Are fractions driving you crazy? Whether you're doing homework, preparing for an exam, or just need quick answers, our fraction calculator can help. Enter any proper or improper fraction, choose your operation (addition, subtraction, multiplication, or division), and get instant results with detailed, step-by-step explanations. It's like having a 24/7 math tutor—completely free!
What is a fraction?
A fraction is a mathematical way of representing a part of a whole, a quantity, or a ratio between two numbers. This math tool lets you input simple or improper fractions, select your mathematical operator, and instantly get a simplified answer or a reduced mixed number. It takes care of the difficult calculations and clearly displays the mathematical process, making it easy to understand how the final result was obtained.
Note: If your math problem contains a whole number before the fraction, you are dealing with a mixed number and should use the mixed number calculator instead.
Also note that word problems asking for a fraction "of" a number (e.g. "what is 3/4 of 5/9?") simply require multiplication.
How to use this tool
Step 1: Enter your first fraction
Enter the numerator (top number) and denominator (bottom number) into the input fields of the first fraction.
Step 2: Choose your operation
Select which calculation you want to perform: Addition (+), Subtraction (−), Multiplication (×), or Division (÷).
Step 3: Enter your second fraction
Enter the numerator and denominator for the second fraction in the same way.
Step 4: Click Calculate
The tool immediately solves the equation and displays your result – completely simplified and converted into a mixed number if the answer is an improper fraction.
Step 5: Review the step-by-step breakdown
Below your result, the tool shows exactly how it got there: by finding a common denominator (for addition/subtraction), multiplying directly (for multiplication), or applying "keep, change, flip" (for division) – allowing you to trace or verify the math yourself.
A note on accuracy: Every result is calculated using exact fraction arithmetic and automatically simplified using the greatest common divisor – never rounded or approximated. All calculations are performed instantly in your browser; nothing you enter is stored or transmitted.
Examples
Examples for Addition
Beispiel 1: What is 2/5 + 1/3?
Beispiel 2: What is 3/4 + 2/8?
Examples for Subtraction
Beispiel 1: What is 5/6 − 1/4?
Beispiel 2: What is 7/8 − 1/3?
Examples for Multiplication
Beispiel 1: What is 3/5 × 2/7?
Beispiel 2: What is 2/3 × 3/4?
Examples for Division
Beispiel 1: What is 5/8 ÷ 1/4?
Beispiel 2: What is 3/4 ÷ 2/5?
Fraction Rules & Concepts
Understanding fractions in everyday life
The easiest way to understand fractions is to think of them as parts of a whole. For example, if you have a box of 24 donuts and your family eats 9 of them, you have consumed 9/24 of the entire box.
Fractions are also great for representing measurements that fall between two whole numbers. If your gym is 5.4 kilometers away, the distance is greater than 5 kilometers but less than 6. That extra 0.4 is a fraction of a kilometer. You can express this distance as "5 and 4 tenths" kilometers.
Rules for calculating with negative fractions
When solving equations with negative fractions, simply attach the minus sign directly to the top number (numerator). If your fraction is -5/7, enter -5 as the numerator and 7 as the denominator.
- If only the top or only the bottom number has a minus sign, the entire fraction becomes negative.
- If both the top and bottom numbers have a minus sign, they cancel each other out, resulting in a positive fraction.
- Just like in normal arithmetic, the same sign always leads to a positive result, while opposite signs always give a negative result.
How to add or subtract fractions with different denominators
You always need to check your denominators (the bottom numbers) before adding or subtracting fractions. If these denominators do not match, you have to find the least common denominator (LCD). Using an online common denominator calculator makes finding this shared base incredibly easy.
Once you have found the common base:
- Determine which number you need to multiply the original denominator by to reach it.
- Multiply the numerator (the top number) by exactly the same value.
- Repeat this for all fractions in your equation.
- Now just add or subtract the numerators while keeping the denominator the same.
- Finally, convert any improper fractions to mixed numbers and simplify your final result.
Simple rules for multiplying and dividing fractions
Multiplication: Simply multiply all the numerators together and do the same for the denominators. Simplify the result at the end.
Division: Use the "keep, change, flip" trick (reciprocal):
- Keep: Leave the first fraction exactly as it is.
- Change: Change the division symbol (÷) to the multiplication symbol (×).
- Flip: Flip the second fraction completely (find its reciprocal).
Then simply multiply directly and simplify the result.
Fraction formulas with cross-multiplication
You can completely bypass the search for the common denominator by using cross-multiplication formulas. This is often a much faster way to solve fractional equations by hand.
Frequently Asked Questions (FAQ)
What if my denominators are different – do I have to find a common denominator myself?
No. The calculator finds the common denominator automatically and shows you the entire step-by-step process so you can see exactly how it got there.
Does the calculator simplify (reduce) the final result?
Yes – every result is automatically reduced to its simplest form. If the answer is an improper fraction, it is also converted into a mixed number.
Can I use this tool for mixed numbers like 2 ¾?
Not directly – this calculator is designed for proper and improper fractions. For a whole number combined with a fraction, use the mixed number calculator instead.
How do I enter a negative fraction?
Add the minus sign to the numerator. For -5/7, enter -5 as the numerator and 7 as the denominator. If both the numerator and denominator are negative, they cancel each other out and the result is positive.
What does "keep, change, flip" mean in division?
This is the method used for dividing fractions: keep the first fraction as it is, change the ÷ to ×, and flip the second fraction (find the reciprocal). Then multiply directly.
How do I calculate a fraction "of" a number, like "What is 3/4 of 5/9"?
"Of" means to multiply. Enter 3/4 and 5/9 and select the multiplication operation.
Why is my answer as an improper fraction shown as a mixed number?
If the numerator of a fraction is larger than its denominator (like an improper result), the calculator automatically converts it to a mixed number, as this is usually the more useful way to read the answer.
Can I calculate more than two fractions at once?
No – the calculator works with two fractions per calculation. For a longer equation, calculate two fractions at a time and then use that result as one of the fractions in your next calculation.
Do I have to cross-multiply, or does the calculator use common denominators?
The calculator finds the actual least common denominator for addition and subtraction (the standard classroom method), rather than just cross-multiplying. Cross-multiplication is shown separately as a faster manual shortcut if you are solving the problem by hand.
Related Calculators
- Mixed Number Calculator – Solve problems with mixed fractions or simplify improper fractions with full calculation steps
- Simplify Fractions Calculator – Quickly reduce any fraction to its simplest form
- GCF Calculator – Understand the math behind reducing fractions by finding the greatest common factor
- Long Division Calculator – Simplify large fractions by hand, showing whole numbers and remainders
Last updated: July 30, 2026