asked Questions
An improper fraction has a numerator larger than or equal to the denominator (e.g., 7/4). It can be converted to a mixed number: 7/4 = 1 3/4. Both represent the same value.
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, 8/12 simplifies to 2/3 because GCD(8,12) = 4.
First find the least common denominator (LCD) for both fractions, then multiply each numerator so both fractions have the same denominator. Add the numerators together while keeping the denominator the same. Finally, simplify the result if possible. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
The fraction is the exact answer; the decimal is a rounded rendering of it. Any fraction whose reduced denominator contains a prime factor other than 2 or 5 repeats forever in decimal — 1/3 is 0.3333..., 5/6 is 0.8333... — so the display has to stop somewhere. When you need an exact value, quote the fraction rather than the decimal.
Negative numerators work and the sign is carried through the arithmetic, including into the mixed-number form. Denominators must be whole numbers of 1 or more, and decimal inputs such as 1.5 are not accepted — convert them to a fraction first (1.5 becomes 3/2). A denominator of zero is undefined and is treated as 1 rather than producing an error.
No. The arithmetic, the GCD reduction and the step-by-step working are all computed in JavaScript in your browser. Nothing is uploaded, stored or logged, and the page works the same with the network disconnected.
Both give a valid common denominator, but multiplying gives a larger one that you then have to reduce away. For 1/6 + 1/8, multiplying gives 48ths while the LCD is 24. The answers agree — 7/24 either way after simplifying — but the LCD route keeps the intermediate numbers small, which matters when you are checking the working by hand.
Use a fraction calculator when the exact rational answer matters: recipe scaling, tolerances, music note lengths, or homework that must be shown in lowest terms. Reach for the Scientific Calculator when you need trigonometry, powers or logarithms, and the GCD / LCM tool when you only want the common denominator itself.
Use Cases
Homework With Shown Working
A student adding 5/12 + 7/18 can check both the answer and the method, because the steps panel names the LCD and the reduction the teacher expects to see.
Reading a Tape Measure
Carpenters working in imperial units convert an awkward 27/16 in. into 1 11/16 in. so it can be found on the tape without counting sixteenths.
Scaling a Recipe by Two Thirds
Cooking for four when the recipe serves six means multiplying every quantity by 2/3, turning 3/4 cup into 1/2 cup without reaching for a decimal.
Comparing Two Fractions
Subtracting one fraction from another settles which is larger and by how much — useful when choosing between a 7/16 and a 3/8 drill bit, or two gear ratios.
Reducing a Ratio to Lowest Terms
Turning a raw count such as 84/210 into 2/5 gives a ratio that can be quoted in a report or read off a chart axis without a calculator.