Lesson 16

Methods for Multiplying Decimals

Let’s look at some ways we can represent multiplication of decimals.

Problem 1

Write three numerical expressions that are equivalent to \((0.0004) \boldcdot (0.005)\).

Problem 2

Find each product. Show your reasoning.

  1. \((1.2) \boldcdot (0.11)\)
  2. \((0.34) \boldcdot (0.02)\)
  3. \(120 \boldcdot (0.002)\)

Problem 3

You can use a rectangle to represent \((0.3) \boldcdot (0.5)\).

  1. What must the side length of each square represent for the rectangle to correctly represent \((0.3) \boldcdot (0.5)\)?
  2. What area is represented by each square?
  3. What is \((0.3) \boldcdot (0.5)\)? Show your reasoning.
A rectangle area model. The rectangle is partitioned into 15 identical squares. There are 5 rows of 3 squares in each row.

Problem 4

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. \(3 \boldcdot 2\)
(From Unit 3, Lesson 17.)

Problem 5

Find the value of \(\frac{49}{50}\div\frac{7}{6}\) using any method.

(From Unit 3, Lesson 7.)

Problem 6

Calculate each difference. Show your reasoning.

  1. \(13.2 - 1.78\)
  1. \(23.11 - 0.376\)
  1. \(0.9 - 0.245\)
(From Unit 3, Lesson 15.)