Fraction Calculator
Add, subtract, multiply, and divide fractions — including mixed numbers. Results shown as simplified fraction, mixed number, and decimal. Runs entirely in your browser, no signup required.
⏱ 8 min read · Complete guide below
First fraction
Second fraction
Result
How to Use the Fraction Calculator
- 1Enter the numerator and denominator for each fraction. For mixed numbers, also enter the whole number on the left.
- 2Select the operation — +, −, ×, or ÷ — from the buttons between the two fractions.
- 3The result appears instantly as a simplified fraction, mixed number, and decimal.
- 4Use the Simplify tab to reduce any single fraction to its lowest terms.
Fraction Rules at a Glance
Addition/Subtraction: requires a common denominator — find the LCM of both denominators, convert, then operate on numerators. Multiplication: numerator × numerator over denominator × denominator, then simplify. Division: multiply by the reciprocal of the divisor. Simplification: divide both numerator and denominator by their GCD.
Why Addition Needs a Common Denominator (But Multiplication Doesn't)
A fraction's denominator tells you the size of each part, and its numerator tells you how many of those parts you have. You can only add or subtract quantities that are the same size, which is why adding fractions requires a common denominator first — thirds and quarters are different sizes, so you rewrite both over twelfths before combining. Multiplication is different: multiplying by a fraction means taking a part of a quantity, so 2/3 × 3/4 asks for “two-thirds of three-quarters,” and you simply multiply straight across, top by top and bottom by bottom, with no common denominator needed. Understanding this distinction is the key to knowing which procedure to apply.
Mixed Numbers and Improper Fractions
A mixed number like 2½ combines a whole number and a fraction, while an improper fraction like 5/2 expresses the same value entirely as a fraction. For arithmetic, improper fractions are almost always easier: convert 2½ to 5/2 by multiplying the whole number by the denominator and adding the numerator (2 × 2 + 1 = 5), do the operation, then convert back to a mixed number at the end if you want a tidy answer. This calculator accepts mixed numbers directly and shows the result in every form — simplified fraction, mixed number, and decimal — so you can read whichever suits your context without converting by hand.
Simplifying and Checking Your Work
A fraction is in its simplest form when the numerator and denominator share no common factor other than one — 6/8 and 3/4 are equal, but 3/4 is simpler and easier to work with. Reducing is done by dividing both parts by their greatest common divisor (GCD). A quick way to sanity-check any fraction result is the decimal equivalent shown alongside it: if 7/4 displays as 1.75, and 1.75 matches your rough mental estimate, the answer is almost certainly right. Getting into the habit of simplifying every result and glancing at its decimal is the fastest way to catch mistakes in fraction arithmetic.
Fraction Tips
Always simplify the result
After any fraction operation, check whether the result can be simplified. 6/8 and 3/4 are the same value — the simplified form is easier to work with.
Mixed numbers in algebra
When solving equations, convert mixed numbers to improper fractions first. 2½ = 5/2. Operations on improper fractions are more straightforward than mixed number arithmetic.
Cross-cancelling before multiply
When multiplying fractions, simplify across the fractions before multiplying to keep numbers small. 4/9 × 3/8: cancel 4 and 8 (÷4), cancel 3 and 9 (÷3) → 1/6.
Division is multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. A÷B/C = A×C/B. This rule never changes — memorize it and fraction division becomes straightforward.
Check with decimals
The decimal equivalent shown in the result lets you quickly sanity-check your answer. 7/4 = 1.75 — if the decimal makes sense, the fraction is likely correct.
Negative fractions
Enter a negative sign in the numerator field for negative fractions. A negative denominator is automatically moved to the numerator during simplification.
What a Fraction Really Is
Fractions confuse people partly because a single fraction like 3/4 actually means three different things at once, and slipping between them is where intuition breaks down. The first meaning is part of a whole: cut a pizza into four equal slices and take three — that is 3/4. The second is division: 3/4 literally means “three divided by four,” which is exactly why dividing the numerator by the denominator gives you the decimal 0.75. The third is a ratio: 3/4 can compare two quantities, three of one thing for every four of another.
These are not competing definitions — they are three windows onto the same idea, and being able to switch between them is what makes fractions click. When you are sharing something, think “part of a whole.” When you need a decimal, remember it is just division. When you are scaling a recipe or a mixture, think “ratio.” The reason school fractions feel abstract is often that only the first meaning gets taught, leaving the division and ratio views — which are the practically useful ones — underdeveloped.
Fractions, Decimals, and Percentages: Three Views of One Number
A fraction, a decimal, and a percentage are three costumes worn by the same value. Three-quarters can be written as 3/4, as 0.75, or as 75%, and converting between them is straightforward: divide to turn a fraction into a decimal, multiply the decimal by 100 to get a percentage, and reverse the steps to go back. Knowing all three forms is genuinely useful because each is best in different situations.
Fractions are exact and often the most natural for reasoning — 1/3 is precise, whereas its decimal 0.333… never ends. They are also cleaner for many hand calculations and for expressing relationships. Decimals are ideal for measurement, money, and anything you will feed into a calculator, and they make sizes easy to compare at a glance. Percentages shine for communication — discounts, statistics, interest rates — because a common denominator of 100 makes them instantly comparable. This calculator shows the decimal alongside every fraction result partly so you always have that second view for sanity-checking and for whichever format your task needs.
Where Fractions Show Up in Real Life
It is tempting to think fractions are a school topic you leave behind, but they are quietly everywhere. Cooking and baking run on them — halving a recipe that calls for 3/4 cup, or scaling one up for a crowd, is fraction arithmetic, and getting the ratios right is the difference between a cake that rises and one that does not. Construction and DIY live in fractions of an inch: measuring, cutting, and fitting materials means constantly adding and comparing fractions like 3/8 and 5/16.
The reach goes further. Finance uses fractions and their percentage cousins for interest, returns, and proportions of a budget; music is built on them, with whole, half, and quarter notes dividing time and octaves defined by frequency ratios; and probability is fundamentally fractional — the chance of rolling a six is 1/6. Even reading a chart or splitting a bill fairly is fraction thinking. Fluency with fractions, and a reliable tool to check the arithmetic, is therefore a genuinely practical skill rather than an academic exercise — which is exactly why understanding the why behind each operation, not just the button to press, pays off well beyond the classroom.
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common denominator (LCD) of both fractions, convert each fraction to an equivalent fraction with the LCD, then add the numerators. For example: 1/3 + 1/4. LCD = 12. So 1/3 = 4/12 and 1/4 = 3/12. Sum = 7/12. The calculator does this automatically.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example: 2/3 × 3/4 = 6/12 = 1/2. It is often easier to cross-cancel before multiplying: 2/3 × 3/4 — cancel the 3s to get 2/1 × 1/4 = 2/4 = 1/2.
How do you divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second fraction. For example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The rule is "keep, change, flip" — keep the first fraction, change division to multiplication, flip the second fraction.
How do I enter mixed numbers?
Enter the whole number in the leftmost field and the fractional part in the numerator and denominator fields. For example, to enter 2½, type 2 in the whole field, 1 in the numerator, and 2 in the denominator.
How do I simplify a fraction?
Switch to the Simplify tab, enter the numerator and denominator, and the calculator shows the simplified form, the GCD used, the decimal, and the mixed number equivalent. Simplification divides numerator and denominator by their greatest common divisor (GCD).
What is the GCD and why does it matter for simplification?
GCD (Greatest Common Divisor) is the largest number that divides both the numerator and denominator evenly. Dividing both by the GCD gives the simplest form. For 6/9: GCD(6,9) = 3, so 6/9 simplifies to 2/3.
Why do you need a common denominator to add fractions but not to multiply them?
The denominator tells you the size of each part, and you can only add parts of the same size — so thirds and quarters must both be rewritten as twelfths before you can add them. Multiplication is different: multiplying by a fraction means taking a part of a quantity, so you just multiply the numerators together and the denominators together with no common denominator required. That is why 1/3 + 1/4 needs conversion but 1/3 × 1/4 does not.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 2½ becomes (2 × 2 + 1)/2 = 5/2. Improper fractions are usually easier for calculation, so convert mixed numbers first, do the arithmetic, then convert back to a mixed number at the end if you want a tidier answer. This calculator handles both forms automatically.
How do I turn a fraction into a decimal or percentage?
Divide the numerator by the denominator to get the decimal — 3/4 is 3 ÷ 4 = 0.75. To get a percentage, multiply that decimal by 100, so 3/4 = 75%. The calculator shows the decimal equivalent of every result automatically, which is handy both for converting and for quickly sanity-checking that a fraction answer is reasonable.
How do I handle negative fractions?
Enter the negative sign in the numerator field. A fraction with a negative numerator, a negative denominator, or a negative whole number all represent negative values, and the calculator keeps track of the sign through each operation. During simplification a negative denominator is moved to the numerator so the result is written in the conventional form, such as −3/4 rather than 3/−4.