7th Grade Math

The product of two positive integers is positive. You can use a pattern

to find the sign of the product of two negative integers.

positive × negative = negative +^3

+ 3

+ 3

negative × negative = positive +^3

(2)(-3)^ = - 6

(1)(-3)^ = - 3

(0)(-3)^ = 0

(-1)(-3)^ = 3

(- 2 )(- 3 )^ = 6

Each product is 3 more than the previous product. This pattern can

also be shown on a number line.

• 6 - 5 - 4 - 3 - 2 - 1 0 1 253 4 6

+ 3 + 3 + 3 + 3

2 (- 3 ) 1 (- 3 ) 0 (- 3 ) - 1 (- 3 ) - 2 (- 3 )

Multiply Integers with the Same Sign

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

Examples 2(6) = 12 - 10(-6) = 60

Multiply Integers with the Same Sign

Find -11(-9).

• 11(-9) = 99 The integers have the same sign. The product is positive.

Find (-4)^2.

(-4)^2 = (-4)(-4) There are two factors of -4.

= 16 The product is positive.

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

• 3(-4)(-2) = -3(-4) Associative Property
  = 12 (-2) - 3 (- 4 ) = 12
  = - 24 12 (- 2 ) = - 24

c. -12(-4) d. (-5)^2 e. -7(-5)(-3)

Exponents

When expressing a

number using exponents,

the base is the factor and

the exponent tells how

many times to use the

base as a factor.

a^3 = a · a · a

Multiplying by Zero Multiplying by Zero

The Multiplicative Property

of Zero states that when

any number is multiplied by

zero, the product is zero.

Lesson 3C Multiply and Divide Integers 105

102_113_C2L3_895130.indd 105 12/29/09 12:50 PM