Multiplication of Integer Numbers

I can multiply positive and negative numbers.

Three Ways

There are three ways to write multiplication.

3 x 4 or 3(4) or

With variables

4y ab

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 #

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

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.

You have $400 in a checking account. Over the next several weeks, you make 6 withdrawals of $40 each.

How much have you withdrawn?

How much is left in the account?

You have $400 in a checking account. Over the next several weeks, you make 6 withdrawals of $40 each.

How much have you withdrawn?

How much is left in the account?

$240

$160

GUIDED PRACTICE for Examples 1, 2 and 3

2. –1(4)

4. –6(–11)

5. –1(–12)(–9)

Find the product.

3. 7(0)

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

3. 7(0) = 0 property of zero

= 66

= 12(–9)

Order of Operations

A set of rules to simplify a numerical expression.

1.Evaluate expressions inside grouping symbols (brackets and parenthesis)

2.Multiply and divide from left to right

3.Add and subtract from left to right

GUIDED PRACTICE for Examples 1, 2 and 3

Evaluate the expression when a = 3, b = –4, and c = –8 .

1. ac – b = 3(–8) – (–4)

2. ac + b = 3(–8) + (–4)

GUIDED PRACTICE for Examples 1, 2 and 3

Evaluate the expression when a = 3, b = –4, and c = –8 .

1. ac – b Substitute 3 for a , –4 for b and –8 for c.= 3(–8) – (–4)

= (–24) – (–4)

= –20 Subtract.

Multiply.

2. ac + b Substitute 3 for a , –4 for b and –8 for c.= 3(–8) + (–4)

= (–24) + (–4) Multiply.

= –28 Add.

9922 = =

(-9)(-9)22 = =

-9-922 = =

9922 = = 9 x 9 = 9 x 9 = 8181

(-9)(-9)22 = = -9 x- 9 = -9 x- 9 = 8181

-9-922 = = -81-81

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 3 Evaluating an Expression with Integers

Evaluate a2 + 3b when a = –5 and b = –11.

+ 3b a2

EXAMPLE 3 Evaluating an Expression with Integers

Evaluate a2 + 3b when a = –5 and b = –11.

+ 3b a2 + 3(–11)= (–5)2

= 25 + 3(–11)

Substitute –5 for a and –11 for b.

Evaluate the power.

= 25 + (–33)

= –8

Multiply.

Add.

Assignment: