Add mixed numbers
Mixed numbers combine a whole number and a fraction, such as (3\frac{1}{4}). To add them, you need to combine the whole parts and the fractional parts correctly, then simplify the result.
Method
- Add the whole numbers.
For example, from (2\frac{1}{3}+4\frac{2}{3}), first add (2+4).
- Add the fractions.
Keep the denominators the same and add the numerators: (\frac{1}{3}+\frac{2}{3}=\frac{3}{3}).
- Simplify or convert if needed.
If the fractional sum is an improper fraction or equals a whole number, rewrite it. Here, (\frac{3}{3}=1).
- Combine everything.
Add the extra whole number to the whole-number sum.
Important idea
If the fractional parts do not have the same denominator, first make equivalent fractions with a common denominator before adding.
Check your answer
- Make sure the fraction is simplified.
- Re-add the whole and fraction parts mentally to see whether the answer is reasonable.
- If the fraction part is greater than or equal to 1, convert it into a whole number plus a fraction.
Example
(2\frac{1}{3}+4\frac{2}{3}=6+\frac{3}{3}=6+1=7).