Thirds
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You learned about halves - now let us learn about thirds! When we cut something into 3 equal parts, each part is called a third.
What Is a Third?
A third is one of three equal parts. When you divide something into 3 equal pieces, each piece is one third.
We write one third as: 1/3
Understanding 1/3
In the fraction 1/3:
- The bottom number (3) tells how many equal parts the whole is divided into
- The top number (1) tells how many parts we are talking about
So 1/3 means "1 out of 3 equal parts"
Thirds Look Like This
A rectangle divided into thirds:
[-----|-----|-----] Three equal parts
Each section is 1/3 of the whole rectangle.
Three Thirds Make a Whole
If you have all three thirds, you have the whole thing!
1/3 + 1/3 + 1/3 = 3/3 = 1 whole
Comparing Halves and Thirds
Which is bigger: 1/2 or 1/3?
- 1/2 means the whole is cut into 2 parts - each part is bigger
- 1/3 means the whole is cut into 3 parts - each part is smaller
1/2 is bigger than 1/3! The more parts you cut, the smaller each part becomes.
Worked Examples
Example 1: Sharing Among Three Friends
Problem: Three friends share a pizza equally. What fraction does each friend get?
Step 1: The pizza is divided among 3 friends
Step 2: Each friend gets 1 of the 3 equal parts
Answer: Each friend gets 1/3 (one third) of the pizza
Example 2: Identifying Thirds
Problem: Is this shape divided into thirds?
[-----|-----|-----]
Step 1: Count the parts: 3 parts
Step 2: Check if they are equal: Yes, all three parts are the same size
Answer: Yes! This shows thirds because there are 3 equal parts.
Example 3: Two Thirds
Problem: A rectangle is divided into 3 equal parts. If you color 2 parts, what fraction did you color?
Step 1: The rectangle has 3 equal parts (bottom number = 3)
Step 2: You colored 2 parts (top number = 2)
Answer: You colored 2/3 (two thirds) of the rectangle
Example 4: One Third of a Group
Problem: There are 9 crayons. What is one third of the crayons?
Step 1: To find one third, divide into 3 equal groups
Step 2: 9 divided into 3 groups = 3 in each group
Answer: One third of 9 crayons is 3 crayons
Example 5: Comparing Fractions
Problem: Which is more: 1/2 of a cookie or 1/3 of the same cookie?
Step 1: 1/2 means cutting into 2 parts
Step 2: 1/3 means cutting into 3 parts
Step 3: When you cut into MORE parts, each part is SMALLER
Answer: 1/2 is more than 1/3
Practice Problems
Try these problems on your own. Click "Show Answer" to check your work!
Problem 1: How many equal parts make thirds?
Show Answer
3 equal parts
Problem 2: A pie is cut into 3 equal slices. You eat one slice. What fraction did you eat?
Show Answer
1/3 (one third)
Problem 3: What is one third of 12?
Show Answer
4 (12 divided into 3 equal groups = 4 each)
Problem 4: How many thirds make one whole?
Show Answer
3 thirds (1/3 + 1/3 + 1/3 = 3/3 = 1 whole)
Problem 5: What is one third of 6?
Show Answer
2
Problem 6: Which is bigger: 1/2 or 1/3?
Show Answer
1/2 is bigger because dividing into 2 parts gives bigger pieces than dividing into 3 parts.
Problem 7: In the fraction 2/3, what does the 3 mean?
Show Answer
The 3 means the whole is divided into 3 equal parts.
Problem 8: A ribbon is cut into 3 equal pieces. Two pieces are blue. What fraction is blue?
Show Answer
2/3 (two thirds)
Problem 9: What is one third of 15?
Show Answer
5
Problem 10: Three brothers share 12 toy cars equally. How many cars does each brother get?
Show Answer
4 cars (12 divided by 3 = 4)
Check Your Understanding
Question 1: How are thirds different from halves?
Show Answer
Halves divide something into 2 equal parts. Thirds divide something into 3 equal parts. Each third is smaller than each half.
Question 2: What fraction is shown if 2 out of 3 parts are colored?
Show Answer
2/3 (two thirds) - The top number shows colored parts, bottom number shows total parts.
Question 3: Why is 1/3 smaller than 1/2?
Show Answer
When you divide something into more parts, each part becomes smaller. Cutting into 3 parts gives smaller pieces than cutting into 2 parts.
Question 4: What is 1/3 of 9 stickers?
Show Answer
3 stickers (9 divided into 3 equal groups = 3 each)
Next Steps
- Practice: Find things at home that can be divided into thirds
- Compare: Draw halves and thirds side by side to see the difference in size
- Challenge: Can you find 1/3 of different numbers?
- Real Life: Share snacks equally among 3 people!