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.

Rectangle divided into 4 smaller rectangles labeled A, B, C, D. Length across top is 3.4 and width is 2.6.

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. \(3 \boldcdot 2\)

Problem 2

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

Large rectangle divided into rectangles A and B. Length across top of rectangle A is 3 point 1. Width of rectangle A is 1. Width of rectangle B is 0 point 4.
  1. Find the areas of sub-rectangles A and B.
  2. 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.

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

Problem 5

Complete the calculations so that each shows the correct sum.

Four calculations with missing digits. 
(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
(From Unit 2, Lesson 12.)