Before the bell rings... Have your covered textbook with you.

1. 3/8 ÷ 2/3 =

2. 182 – 97 + 1306 – 110 =

Before the bell rings... Have your covered textbook with you.

1. 3/8 ÷ 2/3 =

2. 182 – 97 + 1306 – 110 =

9/16

1281

Multiplication of Integer Numbers

Section 2.4

P. 73 - 76

Multiplication When you first learned multiplication, your book

had pictures of equal number of objects in several rows.

You learned that 3 4 meant “three fours.” 3 4 = 4 + 4+ 4 Thus a Pos x Pos = Pos #

Negative Numbers

3 (-4) means “three negative fours” 3 (-4) = (-4)+(-4)+(-4) = -12 Using the addition rules you get -12

Thus a Pos x Neg = Neg #

Three Ways

There are three ways to write multiplication.

3 x 4 or 3(4) or

With variables

4y ab

3 4

Commutative

Remember: multiplication is COMMUTATIVE. (order does not matter)

3 4 = 4 3 and 3 (-4)= - 4 3

The same is true with pos. and neg. #’s

Multiplication Properties

Property of ZeroThe product of a number and zero = 0 -4 x 0 = 0 a (0) = 0

Identity Property of MultiplicationThe product of a number and the

multiplicative identity (1) is the number.(5) (1) = 5 (-27) (1) = -27

Multiplication Rules:

a POSITIVE times a POSITIVE is POSITIVE

a NEGATIVE times a NEGATIVE is POSITIVE

a POSITIVE times a NEGATIVE is NEGATIVE

a NEGATIVE times a POSITIVE is NEGATIVE

Practice: Perform the indicated operation.

4 6=4(-6)=-6 x 4=-6 x -4=

243 1=243 (-1)=-1 x 243=-1 x -243=

Practice: Perform the indicated operation.

4 6=4(-6)=-6 x 4=-6 x -4=

24

-24

-24

24

243243 1=243 (-1)=-1 x 243=-1 x -243=

-243

-243

243

GUIDED PRACTICE for Examples 1, 2 and 3

2. –1(4)

4. –6(–11)

5. –1(–12)(–9)= –108

Different signs, so product is negative.

Same sign, so product is positive.

Product of an integer and 0 is 0.

Multiply from left to right.

Multiply.

Find the product.

= –4 identity

3. 7(0) = 0 property of zero

= 66

= 12(–9)

If there are an even number of negative signs, the answer is __________.

If there are an odd number of negative signs, the answer is __________.

If there are an even number of negative signs, the answer is __________.

If there are an odd number of negative signs, the answer is __________.

positive

negative

EXAMPLE 2

a. –1(6)

b. –8(–2)

c. –15(0)

d. 4(–10)(–12)= 480

Different signs, so product is negative.

Same sign, so product is positive.

Product of an integer and 0 is 0.

Multiply from left to right.

Multiply.

Multiplying Two or More Integers

= –6 identity

= 16

= 0 property of zero

= –40(–12)

Evaluate the expressionEvaluate the expression

( 3)( 6) 2

4 12 2

( 3)( 6) 2

4 12 2

=

=

Evaluate the expressionEvaluate the expression

( 3)( 6) 2

4 12 2

( 3)( 6) 2

4 12 2

= 36

= 96

EXAMPLE 1 Multiplying Integers

Diving

A diver is swimming downward to explore a coral reef. The diver’s depth is changing by –2 feet per second. The diver started at sea level. What is the diver’s position relative to sea level after 10 seconds? after 30 seconds?

a. To find the diver’s position relative to sea level after 10 seconds, use the distance formula d = rt.

d = rt Write the distance formula.

d = –2 (10) Substitute –2 for r and 10 for t.

d = –20 Different signs, so product is negative.

SOLUTION

EXAMPLE 1 Multiplying Integers

d = rt Write the distance formula.

Substitute –2 for r and 30 for t.

Different signs, so product is negative.

The diver’s position relative to sea level is –20 feet.

ANSWER

b. Find the diver’s position relative to sea level after30 seconds.

d (30)–2 =

d = – 60

EXAMPLE 1 Multiplying Integers

d = rt Write the distance formula.

Substitute –2 for r and 30 for t.

Different signs, so product is negative.

The diver’s position relative to sea level is –20 feet.

ANSWER

ANSWER

The diver’s position relative to sea level is –60 feet.

b. Find the diver’s position relative to sea level after30 seconds.

d (30)–2 =

d = – 60

Another way to think about multiplication

The product of two integers with the same sign is POSITIVE.

The product of two integers with different signs is NEGATIVE.

Assignment: P 75 #1 - 23, 36 – 40

NO CALCULATORS!!!

Problems 3-22 there are 6 problems that will have a property listed with the answer to the multiplication problem.

Identity or property of zero