Lesson 5Slide 1

Multiplication by a Whole NumberWO.6 Understand multiplication as repeated addition.

Represent multiplication of whole numbers on the number line.

PR.1 Understand and identify the associative property of addition.

PR.2 Understand and identify the commutative property of addition.

PR.6 Understand and identify the additive property of 0.

Chapter 1

Lesson 5

PR.7 Understand and identify the special properties of 0 and 1 in multiplication and division.

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Lesson 5Slide 2

Objectives

• Define multiplication by whole numbers as repeated addition.

• Apply the commutative property of addition, the additive property of zero, the multiplicative property of one, and the multiplicative property of zero to simplifying expressions and solving equations.

• Interpret and evaluate expressions that use parentheses.

Lesson 5Slide 3

Remember from Before

• What is repeated addition?

• What is a multiple?

Lesson 5Slide 4

Get Your Brain in Gear

Quickly find the solution to each equation.

a. 12 = a + a + a

b. 18 = b + b

c. 6 + c = 14

d. 20 = d + d + d + d

a = 4

b = 9

c = 8

d = 5

Lesson 5Slide 5

What is the value of point d ?

In symbols, this translates to:

2 2 2 2 2 d

Lesson 5Slide 6

Because 2 is defined as 1 + 1, we can re-express d as a repeated addition of 1 + 1:

as

2 2 2 2 2 d

1 1 1 1 1 1 1 1 1 1 d

d = 10

Lesson 5Slide 7

Now that we know the exact location of d we can illustrate it on the number line like this:

Lesson 5Slide 8

Check for Understanding1. What are the values of the variables v and m

in the following equations?

m = 6v = 8

Lesson 5Slide 9

When n = 7, the expression represents:

2 2 2 2 2 2 2

Instead of writing “2” seven times, we can rewrite it using multiplication.

7 2

Lesson 5Slide 10

What expression does the diagram represent when n = 3?

2 2 2

How do we rewrite it using the multiplication symbol?

3 2

Lesson 5Slide 11

Check for Understanding2. Rewrite the following expressions using the

multiplication symbol:

3 × c p × s

4 × h 8 × 5

Lesson 5Slide 12

This means that we repeat the jump +k only once.This means that 1 k k

Lesson 5Slide 13

Multiplicative Property of One

1 k k

This identity is called the Multiplicative Property of One.

Lesson 5Slide 14

Additive Property of Zero

This is called the Additive Property of

Zero.

0k k

Lesson 5Slide 15

What is the value of this expression?

This means we don’t make any +k jumps and we stay at 0.

Lesson 5Slide 16

Multiplicative Property of Zero

This is known as the Multiplicative Property of Zero.

0 0k

Lesson 5Slide 17

Check for Understanding3. What are the values of j, m, n and p in the

following equations? Explain your reasoning.

a. 5 5j b. 7 0m

c. 4 4n d. 1 3p

j = 0 Additive property of zero m = 0 Multiplicative property of zero

n = 1 Multiplicative property of one

p = 3 Multiplicative property of one

Lesson 5Slide 18

Sometimes we will see repeated addition of an expression. Here is b + m added repeatedly 4 times.

b m b m b m b m

Lesson 5Slide 19

With symbols, we indicate a group by using parentheses, like this:

( )b m b m b m b m

4 ( )b m

Lesson 5Slide 20

Check for Understanding4.Use parentheses to write the following

expressions:

z × (1+ a)

v + (h + 1) + h

5 × (k + d)

t + (w + s)

Lesson 5Slide 21

Check for Understanding5. Use parentheses and multiplication to rewrite the

following addition expressions:

a. r + t + w + r + t + w + r + t + w

b. z + 6 + z + 6 + z + 6 + z + 6

c. a + y + a + y

d. p + 3 + p + 3 + p + 3 + p + 3

3 × (r + t + w)

4 × (z + 6)

2 × (a + y)

3 × (p + 3)

Lesson 5Slide 22

Associative Property of Addition

a b c a b c

This identity is called the Associative Property of Addition.

Lesson 5Slide 23

Check for Understanding6. Use symbols to write the following identities:

(r + s) + t = r + (s + t) (c + d + e) = c + (d + e)

a + b + k = a + (b + k) (w + 2) + 3 + 2 = w + 2 + (3 + 2)

Lesson 5Slide 24

v z z z v z v v

We can use the Commutative Property of Addition to reorder the expression so it is a repeated addition of .

v z v z v z v z

v z

4 ( )v z

Lesson 5Slide 25

Check for Understanding7. Simplify the following expressions using

multiplication:

3 × (d + e + f)

2 × (p + 8)

5 × (a + b)

4 × (7 + g)

3 × h + 3 × y or 3 × (h + y)

Lesson 5Slide 26

Multiple Choice Practice1. What property is represented by the following identity?

b = b × 1

2. True or false: The value of n × 5 is always greater than the value 5.

Lesson 5Slide 27

Find the Errors

Correct.

Correct.

This should be m = 0.

This should be 4 × (8 + k).