Mixed Number Calculator
Perform arithmetic on two mixed numbers or convert between improper fractions and mixed numbers. Choose an operation, enter the values, and get the fully simplified result with every step shown.
Formula
Worked example
Add 1 2/3 + 2 1/4. Convert: 1 2/3 = 5/3 and 2 1/4 = 9/4. LCD(3,4) = 12, so 20/12 + 27/12 = 47/12. Reduce: GCD(47,12)=1, so 47/12 = 3 11/12.
What this calculator does
This tool handles two kinds of mixed-number work. In arithmetic mode it adds, subtracts, multiplies, or divides any two mixed numbers or fractions and returns the fully simplified answer as a mixed number, an improper fraction, a decimal, and a percent. In conversion mode it translates between improper fractions and mixed numbers in either direction. Every result is reduced to lowest terms using the greatest common divisor so you never have to simplify by hand.
How the four arithmetic operations work
All four operations start with the same step: convert each mixed number to an improper fraction by multiplying the whole part by the denominator and adding the numerator. Addition and subtraction then find the least common denominator (LCD), scale each fraction, and combine the numerators. Multiplication multiplies the numerators together and the denominators together. Division multiplies the first fraction by the reciprocal of the second. The result is then reduced to lowest terms and, if the numerator is larger than the denominator, converted back to a mixed number.
Improper fractions vs. mixed numbers
An improper fraction has a numerator at least as large as its denominator, such as 7/3, while a mixed number pairs a whole number with a proper fraction, such as 2 1/3. They describe exactly the same quantity. Mixed numbers are easier to picture and read aloud, whereas improper fractions are far easier to combine mathematically, which is why arithmetic always converts to improper form first.
Handling negative values
A negative mixed number such as -2 1/3 means the whole and fractional parts are both on the negative side of zero, equalling -7/3, not -5/3. Apply the negative sign to the whole-number part only and leave the fractional numerator positive. In arithmetic mode, negative mixed numbers in either position are fully supported; the sign is carried through all steps automatically.
Mixed number arithmetic: formula reference
| Operation | Formula | Example |
|---|---|---|
| Add | (ad + cb) / bd | 1 2/3 + 2 1/4 = 3 11/12 |
| Subtract | (ad - cb) / bd | 2 1/4 - 1 2/3 = 7/12 |
| Multiply | ac / bd | 1 2/3 x 2 1/4 = 3 3/4 |
| Divide | ad / bc | 1 2/3 / 2 1/4 = 20/27 |
| Mixed to improper | (whole x den + num) / den | 2 1/3 = 7/3 |
| Improper to mixed | quotient remainder / den | 7/3 = 2 1/3 |
a/b and c/d are the improper-fraction equivalents of the two mixed numbers.
Frequently asked questions
How do I add two mixed numbers?
Convert each to an improper fraction first. Then find the least common denominator, scale both fractions to that denominator, add the numerators, and simplify. For example, 1 2/3 + 2 1/4 becomes 5/3 + 9/4 = 20/12 + 27/12 = 47/12 = 3 11/12.
How do I multiply or divide mixed numbers?
Convert each to an improper fraction. For multiplication, multiply the numerators together and the denominators together, then reduce. For division, multiply the first fraction by the reciprocal of the second (flip numerator and denominator of the second), then reduce. Example: 1 2/3 x 2 1/4 = 5/3 x 9/4 = 45/12 = 3 3/4.
What is an improper fraction?
An improper fraction has a numerator greater than or equal to its denominator, like 7/3 or 5/5. It represents a value of one or more and can always be rewritten as a whole number or a mixed number. The term "improper" is traditional, not a criticism; these fractions are perfectly valid and often more convenient for arithmetic.
Why does the calculator always simplify the result?
A fraction like 4/6 and its simplest form 2/3 are equal, but lowest terms is the standard, cleanest way to state an answer. The calculator divides the numerator and denominator by their greatest common divisor so the fractional part is always fully reduced, regardless of which operation you performed.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number quotient becomes the whole part, and the remainder goes over the original denominator as the fractional part. Then reduce that fraction. Example: 7/3 gives quotient 2, remainder 1, so the result is 2 1/3.
Can I use negative mixed numbers?
Yes. Apply the negative sign to the whole-number part only and leave the fractional numerator positive. For example, -2 1/3 means negative two and one third, which equals -7/3. The calculator handles the sign correctly through all operations.