Example
Straight across: 2/7 + 3/7
2/7 + 3/7 = 5/7
Two sevenths plus three sevenths is five sevenths. The denominator never moves, and 5/7 shares no common factor, so the answer is already finished.
Fraction addition
Adding Fractions Examples
Twelve worked sums covering every case you will meet: like denominators, unlike denominators, improper fractions, and whole or mixed numbers. Find the group that matches your problem, read the steps, then check your own sum in the tool below.
- like denominators
- unlike denominators
- improper fractions
- whole numbers & mixed
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, or 1 1/2 + 2/3.
Visual explanation
Notice the matching parts
These fractions already name pieces of the same size.
First addend3/8
Second addend1/8
Quick answer
Every example below runs the same three moves
Match: if the denominators differ, rename both fractions with a common denominator (skip this when they already match). Add: combine the numerators and keep the denominator. Finish: simplify if the top and bottom share a factor, then regroup any whole that is hiding inside the sum.
The groups below show those moves on one problem type at a time, with the finishing touches highlighted wherever they appear.
like denominators
Adding fractions with like denominators
The pieces already match, so every problem here is one line of counting — plus a simplify or regroup when the sum asks for it.
Example
Simplify the sum: 1/6 + 3/6
1/6 + 3/6 = 4/6 = 2/3
Adding gives 4/6, which is correct but unfinished. Divide the top and bottom by their shared factor 2 to land on the simplest form, 2/3.
Example
Regroup past one whole: 3/5 + 4/5
3/5 + 4/5 = 7/5 = 1 2/5
Seven fifths tops one whole: five of the fifths fold into a whole, leaving two fifths behind. The mixed number 1 2/5 is the expected final form.
improper fractions
Adding improper fractions
Numerators bigger than denominators change nothing about the adding — the wholes are just waiting to be regrouped at the end.
Example
A whole-number sum: 7/3 + 5/3
7/3 + 5/3 = 12/3 = 4
Twelve thirds divide out evenly — every three thirds is one whole, so the sum is exactly 4. The addition step is identical to proper fractions.
Example
A mixed-number sum: 9/5 + 7/5
9/5 + 7/5 = 16/5 = 3 1/5
Sixteen fifths hold three full wholes with one fifth to spare. The improper fraction and 3 1/5 name the same amount — regrouping just shows the wholes.
Example
Unlike denominators too: 5/4 + 7/6
5/4 + 7/6 = 15/12 + 14/12 = 29/12 = 2 5/12
Being improper does not skip the matching step: quarters and sixths are renamed as twelfths first, then the usual rule runs to 29/12, which regroups to 2 5/12.
unlike denominators
Adding fractions with unlike denominators
Different piece sizes must be renamed to a common denominator before anything combines — after that, the rule is the same as always.
Example
Quarter plus third: 1/4 + 2/3
1/4 + 2/3 = 3/12 + 8/12 = 11/12
Twelfths are the common size: 1/4 becomes 3/12 and 2/3 becomes 8/12. Eleven twelfths shares no factor, so the sum stops there.
Example
Common denominator 12: 1/4 + 1/6
1/4 + 1/6 = 3/12 + 2/12 = 5/12
The least common multiple of 4 and 6 is 12. Rewrite each fraction over 12 — 3/12 and 2/12 — then add the numerators for 5/12.
Example
One denominator fits inside the other: 3/10 + 2/5
3/10 + 2/5 = 3/10 + 4/10 = 7/10
When one denominator doubles into the other, only the smaller one needs rewriting: 2/5 becomes 4/10, and tenths add straight across to 7/10.
whole and mixed
Adding whole numbers and mixed numbers
Keep the whole numbers in their own column and add the fractional parts separately — converting to improper fractions also works when the parts differ.
Example
Whole plus fraction: 2 + 3/4
2 + 3/4 = 2 3/4
A whole number beside a fraction simply sits in the whole column — two wholes and three quarters is written 2 3/4. Nothing needs rewriting.
Example
Matching fractional parts: 1 1/4 + 2 1/4
1 1/4 + 2 1/4 = 3 + 2/4 = 3 2/4 = 3 1/2
Add the wholes first (3), then the quarters (2/4). The fractional sum simplifies from 2/4 to 1/2, giving 3 1/2.
Example
Mixed with unlike parts: 1 1/2 + 2/3
1 1/2 + 2/3 = 1 + 3/6 + 4/6 = 1 7/6 = 2 1/6
The halves and thirds become sixths: 3/6 plus 4/6 is 7/6, which carries one more whole into the column. The total regroups to 2 1/6.
Keep learning
Related fraction topics
Common questions
Adding Fractions Examples FAQ
2/7 + 3/7 = 5/7. Both fractions count sevenths, so the numerators add and the denominator stays: two sevenths plus three sevenths makes five sevenths. When the sum needs it, finish with simplifying (1/6 + 3/6 = 4/6 = 2/3) or regrouping (3/5 + 4/5 = 7/5 = 1 2/5).