2. Three Ways
There are three ways to write
multiplication.
3 x 4 or 3(4) or
With variables
4y ab
3i4
3. 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 #
4. 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 #
5. 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
6. 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.
7. 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How much have you withdrawn?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?
8. 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How much have you withdrawn?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
9. GUIDED PRACTICE for Examples 1, 2 and 3
Find the product.
2. –1(4)
3. 7(0)
4. –6(–11)
5. –1(–12)(–9)
10. 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.
Product of an integer and 0 is 0.
Same sign, so product is positive.
Multiply from left to right.
Multiply.
Find the product.
= –4
3. 7(0) = 0 property of zero
= 66
= 12(–9)
11. 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
12. 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)
13. 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 = 3(–8) – (–4) , –4 for b and –8 for c.
= (–24) – (–4)
Multiply.
= –20 Subtract.
2. ac + b = 3(–8) + (–4) Substitute 3 for a , –4 for b and –8 for c.
= (–24) + (–4) Multiply.
= –28 Add.
16. If there are an even number of negative
signs, the answer is __________.
positive
If there are an odd number of negative
signs, the answer is __________.
negative
17. EXAMPLE 3 Evaluating an Expression with Integers
Evaluate a2 + 3b when a = –5 and b = –11.
a2 + 3b
18. EXAMPLE 3 Evaluating an Expression with Integers
Evaluate a2 + 3b when a = –5 and b = –11.
a2 + 3b = (–5)2+ 3(–11)
= 25 + 3(–11)
Substitute –5 for a and –11 for b.
Evaluate the power.
= 25 + (–33)
= –8
Multiply.
Add.
