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Mixed Number Calculator

A mixed number combines a whole number with a proper fraction, like 2 1/3. To convert the improper fraction 7/3 to a mixed number, divide 7 by 3 to get a quotient of 2 with remainder 1, giving 2 1/3. For arithmetic, convert mixed numbers to improper fractions first, perform the operation, then convert back. Enter values below to convert or calculate.

Quick Answer

The improper fraction 7/3 equals the mixed number 2 1/3. To add 1 1/2 + 2 1/3, convert to 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6.

Convert improper fraction to mixed number

Mixed number arithmetic

Common Examples

Input Result
7/3 to mixed number 2 1/3
1 1/2 + 2 1/3 3 5/6
3 1/2 - 1 1/4 2 1/4
1 1/2 x 2 2/3 4
3 1/2 / 1 1/4 2 4/5

How It Works

Converting improper fractions to mixed numbers

An improper fraction has a numerator larger than or equal to the denominator (like 7/3). A mixed number has a whole number part and a proper fraction part (like 2 1/3).

To convert: divide the numerator by the denominator.

  • Whole number = quotient (integer part of the division)
  • Remainder = numerator mod denominator
  • Mixed number = whole remainder/denominator

Converting mixed numbers to improper fractions

Multiply the whole number by the denominator, add the numerator, and place over the original denominator:

(whole x denominator + numerator) / denominator

Mixed number arithmetic

To perform arithmetic with mixed numbers:

  1. Convert each mixed number to an improper fraction
  2. Perform the operation (add, subtract, multiply, or divide)
  3. Simplify the result
  4. Convert back to a mixed number

Worked example

For 1 1/2 + 2 1/3: Convert to improper fractions: 3/2 + 7/3. Find common denominator (6): 9/6 + 14/6 = 23/6. Convert back: 23 / 6 = 3 remainder 5, so the result is 3 5/6.

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Frequently Asked Questions

What is a mixed number?
A mixed number is a number consisting of a whole number and a proper fraction written together, like 3 1/4. It represents the sum of the whole number and the fraction: 3 + 1/4 = 13/4 as an improper fraction.
What is an improper fraction?
An improper fraction is a fraction where the numerator is greater than or equal to the denominator, like 7/3 or 5/5. Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator.
How do you add mixed numbers with different denominators?
Convert each mixed number to an improper fraction, find a common denominator, add the numerators, simplify, and convert back to a mixed number. For example, 2 1/3 + 1 1/4 becomes 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12.
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction, multiply the numerators together and the denominators together, simplify, and convert back. For example, 1 1/2 x 2 2/3 = 3/2 x 8/3 = 24/6 = 4.
Can the result of mixed number arithmetic be a negative number?
Yes. If you subtract a larger mixed number from a smaller one, the result is negative. For example, 1 1/4 - 3 1/2 = 5/4 - 7/2 = 5/4 - 14/4 = -9/4 = -2 1/4.