Quick answer
Convert each mixed number to an improper fraction, add with a common denominator, simplify, then rewrite as a mixed number if the result is improper.
Formula
- W n/d = (W×d + n)/d
- Add improper fractions
- Quotient → whole, remainder → numerator
Introduction
A mixed number like 3 2/5 looks like two parts, but addition is safest when you treat it as one rational value first.
Adding wholes and fractions separately only works in narrow cases. Improper conversion works every time and matches what the calculator does in Mixed form.
If your final sum is correct but still has a common factor, see simplifying fractions after addition before you hand the work in.
Whole number handling
The whole counts complete copies of the unit named by the denominator. In 2 1/4, the 2 means two full fourths-sized wholes, plus one extra fourth.
Improper form packs everything into one numerator: (2×4 + 1)/4 = 9/4. Addition uses that single fraction.
After conversion, the rest of the job is ordinary fraction addition, which the how to add fractions article lists from LCD through simplification.
Conversion formula
- 2 3/5 = (2×5+3)/5 = 13/5
- Add, then divide for mixed output
Do not add denominators from different fractions. After conversion, you are back to standard fraction addition.
If fractional parts already share a denominator, you still convert wholes first unless your teacher teaches a structured partial-sums method.
Step-by-step for mixed sums
- Convert each mixed number Apply (W×d + n)/d to every mixed input.
- Find LCD and scale Same as proper fractions from this point forward.
- Add and simplify Reduce the improper sum, then split into whole and fraction if needed.
Example: 1 2/3 + 1 1/6
Convert: 1 2/3 = 5/3 and 1 1/6 = 7/6.
LCD is 6: 5/3 = 10/6. Add: 10/6 + 7/6 = 17/6.
Divide: 17 ÷ 6 = 2 remainder 5, so 2 5/6. Enter the mixed values in the calculator to confirm.