What is a Mixed Number?
Take 3½: that's 3 whole units plus another half. You'll run into these outside the classroom too, in things like "2¼ cups of flour" or "1¾ hours until we land."
Converting Mixed Numbers to Improper Fractions
Multiply the whole number by the denominator, add the numerator, and keep the same denominator underneath:
3⅔ → (3 × 3 + 2) / 3 = 11/3
5½ → (5 × 2 + 1) / 2 = 11/2
Converting Improper Fractions to Mixed Numbers
Divide the numerator by the denominator. Whatever comes out as the quotient becomes your whole number, and the remainder becomes the new numerator:
17/5 → 17 ÷ 5 = 3 remainder 2 → 3⅖
9/3 → 9 ÷ 3 = 3 remainder 0 → 3 (whole number)
Adding Mixed Numbers
Add the whole numbers on their own, add the fractions on their own (finding a common denominator first if needed), then combine the two results:
Whole: 2 + 1 = 3
Fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1¼
Total: 3 + 1¼ = 4¼
Subtracting Mixed Numbers
Handle the whole numbers and fractions separately here too. If the fraction you're subtracting is bigger than the one you're starting with, borrow 1 from the whole number first:
¼ < ¾, so borrow: 4¼ = 3 + 1¼ = 3 + 5/4
3(5/4) − 1(3/4) = 2(2/4) = 2½
Multiplying Mixed Numbers
Convert both numbers to improper fractions before doing anything else, then multiply straight across - numerators together, denominators together:
= 5/2 × 4/3
= 20/6 = 10/3 = 3⅓
Dividing Mixed Numbers
Same first step: convert to improper fractions. Then multiply by the reciprocal of the second fraction instead of dividing directly:
= 15/4 ÷ 3/2
= 15/4 × 2/3
= 30/12 = 5/2 = 2½
Quick Summary
| Operation | Key step |
|---|---|
| Mixed → improper | (whole × denominator + numerator) / denominator |
| Improper → mixed | Divide, quotient is whole, remainder is numerator |
| Add/Subtract | Common denominator for fractions, handle carries/borrows |
| Multiply/Divide | Always convert to improper fractions first |
Using the Fraction Calculator
The SolverCalc fraction calculator accepts mixed numbers directly, no manual conversion required. Type one in and it converts, calculates, and shows every step along the way.