PRE-ALGEBRA

PRE-ALGEBRA

Lesson 1-9 Warm-Up

PRE-ALGEBRA

What is the “Identity Property of Multiplication”?

What is the “Zero Property of Multiplication”?

What is the Multiplication Property of -1?

Identity Property of Multiplication: A number times 1 is equal to the original number [In other words, the number keeps its identity (doesn’t change) when it is multiplied by one.]

Examples: 1 x (-5) = -5 n x 1 = n

Zero Property of Multiplication: A number times zero is equal to zero.

Examples: 0 x (-17) = 0 n x 0 = 0

Multiplication Property of -1: A number times -1 is equal to the opposite of the original number [In other words, the original number becomes negative if it was positive or positive if it was negative.]

Examples: -1 x (-5) = 5 n x -1 = -n

Multiplying and Dividing Integers (1-9)

PRE-ALGEBRA

How can you use a number line to multiply integers?

Multiplication is repeated addition, so to multiply integers, think of the first integer as the number of groups, or repeated jumps, and the second integer as the interval, or distance, of those jumps. Remember to always start the jumps at zero.

Examples: Show 4 x -3 on a number line.

4 x -3 means “four groups of -3” or “four jumps of intervals of -3”

Examples: Show -3 x -2 on a number line.

3 x -2 means “three groups of -2” or “three jumps of intervals of -2”, so

-3 x -2 means “ the opposite of three groups of -2” or “the opposite of three jumps of intervals of -2”

Multiplying and Diving Integers (1-9)

PRE-ALGEBRA

Use a number line to find 5 • (–2).

The sum of 5 groups of –2 is –10. So, 5 • (–2) = –10.

Start at 0. Make 5 groups of –2 on the number line.

Multiplying IntegersLESSON 2-4

Additional Examples

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A diver is descending from the surface of the water at

a rate of 5 ft/s. Write an expression with repeated addition to

show how far the diver is from the surface of

the water after four seconds.

4 (–5) = (–5) + (–5) + (–5) + (–5) = –20

The diver is 20 feet below the surface of the water.

Use a number line to show repeated addition.

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

PRE-ALGEBRA

How can you use a pattern to multiply integers?

To use a pattern to multiply integers, start with products you know to help you figure out those you don’t.

Examples: Use a pattern to multiply -2(5) and -2(-5)..

Multiplying and Diving Integers (1-9)

PRE-ALGEBRA

a. –2(7)

Use a pattern to find each product.

2(7) = 14 Start with products you know.

1(7) = 7

0(7) = 0

–1(7) = –7 Continue the pattern.

–2(7) = –14  

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

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b. –2(–7)

(continued)

2(–7) = –14 Start with products you know.

1(–7) = –7

0(–7) = 0

–1(–7) = 7 Continue the pattern.

–2(–7) = 14

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

PRE-ALGEBRA

Multiply 6(–2)(–3).

6(–2)(–3) = (–12)(–3) Multiply from left to right. The product of a positive integer and a negative integer is negative.

= 36 Multiply. The product of two negative integers is positive.

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

PRE-ALGEBRA

What are the rules for multiplying positive and negative numbers?

Rule: Multiplying Numbers With the Same Sign – The product of two positive or two negative numbers is positive.

Examples: 5 x 2 = 10 -5 (-2) = 10

Rule: Multiplying Numbers With Different Signs – The product of two numbers with opposite signs (a “+” number times a “–” number or a “-” number with a “+” number) is negative.

Examples: 3 x -6 = -18 -3 (6) = 18

The following patterns are true when multiplying numbers with the same or different signs.

Multiplying and Diving Integers (1-9)

PRE-ALGEBRA

What are the rules for dividing positive and negative numbers?

NOTE: You can use same rules for multiplying positives and negatives.

Rule: Dividing Numbers With the Same Sign – The quotient of two positive or two negative numbers is positive.

Examples: 6 ÷ 3 = 2 : -6 ÷ (-3) = 2

Rule: Multiplying Numbers With Different Signs – The quotient of two numbers with opposite signs (a “+” number divided by a “–” number or a “-” number divided by a “+” number) is negative.

Examples: -6 ÷ 3 = -2 : 6 ÷ -3 = -2

Multiplying and Diving Integers (1-9)

PRE-ALGEBRA

Use the table to find the average of the differences in the values of a Canadian dollar and a U.S. dollar for 2003–2005.

Write an expression for the average.

–29 + (–23) + (–17) 3

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

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(continued)

The quotient of a negative integer and a positive integer is negative.

= –23

For 2003–2005, the average difference was –23¢.

Use the order of operations. The fraction bar acts as a grouping symbol.

–693=

Multiplying and Dividing IntegersLESSON 1-9

Additional Examples

PRE-ALGEBRA

Find each product or quotient.

1. –7(–3) 2. –36 ÷ (–9)

3. –12 • 2 4. 7(–3)

5. –6 • (–2) • (–1)

–24

21 4

–21

–12

Lesson Quiz

Multiplying and Dividing IntegersLESSON 1-9