# Lesson 7

Using Diagrams to Represent Multiplication

### Problem 1

Here is a rectangle that has been partitioned into four smaller rectangles.

For each expression, choose the sub-rectangle whose area, in square units, matches the expression.

1. $$3 \boldcdot (0.6)$$
2. $$(0.4) \boldcdot 2$$
3. $$(0.4) \boldcdot (0.6)$$
4. $$3 \boldcdot 2$$

### Solution

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### Problem 2

Here is an area diagram that represents $$(3.1) \boldcdot (1.4)$$.

1. Find the areas of sub-rectangles A and B.
2. What is the area of the 3.1 by 1.4 rectangle?

### Solution

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### Problem 3

Draw an area diagram to find $$(0.36) \boldcdot (0.53)$$. Label and organize your work so that it can be followed by others.

### Solution

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### Problem 4

Find each product. Show your reasoning.

1. $$(2.5) \boldcdot (1.4)$$
2. $$(0.64) \boldcdot (0.81)$$

### Solution

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### Problem 5

Complete the calculations so that each shows the correct sum.

### Solution

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(From Unit 5, Lesson 3.)

### Problem 6

Diego bought 12 mini muffins for $4.20. 1. At this rate, how much would Diego pay for 4 mini muffins? 2. How many mini muffins could Diego buy with$3.00? Explain or show your reasoning. If you get stuck, consider using the table.
number of
mini muffins
price in
dollars
12 4.20

### Solution

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(From Unit 2, Lesson 12.)