## Divide Objects into Groups

## Opening

# Divide Objects into Groups

You can find 12 ÷ 4 by dividing 12 objects into 4 equal groups.

- How can you use a similar method to find $\frac{8}{9}\xf74$?
- Discuss this question with your partner.

You can find 12 ÷ 4 by dividing 12 objects into 4 equal groups.

- How can you use a similar method to find $\frac{8}{9}\xf74$?
- Discuss this question with your partner.

Devise strategies for dividing a fraction by a whole number.

Mia wants to divide $\frac{8}{9}$ by 4. She draws two different models to represent the fraction $\frac{8}{9}$.

Use one of Mia’s models of $\frac{8}{9}$, or make your own model of the fraction, to help you solve the problem.

- Divide $\frac{8}{9}$ by 4.
- Write a division equation to represent what you did.
- Use multiplication to check your answer.

Can you divide your model into 4 equal parts? What is the size of each part?

There is $\frac{3}{4}$ quart of juice left in a carton. If the 6 members of the Nelson family share the juice equally, how much (in quarts) will each person get?

- Write the division expression that you need to solve this problem.
- Make a model.
- Use your model, or use a method that does not involve a model if you prefer, to solve the problem.
- Use multiplication to check your answer.

Can you find an equivalent fraction for 3 4 that is easy to divide into 6 equal parts?

Carlos knows that division and multiplication are inverse operations. He knows, for example, that dividing by 4 is the same as multiplying by $\frac{1}{4}$. He thinks that he can use this inverse relationship to help him divide a fraction by a whole number.

To solve $\frac{8}{9}$ ÷ 4, Carlos writes the expression $\frac{8}{9}$ × $\frac{1}{4}$. He multiplies to get $\frac{8}{36}$, and then simplifies $\frac{8}{36}$ to the equivalent fraction $\frac{2}{9}$. Carlos writes this answer: $\frac{8}{9}$ ÷ 4 = $\frac{2}{9}$.

- Use Carlos’s method to solve $\frac{9}{5}$ ÷ 3.
- Use multiplication to check your answer.

- Explain how you solved each problem.
- Provide a comparison of the three problems.
- What is similar about the problems?
- What is different about the problems?

- Create a real-world problem that can be solved by finding $\frac{2}{3}\xf75$.

Take notes about your classmates’ methods for dividing a fraction by a whole number.

As your classmates present, ask questions such as:

- Where in your model do you see the total amount that you divided into equal groups?
- Where in your model do you see the number of equal groups?
- Where in your model do you see the size of each group?
- How can you use what you know about equivalent fractions to make the problem easier?
- What do you know about the relationship between multiplication and division? How can this relationship help you solve the problem?

Solve the problems using the method of your choice.

- $\frac{5}{6}\xf75$
- $\frac{3}{7}\xf76$
- $\frac{5}{8}\xf78$
- $\frac{15}{8}\xf75$

Use one of the following strategies or one of your own.

- Visualize the problem.
- Draw a model.
- Use the fact that division is the inverse of multiplication. For example, dividing by 2 is the same as multiplying by 1 2 .

Write a summary about how to divide a fraction by a whole number.

Check your summary.

- Do you describe at least one way that you can use a model to divide a fraction by a whole number?
- Do you explain how to use the inverse relationship between multiplication and division to divide a fraction by a whole number?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**One thing that still confuses me about dividing a fraction by a whole number is …**