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Mixed Number Calculator

Work with mixed numbers like 2 1/3 and 1 3/4 directly, or convert between mixed numbers and improper fractions.

Answer

4 1/12

Improper fraction
49/12
Decimal
4.083333
Show working
  1. 2 1/3 = 7/3
  2. 1 3/4 = 7/4
  3. LCM(3, 4) = 12
  4. 7/3 = 28/12, 7/4 = 21/12
  5. 28/12 + 21/12 = 49/12
  6. 49/12 = 4 1/12

How to use

  1. Choose Calculate, → Improper or → Mixed.
  2. Type mixed numbers as whole part, space, fraction (2 1/3).
  3. Read the answer as a mixed number and as an improper fraction, with the steps.

Good to know

To calculate, each mixed number is first turned into an improper fraction: 2 1/3 = (2 × 3 + 1)/3 = 7/3. The sum is then done with the LCM method (or by multiplying / flipping for × and ÷), simplified, and turned back into a mixed number.

Improper to mixed: divide the numerator by the denominator. The quotient is the whole part, the remainder is the new numerator: 17/5 → 17 ÷ 5 = 3 remainder 2 → 3 2/5. Mixed to improper: whole × denominator + numerator, over the same denominator.

A minus sign applies to the whole mixed number: −2 1/3 means −(2 + 1/3) = −7/3, not −2 + 1/3. That is a common slip in exams. All working is exact, with no rounding.

Questions

How do I add mixed numbers?

Convert both to improper fractions, add them with a common denominator and convert back. 2 1/3 + 1 3/4 = 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator and add the numerator: 3 2/5 = (3 × 5 + 2)/5 = 17/5.

How do I convert an improper fraction to a mixed number?

Divide: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.

Can I multiply mixed numbers without converting?

Not correctly. Always convert to improper fractions first, otherwise you miss the cross terms. 1 1/2 × 1 1/2 is 9/4 = 2 1/4, not 1 1/4.

How do I type a negative mixed number?

Put the minus sign first: −2 1/3.

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