# Lesson 7

Using Diagrams to Represent Multiplication

Let’s use area diagrams to find products.

### 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.

- \(3 \boldcdot (0.6)\)
- \((0.4) \boldcdot 2\)
- \((0.4) \boldcdot (0.6)\)
- \(3 \boldcdot 2\)

### Problem 2

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

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

### 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.

### Problem 4

Find each product. Show your reasoning.

- \((2.5) \boldcdot (1.4)\)
- \((0.64) \boldcdot (0.81)\)

### Problem 5

Complete the calculations so that each shows the correct sum.

### Problem 6

Diego bought 12 mini muffins for $4.20.

- At this rate, how much would Diego pay for 4 mini muffins?
- 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 |