Mixed Numbers
The calculator converts mixed numbers to improper fractions and improper fractions to mixed numbers with a step-by-step solution.
The mixed number calculator converts a mixed number to an improper fraction and an improper fraction to a mixed number, with a step-by-step solution and simplification.
Proper and improper fractions
- A proper fraction has a numerator smaller than the denominator: 3/4, 2/7. It is less than one.
- An improper fraction has a numerator greater than or equal to the denominator: 7/4, 5/5. It is one or more.
- A mixed number is a whole part plus a proper fraction: 13/4 = 1 + 3/4.
How to convert a mixed number to an improper fraction
Multiply the whole part by the denominator and add the numerator. The result is the new numerator; the denominator stays the same:
ab/c = a · c + b/c
Example. 23/4 = 2 · 4 + 3/4 = 11/4
How to convert an improper fraction to a mixed number
Divide the numerator by the denominator with a remainder. The quotient is the whole part, the remainder is the numerator of the fraction part, and the denominator stays the same.
Example. 17/5: 17 ÷ 5 = 3 R 2, so 17/5 = 32/5
Negative mixed numbers
The minus sign in front of a mixed number applies to the whole number: −21/3 = −(2 + 1/3) = −7/3. So convert the number without the minus and put the minus in front of the result.
Mixed numbers are convenient for answers ("two and a half pizzas"), while improper fractions are convenient for calculations: to multiply or divide mixed numbers, convert them to improper fractions first.