Grade: Grade 2 Subject: Mathematics Unit: Fractions: Halves & Thirds SAT: Algebra ACT: Math

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!