# Lesson 4

How Many Groups? (Part 1)

Let’s play with blocks and diagrams to think about division with fractions.

### Problem 1

Consider the problem: A shopper buys cat food in bags of 3 lbs. Her cat eats $$\frac34$$ lb each week. How many weeks does one bag last?

1. Draw a diagram to represent the situation and label your diagram so it can be followed by others. Answer the question.

2. Write a multiplication or division equation to represent the situation.

3. Multiply your answer in the first question (the number of weeks) by $$\frac34$$. Did you get 3 as a result? If not, revise your previous work.

### Problem 2

Use the diagram to answer the question: How many $$\frac13$$s are in $$1\frac23$$? The hexagon represents 1 whole. Explain or show your reasoning.

### Problem 3

Which question can be represented by the equation $${?}\boldcdot \frac18=3$$?

A:

How many 3s are in $$\frac18$$?

B:

What is 3 groups of $$\frac18$$?

C:

How many $$\frac 18$$s are in 3?

D:

What is $$\frac 18$$ of 3?

### Problem 4

Write two division equations for each multiplication equation.

1. $$15\boldcdot \frac25 = 6$$
2. $$6 \boldcdot \frac43 = 8$$
3. $$16\boldcdot \frac78 = 14$$

### Problem 5

Noah and his friends are going to an amusement park. The total cost of admission for 8 students is $100, and all students share the cost equally. Noah brought$13 for his ticket. Did he bring enough money to get into the park? Explain your reasoning.

(From Unit 4, Lesson 2.)

### Problem 6

Write a division expression with a quotient that is:

1. greater than $$8 \div 0.001$$
2. less than $$8 \div 0.001$$
3. between $$8 \div 0.001$$ and $$8 \div \frac{1}{10}$$
(From Unit 4, Lesson 1.)

### Problem 7

Find each unknown number.

1. 12 is 150% of what number?
2. 5 is 50% of what number?
3. 10% of what number is 300?
4. 5% of what number is 72?
5. 20 is 80% of what number?
(From Unit 3, Lesson 14.)