Match the fraction denominators
The whole numbers never need rewriting; the fraction parts must be the same size before their numerators combine. Rename halves and thirds as sixths, and so on.
Adding fractions
Adding Mixed Fractions
Mixed numbers add in two columns — wholes with wholes, parts with parts — with one new event to watch for: fraction parts that overflow into an extra whole. Match the denominators, add, carry if needed, simplify.
- add the wholes and the parts
- carry when parts fill a whole
- common denominators first
- improper fractions also work
Visual addition tool
See how fraction parts become ready to add
Start with one problem, make the parts match when needed, then combine them.
Type the full expression
Examples: 1/4 + 2/3, 2 + 3/4, 1 1/2 + 2/3, or 1/6 + 2/6 + 3/6.
Visual explanation
Notice the part sizes
The fractions name pieces of different sizes, so they cannot be combined yet.
First addend5/4
1 whole
Second addend5/2
2 wholes
1/4 part
1/2 part
These pieces are not the same size yet.
Quick answer
Two columns, one carry rule
In 2 1/3 + 1 1/2, rename the parts as sixths: 2 2/6 + 1 3/6. The wholes add to 3 and the parts to 5/6, and nothing carries — the answer is 3 5/6.
When the parts overflow, carry: 1 5/6 + 2 3/4 = 1 10/12 + 2 9/12 = 3 19/12, and 12 of those twelfths fold into a fourth whole, leaving 4 7/12.
The method
Four steps: match, add, carry, simplify
Add the whole numbers and the numerators
Work in two columns: wholes with wholes, parts with parts. In 2 1/3 + 1 1/2, the wholes give 3 and the parts give 2/6 + 3/6 = 5/6.
Carry when the parts fill a whole
If the fraction sum reaches the denominator, regroup it into wholes: 3 19/12 becomes 4 7/12, because 12 of the twelfths fold into one more whole.
Simplify the fraction part
Finish the way every fraction addition finishes: reduce the fraction if top and bottom share a factor, as in 3 2/4 = 3 1/2.
Worked example
Like denominators, no carry: 1 1/4 + 2 2/4
1 1/4 + 2 2/4 = 3 3/4
The parts already match, so the wholes add (1 + 2 = 3) and the parts add (1/4 + 2/4 = 3/4). The fraction 3/4 is below one whole, so nothing carries and 3/4 is already in lowest terms.
Worked example
Unlike denominators: 2 1/3 + 1 1/2
2 1/3 + 1 1/2 = 2 2/6 + 1 3/6 = 3 5/6
Halves and thirds become sixths: 1/3 stretches to 2/6 and 1/2 to 3/6. The wholes add to 3 and the parts to 5/6, which stays below a whole — no regrouping, no simplifying.
Worked example
Carrying into a new whole: 1 5/6 + 2 3/4
1 5/6 + 2 3/4 = 1 10/12 + 2 9/12 = 3 19/12 = 4 7/12
The parts sum to 19/12, which tops one whole. Twelve twelfths fold into a fourth whole, leaving 7/12: the answer regroups from 3 19/12 to 4 7/12.
Worked example
Improper-fraction method: 3 1/2 + 1 3/5
3 1/2 + 1 3/5 = 7/2 + 8/5 = 35/10 + 16/10 = 51/10 = 5 1/10
Converting both mixed numbers to improper fractions first turns the problem into one addition: 51/10, which regroups to 5 wholes and 1 tenth. Both methods always agree.
The carry is the only new idea
Students who can add fractions can add mixed numbers, because the only new event is a fraction sum that reaches one whole. It behaves exactly like carrying in column addition: 19/12 holds 12/12 inside it, so one whole moves into the whole-number column and 7/12 stays behind. The columns keep the two units apart while the carry connects them.
The improper-fraction method hides the carry inside the numerator instead: 1 5/6 + 2 3/4 = 11/6 + 11/4 = 22/12 + 33/12 = 55/12, which regroups once at the end to 4 7/12. One regroup instead of one carry — the same amount of bookkeeping, moved to a different place in the problem. Students should run both methods on the same problem at least once to see that they are two views of one value.
Compare with adding improper fractionsCommon mistakes when adding mixed fractions
- Adding the denominators: The classic error survives mixed numbers: 1/2 + 1/5 is not 2/7. The denominator names the size of the pieces, and adding numerators never changes that size — rename to a common denominator instead.
- Missing the carry: A fraction sum of 19/12 still holds a whole inside it. Leaving 3 19/12 as the final answer is unfinished — 12 of those twelfths are a whole, so the expected form is 4 7/12.
- Adding wholes to parts: The whole-number column and the fraction column stay separate until the end. Mixing them — adding the 2 of 2 1/3 into the sixths — scrambles the two units the mixed number keeps apart.
Practice routine
Say whether a carry is coming before you add
After matching denominators, compare each fraction part to one whole. Predict the carry (or its absence), then add and check against your prediction.
TryWhat to noticeAnswer
1 1/4 + 2 2/4Like denominators; simplify the fraction part.3 3/4
2 1/3 + 1 1/2Rename to sixths before the parts combine.3 5/6
1 5/6 + 2 3/4The parts overflow a whole — carry.4 7/12
3 1/2 + 1 3/5Improper-fraction method as a check.5 1/10
2 2/3 + 3 3/4Twelfths with a carry and a simplify.6 5/12
Keep learning
Related fraction topics
Common questions
Adding Mixed Fractions FAQ
Give the fraction parts a common denominator, add the whole numbers and the numerators in separate columns, then carry if the fraction parts fill one whole and simplify the leftover fraction. For example, 2 1/3 + 1 1/2 = 2 2/6 + 1 3/6 = 3 5/6.