Bell Work:On a scale drawing of a house, one inch represents 8 feet. How wide is the garage if it is 2 ½ inches wide on the drawing?

Answer:20 feet

LESSON 36: MULTIPLYING AND DIVIDING INTEGERS, MULTIPLYING AND DIVIDING TERMS

On this number line we illustrate the multiplication and division of integers. The arrows show that 2 times -4 is -8.

The illustration also shows that if we divide -8 into 2 parts, each part is -4.

-8/2 = -4

Likewise, the illustration shows that the number is -4s in -8 is 2.

-8/-4 = 2

From these illustrations notice these relationships:

2(-4) = -8 different signs = negative product

-8/2 = -4 different signs = negative quotient

-8/-4 = 2 same signs = positive quotient

When we multiply two negative numbers like (-3)(-2), we can think about the multiplication as the “opposite of 3 times -2”. Since 3(-2) is -6, the opposite of 3(-2) is the opposite of -6 which is positive 6.

(-3)(-2) = 6 same signs = positive product

Practice:Simplifya) (-10)(-5)b) (+10)(-5)c) -10/-5d) 10/-5

Answer:a) = 50b) = -50c) = 2d) = -2

Practice:Every month $25 is automatically deducted from Newton’s checking account to pay for Internet service. Write an expression using integers that shows the effect on Newton’s account of six months of charges.

Answer:Each month’s charge subtracts $25. we can represent the change as -25. = 6(-25)= -150$150 deducted

Since the product of two negative numbers is a positive number, squaring a negative number results in a positive number.

(-5) = (-5)(-5) = 25

2

However, cubing a negative number results in a negative number.

(-2) = (-2)(-2)(-2) = 4(-2) = -8

3

Practice:Simplifya) (-1)b) (-1)

5

6

Answer:a) = -1b) = 1

Practice:For y = x , find y if x is -2.2

Answer:y = (-2)(-2)= 4

Practice:If x = 9, then x can be which two numbers?

2

Answer:Both 3 and -3

We could have also said the square root of 9 which equals 3 and -3.

Arithmetic with Two Integers

Operation Rule

+To find the sum of addends with different signs:1. Subtract the absolute values of the

addends2. Take the sign of the addend with the

greater absolute value.To find the sum of addends with the same sign:3. Add the absolute values of the addends4. Take the sign of the addends

− Instead of subtracting a number, add its opposite

×

÷

1. Multiply of divide as indicated2. If the two numbers have the same sign,

the answer is positive. If the two numbers have different signs, the answer is negative.

Multiplying and Dividing Terms:In Lesson 31 we add and subtracted terms. In this lesson we will multiply and divide terms.

Example:Simplify

(6x y)(-2xyz)2

Answer:(6x y)(-2xyz)= (6)(-2)(x)(x)(x)(y)(y)(z)= -12x y z

2

3 2

Practice:Simplify

6x y -2xyz

2

Answer: 6x y -2xyz= 2 3 x x y -2 x y z= -3x z

2

Practice:Expand

3x(2x – 4)

Answer:3x(2x – 4)= 3x(2x) – 3x(4)= 6x – 12x 2

Practice:Expand

-3x(2x – 4)

Answer:-3x(2x – 4) = -3x(2x) – -3x(4)= -6x + 12x2

HW: Lesson 36 #1-30Due Tomorrow