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

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)

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

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

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

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

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

Multiply More Than One Integer -4(-5)(-8) = -7(11)(-2) = -160 164

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

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