Multiplying and Dividing Real Numbers

Objective: To multiply and divide real numbers.

Essential Understanding

• The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations.

Essential Understanding

• The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations.

• The product of two positive numbers is positive.• The product of two negative numbers is positive.• The product of a positive and a negative is negative.

Problem 1

• Find each product.

• 12(-8) = -96• 24(0.5) = 12

9)3( 2

83

21

43

Problem 2

• Simplify each square root.

525

72

494

494

Problem 4

• Divide the following fractions.

89

23

43

32

43

Class Work

• Page 42• 8-18 even

Homework

• Page 42• 9-47 odd

The Distributive Property

• Let a, b, and c be real numbers.

• a(b+c) = ab + ac• (b+c)a = ba + ca• a(b – c) = ab – ac• (b – c )a = ba - ca

Problem 1

• 3(x + 8) = 3x + 24

• (5b – 4)(-7) = -35b + 28

Got it?

a) 5(x + 7)

b)

c)

)3(12 61 t

))(12( yy

Got it?

a) 5(x + 7) = 5x + 35

b)

c)

)3(12 61 t

))(12( yy

Got it?

a) 5(x + 7) = 5x + 35

b)

c)

tt 236)3(12 61

))(12( yy

Got it?

a) 5(x + 7) = 5x + 35

b)

c)

tt 236)3(12 61

yyyy 22))(12(

Problem 2

• What sum or difference does this represent?

5

27 x

Problem 2

• What sum or difference does this represent?

52

57

51 )27(

5

27

xx

x

Got it?

• What sum or difference does each expression represent?

3

164 x

6

311 x

8

24 x

Got it?

• What sum or difference does each expression represent?

316

34

31 )164(

3

164

xx

x

6

311 x

8

24 x

Got it?

• What sum or difference does each expression represent?

xxxx

21

611

63

611

61 )311(

6

311

8

24 x

316

34

31 )164(

3

164

xx

x

Got it?

• What sum or difference does each expression represent?

xxxx

21

611

63

611

61 )311(

6

311

xxxx

41

21

82

84

81 )24(

8

24

316

34

31 )164(

3

164

xx

x

Problem 3

• What is the simplified form of ?)32( xy

Problem 3

• What is the simplified form of ?

• Distribute the negative to both terms.

)32( xy

xy 32

Got it?

• What is the simplified form of each expression?

)31( x

)5( a

Got it?

• What is the simplified form of each expression?

31)31( xx

5)5( aa

Like Terms

• You can simplify an algebraic expression by combining the parts of the expression that are alike.

Like Terms

• You can simplify an algebraic expression by combining the parts of the expression that are alike.

• Term- A number, variable, or the product of a number and one or more variables.

Like Terms

• You can simplify an algebraic expression by combining the parts of the expression that are alike.

• Term- A number, variable, or the product of a number and one or more variables.

• Constant- A term that has no variable.

Like Terms

• You can simplify an algebraic expression by combining the parts of the expression that are alike.

• Term- A number, variable, or the product of a number and one or more variables.

• Constant- A term that has no variable.• Coefficient- A numerical factor of a term.

Like Terms

• You can simplify an algebraic expression by combining the parts of the expression that are alike.

• Term- A number, variable, or the product of a number and one or more variables.

• Constant- A term that has no variable.• Coefficient- A numerical factor of a term.• Like terms have the same variable factors.

Problem 5

• Combine like terms.

222 1028 xxx

Problem 5

• Combine like terms.

222 1028 xxx

46335 yxx

Problem 5

• Combine like terms.

222 1028 xxx

162

43635

46335

yx

yxx

yxx

Got it?

• Simplify by combining like terms.

yy 3

44 57 mnmn

zyyzzy 333 67

Got it?

• Simplify by combining like terms.

yyy 23

444 1257 mnmnmn

33333 6867 yzzyzyyzzy

Homework

• Page 50• 9-63 odd