Math calculator
Fraction Calculator
Add, subtract, multiply, or divide fractions and mixed numbers and get an exact simplified answer with its mixed-number and decimal forms.
Leave Whole blank for a simple fraction. Leave Numerator and Denominator blank for a whole number.
Exact result
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What is a fraction?
A fraction represents part of a whole. The numerator is the number above the line, and the denominator is the number below it. The denominator cannot be zero.
How fraction operations work
To add or subtract fractions, find a common denominator, then add or subtract the adjusted numerators. To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal of the second fraction.
How fractions are simplified
The calculator divides the numerator and denominator by their greatest common divisor. This produces an equivalent fraction in lowest terms while preserving the exact value.
Mixed numbers and improper fractions
An improper fraction has a numerator at least as large as its denominator, such as 6/5. Its mixed-number form is 1 1/5. Enter a mixed number with the optional Whole, Numerator, and Denominator fields.
Worked examples
For 1/2 + 1/3, use denominator 6: 3/6 + 2/6 = 5/6.
For 4/5 ÷ 2/3, multiply by the reciprocal: 4/5 × 3/2 = 12/10 = 6/5 = 1 1/5.
Negative signs are normalized to the numerator, so −1/2 + 3/4 = 1/4.
Frequently asked questions
Can I enter a whole number?
Yes. Enter it in Whole and leave Numerator and Denominator blank. A blank denominator is treated as 1.
Why can't the denominator be zero?
Division by zero is undefined, so the calculator rejects zero denominators and division by a zero-valued fraction.
Are the exact results rounded?
No. Exact results use integer arithmetic. The decimal display shows up to 12 digits and adds an ellipsis when the decimal repeats or continues.
How the fraction calculator works
Enter two fractions, pick an operation (+, −, ×, or ÷), and the calculator returns the exact answer in lowest terms. Each fraction has three boxes: Whole, Numerator, and Denominator. Leave Whole blank for a plain fraction such as 3/4, fill in all three for a mixed number such as 2 3/8, or type only a whole number and leave the other two blank to use an integer (a blank denominator counts as 1).
Four results are shown. The exact result is the reduced fraction. The mixed number rewrites an improper result with a whole part. The decimal shows the value to 12 digits and adds an ellipsis if the digits repeat or continue. The intermediate line shows the raw answer before simplification, which is useful for checking homework because it matches the step you would write on paper.
All arithmetic is done with exact integers rather than floating-point decimals, so there is no rounding error and numerators or denominators with dozens of digits are handled correctly. Inputs must be whole numbers; decimals such as 1.5 are not accepted, and a denominator of zero or division by a fraction equal to zero shows an error instead of a result.
Fraction formulas
Addition and subtraction need a common denominator, and the simplest one to find is the product of the two denominators. To add 3/4 and 5/6: (3 × 6 + 4 × 5) ÷ (4 × 6) = (18 + 20) ÷ 24 = 38/24. That is the intermediate result. The greatest common divisor of 38 and 24 is 2, so the reduced answer is 19/12, which is 1 7/12 as a mixed number and 1.58333… as a decimal.
Multiplication is the most direct operation: multiply straight across. Division means multiplying by the reciprocal of the second fraction, so 2/3 ÷ 4/9 becomes 2/3 × 9/4 = 18/12, which reduces to 3/2, or 1 1/2, or 1.5.
Simplifying, mixed numbers, and decimals
A fraction is in lowest terms when its numerator and denominator share no factor other than 1. The calculator finds the greatest common divisor (GCD) of the two numbers and divides both by it. For 24/36 the GCD is 12, so the fraction reduces to 2/3. The value never changes during this step; only the way it is written does.
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole part and the remainder stays over the original denominator: 19 ÷ 12 is 1 with remainder 7, giving 1 7/12. To convert a mixed number back, multiply the whole by the denominator and add the numerator: 2 3/8 = (2 × 8 + 3)/8 = 19/8.
A reduced fraction has a terminating decimal only when its denominator has no prime factors other than 2 and 5. That is why 3/8 = 0.375 ends but 1/3 = 0.333… and 5/12 = 0.41666… repeat forever. The calculator stops at 12 digits and marks repeating or truncated decimals with an ellipsis so you know the decimal is not exact.
Entering negative fractions
Put the minus sign on the whole number if there is one, otherwise on the numerator. A negative mixed number is read the way it is written in math class: −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. The sign is always moved to the numerator in the output, so entering 3 over −4 produces −3/4.
Subtracting a negative fraction adds it, and multiplying or dividing two negatives gives a positive. For example, −1/2 + 3/4 = −2/4 + 3/4 = 1/4, and −2/3 × −3/5 = 6/15 = 2/5.
Common mistakes to avoid
- Adding denominators – 1/2 + 1/3 is 5/6, not 2/5; only the numerators are added once the denominators match
- Flipping the wrong fraction – when dividing, take the reciprocal of the second fraction only: 3/5 ÷ 2/7 = 3/5 × 7/2
- Cancelling across a plus sign – you can cancel common factors when multiplying, but not inside a sum
- Forgetting the whole part – 2 1/4 × 2 is 4 1/2, not 2 2/4; convert mixed numbers to improper fractions first
- Reading a decimal as exact – 0.333… is an approximation of 1/3, so keep fractions in fraction form until the last step
- Typing decimals – enter 1.5 as 3/2 or as whole 1 with 1/2, since the inputs accept whole numbers only
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, add the numerators, and keep the denominator. For 1/4 + 2/3, use 12: 3/12 + 8/12 = 11/12.
How do you divide fractions?
Keep the first fraction, change the division to multiplication, and flip the second fraction. For example, 3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10, which is 2 1/10 as a mixed number.
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number quotient is the whole part and the remainder goes over the denominator. For 17/5, 17 ÷ 5 is 3 remainder 2, so 17/5 = 3 2/5.
How do you simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor. The GCD of 24 and 36 is 12, so 24/36 simplifies to 2/3. The calculator reduces every result automatically.
Can I enter decimals or a whole number?
Whole numbers yes, decimals no. Type a whole number in the Whole box and leave the fraction boxes blank. Convert decimals to fractions first, for example 0.75 as 3/4 or 1.5 as 3/2.
Why does the decimal result end with an ellipsis?
The ellipsis means the decimal does not terminate within 12 digits, usually because it repeats. Fractions whose reduced denominator contains a prime factor other than 2 or 5, such as 1/3 or 5/12, always produce repeating decimals.