Adding unlike fractions is two steps: match the units, then count them.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
1/2 + 1/3 becomes 3/6 + 2/6, which is 5 sixths.
The unit still does not change
Once both are sixths, adding them gives sixths. Only the count grows.
Subtraction is the same
3/4 − 1/6 becomes 9/12 − 2/12, which is 7 twelfths.
The three steps
Find a common denominator. Convert both fractions. Add the numerators and keep the denominator. For 2/3 + 3/4: twelfths, then 8/12 + 9/12 = 17/12. Every unlike-fraction addition is these same three steps in the same order.
The denominator does not get added
Once both fractions count twelfths, adding gives twelfths — 17 of them. Adding the denominators would be like concluding that 8 metres plus 9 metres is 17 square metres. The unit names what you are counting; it is not part of the count.
Finish the answer properly
17/12 is more than a whole, so it can be written 1 5/12. And if the answer shares a factor top and bottom, simplify it. An unfinished answer is not wrong, but the simplest form is easier to judge for size and easier to compare.
Estimate with benchmarks first
2/3 is a bit over a half and 3/4 is a bit under one, so expect something around 1 1/2. The answer 1 5/12 fits. A benchmark estimate catches the add-the-denominators error instantly, since 5/7 would be less than one.
Step 2: Try It Yourself
Set both bottom numbers the same to add them.
3/6
2/6
5/6
3 sixths plus 2 sixths is 5 sixths, which is written 5/6.
The denominator names what is being counted. It does not change.
Step 3: Watch an Example
One step at a time.
Watch Leo Add 3/4 and 1/6
Leo adds two fractions with different units.
- Step 1
He finds a shared unit: twelfths.
Step 4: Your Turn
Practice makes it stick.
The Two Jugs
Problem 1 of 2
1/2 litre plus 1/4 litre, in quarters. What is the top number?
The Walk
Problem 2 of 2
2/3 mile plus 1/6 mile, in sixths. What is the top number?
Match and Count
1 of 4
1/2 + 1/3, in sixths. What is the top number?
2 of 4
1/4 + 2/5, in twentieths. What is the top number?
3 of 4
3/4 − 1/6, in twelfths. What is the top number?
4 of 4
5/6 − 1/2, in sixths. What is the top number?
Step 5: Quick Check
Show what you know.
Question 1 of 2
2/3 + 1/4, in twelfths. What is the top number?
Question 2 of 2
What are the two steps for adding unlike fractions?
What You Learned
- Rewrite both fractions in one shared unit.
- Then count the units.
- Never add the bottom numbers.