2/5 + 1/5 is two fifths plus one fifth, which is three fifths.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The bottom number does not move
You still have fifths. Only how many changed.
It works like objects
2 apples plus 1 apple is 3 apples, not 3 pairs. The name of the thing stays.
Subtraction is the same
4/7 − 2/7 is four sevenths take away two sevenths, leaving two sevenths.
Same unit means you can just count
2/8 + 3/8 is two eighths plus three eighths, which is five eighths. You count the pieces because they are all the same size. The bottom number stays 8 because the piece size has not changed — only how many you have.
Why the denominator does not change
Adding 2 apples and 3 apples gives 5 apples, not 5 apple-squareds. The unit is a label, not a quantity being added. Writing 2/8 + 3/8 = 5/16 is the same error as concluding that two apples plus three apples is five pairs.
Subtraction works identically
5/8 - 3/8 = 2/8. Take pieces away and count what is left; the unit is unchanged. Everything true of same-unit addition is true of same-unit subtraction, which is why they are taught together.
When the total passes one
5/8 + 6/8 = 11/8, which is more than one whole. You can leave it as 11/8 or write it as 1 3/8. Neither form is more correct; the improper fraction is easier to calculate with and the mixed number is easier to picture.
Step 2: Try It Yourself
The third bar is the answer.
2/5
1/5
3/5
2 fifths plus 1 fifth is 3 fifths, which is written 3/5.
The denominator names what is being counted. It does not change.
Step 3: Watch an Example
One step at a time.
Watch Leo Add 3/8 and 2/8
Leo adds two fractions in eighths.
- Step 1
He reads them out loud: three eighths plus two eighths.
Step 4: Your Turn
Practice makes it stick.
The Pizza
Problem 1 of 2
Ana eats 2/8 of a pizza and Leo eats 3/8. How much is eaten, in eighths?
eighths
The Juice
Problem 2 of 2
A jug is 6/10 full. Ana drinks 2/10. How many tenths are left?
tenths
Count the Units
1 of 4
2/6 + 3/6. What is the top number of the answer?
2 of 4
2/6 + 3/6. What is the bottom number of the answer?
3 of 4
7/9 − 4/9. What is the top number of the answer?
4 of 4
Does the bottom number change when you add like fractions?
Step 5: Quick Check
Show what you know.
Question 1 of 2
3/10 + 4/10. What is the top number of the answer?
Question 2 of 2
Why does the bottom number stay the same?
What You Learned
- Add fractions with the same unit by counting the units.
- The bottom number names the unit, so it stays.
- Subtraction works the same way.