Or add whole numbers and fractions separately1+2=3 (whole parts). ½+⅓=5/6 (fraction parts). Total: 3+5/6=3⅚.
Preguntas Frecuentes
Why can't I add 1/2+1/3 and get 2/5?
Because the denominators represent the size of each piece. Halves and thirds are different sized pieces. You must find a common piece size (the LCM) first.
When is the LCM just the product of the denominators?
When the denominators share no common factors. LCM(3,4)=12=3×4. But LCM(4,6)=12≠24 because they share factor 2.
How do I add more than two fractions?
Same method: find LCM of all denominators at once, convert all fractions, then add all numerators.
Why You Cannot Add 1/2 + 1/3 Directly
1
Find the LCM of denominators1/2+1/3: LCM(2,3)=6. Multiples of 2: 2,4,6. Multiples of 3: 3,6. LCM=6.
2
Convert both fractions to the same denominator1/2: multiply top and bottom by 3 → 3/6. 1/3: multiply by 2 → 2/6. Now pieces are the same size!
3
Add the numerators, keep the denominator3/6+2/6=(3+2)/6=5/6. Never add denominators.
4
Simplify if possible5/6: GCD(5,6)=1. Already in simplest form.
Adding Mixed Numbers — Step by Step
1
Method 1: Convert to improper fractions1½+2⅓ → 3/2+7/3. LCM=6. 9/6+14/6=23/6=3⅚.
2
Method 2: Add whole and fraction parts separatelyWhole: 1+2=3. Fractions: ½+⅓=5/6. Total: 3⅚. Same result!
1/2+1/3
5/6
3/4+1/6
11/12
2/5+3/4
23/20
1/4+1/8
3/8
5/6+1/4
13/12
2/3+3/5
19/15
1/3+1/4+1/6
3/4
7/8+1/4
9/8=1⅛
1½+2⅓
3⅚
2¾+1⅛
3⅞
3+½+¼
3¾
1⅓+1⅓
2⅔
Quick Reference — Common LCMs
Denominators
LCM
Example
2 and 3
6
1/2+1/3=5/6
2 and 4
4
1/2+1/4=3/4
3 and 4
12
1/3+1/4=7/12
4 and 6
12
3/4+1/6=11/12
5 and 4
20
2/5+3/4=23/20
Preguntas Frecuentes
What is the fastest way to find the LCM?
For two small numbers: list multiples of the larger one until the smaller one divides it. For larger numbers: use prime factorization.
What if I multiply the denominators instead of finding LCM?
It works but gives bigger numbers to simplify later. 1/4+1/6: denominators product=24. LCM=12. Both give 5/12, but LCM is simpler.
How do I add three fractions?
Find the LCM of all three denominators at once, convert all fractions, then add all numerators.