# Lesson 6

Using Diagrams to Find the Number of Groups

Let’s draw tape diagrams to think about division with fractions.

### Problem 1

We can think of $$3\div \frac14$$ as the question “How many groups of $$\frac14$$ are in 3?” Draw a tape diagram to represent this question. Then find the answer.

### Problem 2

Describe how to draw a tape diagram to represent and answer $$3 \div \frac35 = {?}$$ for a friend who was absent.

### Problem 3

How many groups of $$\frac12$$ day are in 1 week?

1. Write a multiplication equation or a division equation to represent the question.
2. Draw a tape diagram to show the relationship between the quantities and to answer the question. Use graph paper, if needed.

### Problem 4

Diego said that the answer to the question “How many groups of $$\frac56$$ are in 1?” is $$\frac 65$$ or $$1\frac15$$. Do you agree with him? Explain or show your reasoning.

### Problem 5

Select all the equations that can represent the question: “How many groups of $$\frac45$$ are in 1?”

A:

$${?} \boldcdot 1=\frac45$$

B:

$$1 \boldcdot \frac45 = {?}$$

C:

$$\frac45 \div 1 = {?}$$

D:

$${?} \boldcdot \frac45 =1$$

E:

$$1\div \frac45 = {?}$$

(From Unit 4, Lesson 5.)

### Problem 6

Calculate each percentage mentally.

1. What is 10% of 70?
2. What is 10% of 110?
3. What is 25% of 160?
4. What is 25% of 48?
5. What is 50% of 90?
6. What is 50% of 350?
7. What is 75% of 300?
8. What is 75% of 48?
(From Unit 3, Lesson 14.)