1. 2-4 Multiplying Integers
How are the signs of factors and products related?

2. Multiply Integers
Multiplication is repeated addition. So, 3(-7) means that -7 is used as an addend 3 times.
3(-7) = (-7) + (-7) + (-7)
By the Commutative Property of Multiplication, 3(-7) = -7(3)

3. Key Concept
The product of two integers with different signs is negative.

4. Please find each product.
5(-6)=
-4(16)=
8(-12)=
-9(11)=
-30
-64
-96
-99

5. The product of two positive integers is positive
The product of two positive integers is positive. We will use a pattern to show the sign of the product of two negative numbers. (-4)(2) = -8 (-4)(1) = -4 (-4)(0) = 0 (-4)(-1) = 4 (-4)(-2) = 8
One positive and one
negative factor:
Negative Product +4 +4 +4
Two negative factors:
Positive Product +4

6. Key Concept
The product of two integers with the same sign is positive.

7. Multiply Integers With the Same Sign
(-6)(-12) = (-4)(-16) =
72 64

8. Multiply More Than One Integer
-4(-5)(-8) = -7(11)(-2) =

9. Simplify Algebraic Expressions
Simplify -4(9x) (-49)x -36x Simplify -2x(3y) (-2)(x)(3)(y) (-23)(xy) -6xy
Simplify -7(6k) -42k Simplify 8a(-5b) -40ab

10. Evaluate Algebraic Expressions
Please evaluate 4ab if a = 3 and b = -5 [4(3)](-5) 12(-5) -60
Please evaluate -3xy if x = -4 and y = 9 108