Overview
What this calculator does
Add, subtract, multiply, and divide fractions and mixed numbers, and get the answer three ways: as a simplified fraction, as a mixed number, and as a decimal. A step-by-step breakdown shows exactly how the result was reached, so it's as useful for learning as it is for getting a quick answer.
Different denominators
How to add and subtract fractions
You can only add or subtract fractions that share a denominator. When they differ, you first find a common one.
The steps
- Find a common denominator (multiplying the two denominators always works)
- Convert each fraction to that denominator
- Add or subtract the numerators, keep the denominator
- Simplify the result
Example: 1/2 + 1/3. Common denominator is 6: 3/6 + 2/6 = 5/6. Already in lowest terms, so 5/6 is the answer.
The easy one
How to multiply fractions
Multiplication needs no common denominator. Multiply the numerators together and the denominators together, then simplify.
2/3 × 3/4 = 6/12 = 1/2. You can also "cross cancel" before multiplying to keep numbers small: the 3s cancel, leaving 2/1 × 1/4 = 2/4 = 1/2.
Keep, change, flip
How to divide fractions
To divide by a fraction, multiply by its reciprocal (flip the second fraction upside down). This is the "keep, change, flip" rule:
- Keep the first fraction
- Change ÷ to ×
- Flip the second fraction
1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. It makes sense: how many quarters fit in a half? Two.
Two forms of the same value
Mixed numbers and improper fractions
A mixed number like 2 ¾ combines a whole number and a fraction. An improper fraction like 11/4 has a numerator larger than the denominator. They're equal:
- Mixed to improper: multiply whole × denominator, add numerator. 2¾ = (2×4 + 3)/4 = 11/4
- Improper to mixed: divide. 11/4 = 2 remainder 3 = 2¾
To enter a mixed number, put the whole part in the left box and the fraction in the numerator/denominator boxes. The calculator converts to an improper fraction internally, does the math, and gives you both forms back.
Lowest terms
Simplifying fractions
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD).
8/12: the GCD of 8 and 12 is 4, so divide both by 4 to get 2/3. Every answer here is automatically simplified.
Behind the scenes
Privacy and how it runs
Runs in your browser
Common questions
What is 1/2 + 1/4?
Common denominator 4: 2/4 + 1/4 = 3/4. As a decimal, 0.75.
What is 2/3 of a number?
Multiply the number by 2/3. Two-thirds of 90 is 90 × 2/3 = 60. For "fraction of a quantity" problems, multiplication is the operation.
How do I turn a fraction into a percentage?
Convert to a decimal (numerator ÷ denominator), then multiply by 100. 3/4 = 0.75 = 75%. The decimal is shown with every answer.
Why does my fraction simplify to a whole number?
When the numerator is a multiple of the denominator, the fraction equals a whole number. 6/3 = 2, 8/4 = 2. The calculator shows the whole number in that case.
Can it handle negative fractions?
Yes. Put a minus sign on the whole number or the numerator. The calculator keeps track of the sign and always displays the denominator as positive.
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