Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions. Get the simplified fraction, its decimal value, and the mixed number — all in one click.
- 01Add, subtract, multiply, and divide fractions instantly.
- 02Get the answer in lowest terms with every step shown.
- 03Convert any fraction to a decimal and to a mixed number.
- 04Works with proper, improper, and negative fractions.
- 05100% free and private — every calculation runs in your browser.
Fraction Calculator
Enter two fractions and choose an operation
Result
Decimal
0.833333
Simplified fraction
5/6
Step-by-step solution
- 01Set up the problem: 1/2 + 1/3
- 02Find a common denominator: 2 × 3 = 6. Rewrite each fraction over 6.
- 03Combine the numerators over the common denominator to get 5/6.
- 04The fraction 5/6 is already in lowest terms.
Why Use This Fraction Calculator
All Four Operations
Add, subtract, multiply, and divide fractions in a single tool. The adding fractions calculator finds a common denominator, the subtracting fractions calculator handles the difference, and multiplying and dividing fractions work straight across — so you never need a separate calculator for each operation.
Step-by-Step Working
See exactly how the answer is found: setting up the problem, finding the common denominator (or the reciprocal for division), combining the numerators, and simplifying the result. Perfect for homework, exam revision, and understanding how to add fractions rather than just getting the number.
Always Simplified
Every result is automatically reduced to lowest terms using the greatest common divisor, so this doubles as a simplify fractions calculator. You always get the cleanest possible answer without having to cancel common factors by hand.
Decimal and Mixed Number
Alongside the simplified fraction you instantly get the fraction to decimal conversion and, when the answer is improper, the equivalent mixed number. The built-in mixed number calculator makes the result easy to read and compare.
Exact Integer Arithmetic
Calculations use exact integer math rather than floating-point approximations, so results are precise and never suffer rounding errors. Proper fractions, improper fractions, and negative fractions are all fully supported.
Free, Instant, and Private
Everything runs entirely in your browser with no server round-trips, no signup, and no limits. Your numbers never leave your device, and answers appear the moment you click Calculate.
How the Fraction Calculator Works
A fraction represents a part of a whole, written as a numerator over a denominator — for example 3/4 means three parts out of four. This fraction calculator lets you add, subtract, multiply, or divide any two fractions and returns the answer in lowest terms, as a decimal, and as a mixed number where applicable.
Whether you are a student learning how to add fractions, a parent helping with homework, or anyone who needs a quick, accurate answer, this fraction calculator shows every step so the method is as clear as the result.
- Adding and Subtracting Fractions
- To add or subtract fractions you first need a common denominator. The calculator multiplies the two denominators, rewrites each fraction over that common denominator, then adds or subtracts the numerators. The formula is (n1·d2 ± n2·d1) ÷ (d1·d2), after which the result is simplified.
- Multiplying Fractions
- Multiplying fractions is the simplest operation: multiply the numerators together and the denominators together, so n1/d1 × n2/d2 = (n1·n2) ÷ (d1·d2). No common denominator is needed. The calculator then reduces the product to its lowest terms.
- Dividing Fractions
- To divide fractions, multiply the first fraction by the reciprocal of the second — flip the second fraction and multiply. So n1/d1 ÷ n2/d2 = (n1·d2) ÷ (d1·n2). This 'keep, change, flip' rule is applied automatically, and the answer is simplified.
- Simplifying and Converting
- After computing the raw result, the calculator divides the numerator and denominator by their greatest common divisor to give the fraction in lowest terms. It also converts that fraction to a decimal and, when the numerator is larger than the denominator, to a mixed number.
How to Use the Fraction Calculator
- 01
Enter the first fraction
Type the numerator in the top box and the denominator in the bottom box of the first fraction. Whole numbers, including negatives, are supported — for example 1 over 2 for the fraction 1/2.
- 02
Choose an operation
Select add (+), subtract (−), multiply (×), or divide (÷) from the operation selector between the two fractions. This tells the calculator which fraction operation to perform.
- 03
Enter the second fraction
Type the numerator and denominator of the second fraction in the same way. Remember that a denominator can never be zero, and for division the second fraction cannot be zero.
- 04
Read the result and steps
Click Calculate to see the simplified fraction, its decimal value, and the mixed number. Below that, the step-by-step solution shows the common denominator, the combined numerator, and how the answer was reduced to lowest terms.
Tips for Working With Fractions
Always Simplify the Answer
A fraction like 4/8 is correct but not in its simplest form. Reduce every answer to lowest terms by dividing the numerator and denominator by their greatest common divisor — the calculator does this for you so 4/8 becomes 1/2.
Find a Common Denominator First
When adding or subtracting fractions, you can only combine the numerators once the denominators match. Rewrite both fractions over a common denominator before adding or subtracting — this is the most common source of mistakes.
Keep, Change, Flip for Division
Dividing by a fraction means multiplying by its reciprocal. Keep the first fraction, change the division to multiplication, and flip the second fraction. For example, 1/2 ÷ 3/4 = 1/2 × 4/3.
Don't Multiply Denominators When Adding
A frequent error is adding numerators and denominators straight across, like 1/2 + 1/3 = 2/5. That is wrong — you need a common denominator first, which gives 3/6 + 2/6 = 5/6.
Convert Mixed Numbers Before Calculating
If you start with a mixed number such as 2 1/2, convert it to the improper fraction 5/2 before adding, subtracting, multiplying, or dividing. Multiply the whole number by the denominator and add the numerator.
Check With the Decimal
Use the decimal value as a quick sanity check. If 1/2 + 1/3 gives 5/6 ≈ 0.833, that is clearly between 0.5 and 1, which matches expectations. The decimal helps you catch errors at a glance.
Fraction Formulas and Definitions
What is a fraction?
A fraction expresses a part of a whole as a numerator divided by a denominator. The numerator (top number) counts how many parts you have, and the denominator (bottom number) tells how many equal parts make up the whole. A proper fraction is less than 1 (numerator smaller than denominator), while an improper fraction is 1 or greater.
Key things the calculator does
- Adds, subtracts, multiplies, and divides any two fractions.
- Reduces every answer to lowest terms using the greatest common divisor.
- Converts the result to a decimal and to a mixed number where applicable.
- Shows a clear step-by-step solution for each fraction operation.
Common denominator vs reciprocal
Addition and subtraction require a common denominator so the parts are the same size before you combine them. Division does not — instead you multiply by the reciprocal (the flipped second fraction). Multiplication needs neither: you simply multiply numerators and denominators straight across.
Key Fraction Formulas
Adding fractions
a/b + c/d = (a·d + c·b) ÷ (b·d)
Example: 1/2 + 1/3 = (3 + 2) ÷ 6 = 5/6.
Subtracting fractions
a/b − c/d = (a·d − c·b) ÷ (b·d)
Example: 3/4 − 1/2 = (6 − 4) ÷ 8 = 2/8 = 1/4.
Multiplying fractions
a/b × c/d = (a·c) ÷ (b·d)
Example: 2/3 × 3/4 = 6 ÷ 12 = 1/2.
Dividing fractions
a/b ÷ c/d = (a·d) ÷ (b·c)
Example: 1/2 ÷ 3/4 = (1·4) ÷ (2·3) = 4/6 = 2/3.
Simplifying a fraction
a/b = (a ÷ g) / (b ÷ g), where g = gcd(a, b)
Example: 8/12 with g = 4 becomes 2/3.
Fraction to decimal
a/b = a ÷ b
Example: 3/4 = 3 ÷ 4 = 0.75.
Fraction Calculator FAQ
Q01How do I add fractions?
To add fractions, give them a common denominator, then add the numerators and keep the denominator the same. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. The formula is (n1·d2 + n2·d1) ÷ (d1·d2), and you simplify the result afterwards. This adding fractions calculator does every step and shows the working.
Q02How do I subtract fractions?
Subtracting fractions works the same way as adding: find a common denominator, then subtract the numerators. For example, 3/4 − 1/2 becomes 3/4 − 2/4 = 1/4. The subtracting fractions calculator finds the common denominator, combines the numerators, and reduces the answer to lowest terms automatically.
Q03How do I multiply fractions?
Multiplying fractions is straightforward: multiply the numerators together and the denominators together, with no common denominator required. For example, 2/3 × 3/4 = 6/12 = 1/2 after simplifying. The calculator multiplies straight across and then reduces the product to its simplest form.
Q04How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second — flip the second fraction and multiply. For example, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3. This is the 'keep, change, flip' rule, and the dividing fractions calculator applies it for you and simplifies the answer.
Q05How do I simplify a fraction?
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 has a GCD of 4, so it simplifies to 2/3. This tool works as a simplify fractions calculator and always returns the answer in lowest terms.
Q06How do I convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. The calculator shows the decimal value of every result automatically, so you get the fraction to decimal conversion without any extra steps.
Q07What is a mixed number and when do I get one?
A mixed number combines a whole number with a proper fraction, like 1 1/2. You get a mixed number when the answer is an improper fraction (the numerator is larger than the denominator). For example, 7/4 equals the mixed number 1 3/4. The built-in mixed number calculator displays this form whenever it applies.
Q08Can I use negative fractions, and is the calculator free?
Yes. You can enter negative numerators or denominators, and the calculator normalises the sign so the denominator stays positive. It works with proper, improper, and negative fractions. The fraction calculator is completely free with no signup, no limits, and runs entirely in your browser so your input is never sent to a server.