Word Problems with Halves and Thirds
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Word problems help us use fractions in real life! Let's learn how to solve problems about halves and thirds.
Steps to Solve Fraction Word Problems:
- Read carefully. What is the problem about?
- Find the fraction words. Look for "half," "halves," "third," or "thirds."
- Draw a picture. Sketch the whole thing and divide it into parts.
- Answer the question. What does the problem ask?
Key Words to Look For:
- "Split in half" or "cut in half" = 2 equal parts
- "Divide into thirds" or "cut into thirds" = 3 equal parts
- "Share equally" = make equal parts
- "One half" = 1 out of 2 equal parts (1/2)
- "One third" = 1 out of 3 equal parts (1/3)
Examples
Example 1: Sharing a Sandwich
Emma and her brother want to share a sandwich equally. What fraction does each person get?
Think:
- There are 2 people sharing.
- They want to share equally.
- Cut the sandwich into 2 equal parts.
Answer: Each person gets 1/2 (one half) of the sandwich.
Example 2: Sharing a Pizza
Three friends share a small pizza equally. What fraction does each friend get?
Think:
- There are 3 friends sharing.
- They want to share equally.
- Cut the pizza into 3 equal parts.
Answer: Each friend gets 1/3 (one third) of the pizza.
Example 3: Coloring a Shape
A rectangle is split into 2 equal parts. Jake colors 1 part blue. What fraction is blue?
Think:
- The rectangle has 2 equal parts (halves).
- Jake colored 1 of the 2 parts.
Answer: 1/2 (one half) of the rectangle is blue.
Example 4: Eating a Brownie
Mom cut a brownie into 3 equal pieces. Sam ate 2 pieces. What fraction did Sam eat?
Think:
- The brownie has 3 equal parts (thirds).
- Sam ate 2 of the 3 parts.
Answer: Sam ate 2/3 (two thirds) of the brownie.
Practice
Solve these word problems about halves and thirds. Draw a picture to help!
Problem 1
Lily has a granola bar. She breaks it in half to share with her friend. What fraction does each girl get?
Show Answer
Each girl gets 1/2 (one half) of the granola bar.
Problem 2
Dad made a cake and cut it into 3 equal pieces for his 3 children. What fraction of the cake does each child get?
Show Answer
Each child gets 1/3 (one third) of the cake.
Problem 3
A flag is divided into 3 equal stripes. Two stripes are red and one stripe is white. What fraction of the flag is red?
Show Answer
2/3 (two thirds) of the flag is red.
Problem 4
Tom reads half of his book on Monday. What fraction of the book is left to read?
Show Answer
1/2 (one half) of the book is left. The whole book has 2 halves. If Tom read 1 half, there is 1 half left.
Problem 5
Maria's garden has 3 equal sections. She plants flowers in 1 section and vegetables in 2 sections. What fraction has vegetables?
Show Answer
2/3 (two thirds) of the garden has vegetables.
Problem 6
Ben and his sister share an apple equally. Ben eats his piece. What fraction of the apple is gone?
Show Answer
1/2 (one half) of the apple is gone.
Problem 7
A chocolate bar has 3 equal pieces. Amy eats 1 piece and saves the rest. What fraction did Amy save?
Show Answer
Amy saved 2/3 (two thirds) of the chocolate bar. She ate 1 of 3 pieces, so 2 pieces (two thirds) are left.
Problem 8
Two students need to share one piece of paper equally for an art project. How should they fold the paper, and what fraction will each student have?
Show Answer
They should fold the paper in half. Each student will have 1/2 (one half) of the paper.
Problem 9
Grandma baked a pie and cut it into 3 equal slices. The family ate all 3 slices. Write how many thirds they ate as a fraction.
Show Answer
They ate 3/3 = 1 whole pie. Three thirds equals one whole!
Problem 10
A rope is cut into 2 equal pieces. Each piece is then cut into 3 equal parts. How many total pieces are there?
Show Answer
There are 6 total pieces. First cut: 2 pieces. Then each piece is cut into 3 parts: 2 x 3 = 6 pieces.
Problem 11
Carlos and his 2 friends want to share a watermelon equally. What fraction should each person get?
Show Answer
Each person gets 1/3 (one third). There are 3 people total (Carlos + 2 friends = 3), so cut into 3 equal parts.
Problem 12
Sofia colored half of a circle red. Her friend colored the other half blue. What fraction of the circle is now colored?
Show Answer
The whole circle is colored. 1/2 + 1/2 = 2/2 = 1 whole.
Check Your Understanding
Make sure you can answer these questions:
1. If 2 people share something equally, what fraction does each person get?
Show Answer
Each person gets 1/2 (one half).
2. If 3 people share something equally, what fraction does each person get?
Show Answer
Each person gets 1/3 (one third).
3. What is the first step when solving a fraction word problem?
Show Answer
Read the problem carefully and understand what it is asking.
Next Steps
- Write your own word problems using halves and thirds
- Look for fractions in everyday life (sharing food, dividing things)
- Continue to the Common Mistakes lesson to avoid errors