The rule
a b/c = (a × c + b) ÷ c
Why it works
A mixed number is a whole part plus a fraction. To turn it into a single fraction, convert the whole part into that many pieces of the same size and add the ones you already have.
How to do it by hand
- Multiply the whole part by the denominator
- Add the numerator
- Keep the same denominator
- Simplify if the result has a common factor
What is worth knowing
Mixed numbers are for reading and improper fractions are for calculating, which is why recipes say 2½ cups and algebra says 5/2. Trying to multiply mixed numbers directly is the classic trap: 2½ × 1½ is not 2¾, because the whole parts and fractions do not multiply separately. Convert both to improper fractions first and the answer, 15/4, comes out correctly. A properly written mixed number always has a proper fraction: 2 5/3 is not wrong exactly, but it is hiding a whole unit and should be 3 2/3.