Chapter 2 Section 5

Multiplying Integers

Multiplying Two Integers with Different Signs

• Words: The product of two integers with different signs.

• Numbers: 3(-2) = -6, -2(3) = -6

Example 1

Find each product.6(-8)6(-8) = 6 -8 =∙ -48

The factors have different signs, so the

answer will be negative.

Example 2

Find each product.-5(9)-5(9) = -5 9 =∙ -45

The factors have different signs, so the

answer will be negative.

Your Turn

Find each product.10(-3)

Your Turn

Find each product.-7(7)

Your Turn

Find each product.15(-3)

Multiplying Two Integers with the Same Signs

• Words: The product of two integers with the same signs is positive.

• Numbers: 3(2) = 6, -2(-3) = 6

Example 3

Find each product.15(2)15(2)= 15 2 =∙ 30

The factors have the same signs, so the

answer will be positive.

Example 4

Find each product.-5(-6)-5(-6) = -5 -6 =∙ 30

The factors have the same signs, so the

answer will be positive.

Your Turn

Find each product.11(9)

Your Turn

Find each product.-6(-7)

Your Turn

Find each product.-10(-8)

To find the product of three or more numbers, multiply the first two numbers. Then multiply the results by the next number, until you come to the end.

Example 5

Find each product. 8(-10)(-4) 8(-10) = -80 -80(-4)= 320

Example 5

Find each product. 5(-3)(-2)(-2)5(-3) = -15-15(-2)= 3030(-2)= -60

Your Turn

Find each product.-2(-3)(4)

Your Turn

Find each product.6(-2)(3)

Your Turn

Find each product.(-1)(-5)(-2)(-3)

You can use the rules for multiplying integers to evaluate algebraic expressions and to

simplify expressions.

Example 7

Evaluate 2xy of x = -4 and y = -2.2xy = 2(-4)(-2) or 2 -4 -2∙ ∙ = -8(-2)

= 16

Example 8

Simplify (2a)(-5b).(2a) (-5b) = (2)(a)(-5)(b) = 2 -5 (a)(b)∙ = -10ab

Your Turn

Evaluate -5n if n = -7.

Your Turn

Simplify 12(-3z)