Download C3 2.4 Notes

LESSON 2.4 Multiplying Integers
Goal: Multiply integers
Warm-up: Evaluating The Product of Two Integers
In this activity, you will use patterns to evaluate the sign of the product of two integers.
1. Use the pattern of the products to complete the table.
Expression
Product
33
9
32
6
31
3
30
_____
3  (l)
_____
3 • (2)
_____
What can you say about the product of a positive integer and a negative integer?
2. Use your conclusion in number 1 to complete the first three rows of the table. Look for a
pattern in the products. Use the pattern to complete the table.
Expression
Product
3  (2)
_____
2  (2)
_____
1  (2)
_____
0  (2)
_____
1  (2)
_____
2  (2)
_____
What can you say about the product of a negative integer and a negative integer?
Multiplying Integers
Words
The product of two integers
with the same sign is _______________.
Numbers
3  5=
–4  (–6) =
The product of two integers
with different signs is __________ .
3  (–5) =
–4  6 =
1
EXAMPLE 1 - Multiplying Integers
You drop a rock into the ocean. The rock's depth is changing by –3 feet per second. If you dropped
the rock at sea level, what is the position of the rock after 30 seconds?
To find the position of the rock relative to sea level after 30 seconds, use the distance formula d = rt.
d = rt
Now You Try It! Use the information above.
Find the position of the rock relative to sea level after 45 seconds.
EXAMPLE 2 - Multiplication Properties
1. Multiplication Property of Zero
Words: The product of a number and 0 is ________ .
Numbers: –2  0= _____
Algebra: For any value of a, a  0 = _____
2. Identity Property of Multiplication
Words The product of a number and _____ is the same integer.
Numbers 7(
)=7
Algebra For any value of a, a (1) = a.
3. Inverse Property of Multiplication:
Words The product of a number and it’s _____________________ equals ________.
Numbers 7(
)=1
Algebra For any value of a, a (
1
) = a.
a
EXAMPLE 3 - Multiplying More than Two Integers
a. –1(10)(-25)=
b. –9(–4)(2)(3) =
c. –12(0)(-1) =
d. -5(-5)(-5)=
Remember that when
you multiply a
number by – 1, the
product is the
opposite of the
original number.
2
When you multiply more than two positive or negative integers:
If there is an ____________ number of negative signs, the product is ________________.
If there is an ____________ number of negative signs, the product is ________________.
EXAMPLE 4 - Evaluating an Expression with Integers
Evaluate –4b – a 2 when a = –8 and b = –12.
Now You Try It! Find the Product.
1. –1(5)
2. 8(0)
3. –7(–12)
4. –2(–10)(–9)
Evaluate the expression when a = 4, b = –5, and c = –6.
5. ac – b
6. ac + b
7. a 2 + bc
8. ab – c
2
3