Add, subtract, multiply, divide and simplify fractions. Supports proper fractions, improper fractions, and mixed numbers.
To add or subtract fractions, give them a common denominator, then add or subtract the numerators. To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction and multiply. Always simplify the result by dividing the top and bottom by their greatest common factor. This fraction calculator does all four operations with clear steps.
For mixed numbers, add the whole number in the field above the fraction line.
Simplify a Single Fraction
| Form | Value |
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A fraction calculator is a tool that adds, subtracts, multiplies, divides and simplifies fractions for you, showing each step. It saves time and helps you check your own working. This calculator for fractions also converts between mixed numbers and improper fractions, so you can handle any fraction problem in one place.
A fraction represents a part of a whole. It has two numbers: the numerator (top) shows how many parts you have, and the denominator (bottom) shows how many equal parts the whole is divided into. In 3/4, the numerator is 3 and the denominator is 4.
| Type | What It Means | Example |
|---|---|---|
| Proper fraction | Numerator smaller than denominator (less than 1) | 3/4 |
| Improper fraction | Numerator equal to or larger than denominator (1 or more) | 7/4 |
| Mixed number | A whole number plus a proper fraction | 1 3/4 |
| Equivalent fractions | Different fractions with the same value | 1/2 = 2/4 = 4/8 |
Each operation follows a simple rule:
| Operation | Formula | Example | Explanation |
|---|---|---|---|
| Addition | a/b + c/d = (ad + cb)/bd | 1/2 + 1/3 = 5/6 | Common denominator, add tops |
| Subtraction | a/b − c/d = (ad − cb)/bd | 3/4 − 1/2 = 1/4 | Common denominator, subtract tops |
| Multiplication | a/b × c/d = ac/bd | 2/3 × 3/5 = 6/15 = 2/5 | Multiply straight across, simplify |
| Division | a/b ÷ c/d = ad/bc | 1/2 ÷ 1/4 = 4/2 = 2 | Flip the second, then multiply |
| Simplify | Divide top and bottom by GCF | 8/12 = 2/3 | Reduce to lowest terms |
For any fraction problem, follow this order:
Fractions are used far beyond the classroom:
a/b ± c/d = (ad ± cb) / bd — then simplifya/b × c/d = ac / bda/b ÷ c/d = ad / bc (keep, change, flip)GCF(whole × denominator + numerator) / denominator
1) 2/4 = 1/2 2) 1/3 3) 1/4 4) 3 5) 3/4
1) 8/12 + 9/12 = 17/12 = 1 5/12 2) 10/12 − 3/12 = 7/12 3) 5/2 × 3/5 = 15/10 = 3/2 = 1 1/2 4) 7/8 × 4/3 = 28/24 = 7/6 = 1 1/6 5) 11/4 = 2 3/4
What is a fraction?
A fraction represents part of a whole. It is written as two numbers separated by a line: the numerator on top shows how many parts you have, and the denominator on the bottom shows how many equal parts make up the whole. For example, 3/4 means three of four equal parts.
What is the numerator and denominator?
The numerator is the top number of a fraction and counts how many parts you have. The denominator is the bottom number and shows how many equal parts the whole is divided into. In 5/8, the numerator is 5 and the denominator is 8.
How do you add fractions?
Give the fractions a common denominator, then add the numerators and keep the denominator. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. If the denominators are already the same, just add the top numbers. Simplify the answer if possible.
How do you subtract fractions?
Find a common denominator, then subtract the numerators while keeping the denominator. For example, 3/4 − 1/2 becomes 3/4 − 2/4 = 1/4. The method is the same as addition, only you subtract instead of add. Always simplify the result.
How do you multiply fractions?
Multiply the numerators together and the denominators together — no common denominator is needed. For example, 2/3 × 3/5 = 6/15, which simplifies to 2/5. You can simplify before or after multiplying to keep the numbers small.
How do you divide fractions?
Keep the first fraction, change the sign to multiply, and flip the second fraction (use its reciprocal). For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 2. This is the "keep, change, flip" rule, which turns every division into a multiplication.
How do you simplify fractions?
Divide the numerator and denominator by their greatest common factor. For example, 8/12 has a greatest common factor of 4, so it simplifies to 2/3. A fraction is fully simplified when the top and bottom share no common factor other than 1.
What are equivalent fractions?
Equivalent fractions have the same value but different numbers, such as 1/2, 2/4 and 4/8. You create them by multiplying or dividing the numerator and denominator by the same number. They are useful for finding a common denominator when adding or subtracting.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number part of the answer becomes the whole number, and the remainder becomes the new numerator over the same denominator. For example, 7/4 = 1 remainder 3, which is 1 3/4.
How do you 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, 1 3/4 becomes (1 × 4 + 3)/4 = 7/4. Do this before adding, subtracting, multiplying or dividing mixed numbers.
What is the lowest common denominator?
The lowest common denominator is the smallest number that all the denominators divide into evenly. It is the least common multiple of the denominators. Using it keeps the numbers small when adding or subtracting fractions, though any common denominator will work.
Does this fraction calculator show the steps?
Yes. The calculator shows each stage of the working — finding a common denominator, applying the operation, and simplifying — so you can follow the method and learn it, not just see the final answer. That makes it useful for students as well as quick calculations.
Are fractions rational numbers?
Yes. A fraction is a rational number — any value that can be written as one integer divided by another (a non-zero denominator). Whole numbers and integers are also rational because they can be written over 1, such as 5 = 5/1. Fractions, decimals that terminate or repeat, and integers all belong to the rational numbers.
What is the difference between a fraction and a decimal?
A fraction shows a part of a whole using a numerator and denominator, like 3/4. A decimal shows the same value using place value after a point, like 0.75. They are two ways of writing the same rational number, and you can convert between them by dividing the numerator by the denominator.