1) variables2) algebraic expression3) factors4) product

Variables and Expressions Variables and Expressions

Write mathematical expressions for verbal expressions. Write verbal expressions for mathematical expressions.

5) power6) base7) exponent8) evaluate

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Variables and Expressions Variables and Expressions

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Perimeter = a + b + c

Variables and Expressions Variables and Expressions

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Perimeter = a + b + c

In this algebraic expression, the letters a, b, and c are called ________.

Variables and Expressions Variables and Expressions

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Perimeter = a + b + c

In this algebraic expression, the letters a, b, and c are called ________.variables

Variables and Expressions Variables and Expressions

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Perimeter = a + b + c

In this algebraic expression, the letters a, b, and c are called ________.variables

In algebra, variables are symbols used to represent unspecified numbers or values.

Variables and Expressions Variables and Expressions

What algebraic expression can be used to find the perimeter of the triangle below?

a b

c

Perimeter = a + b + c

In this algebraic expression, the letters a, b, and c are called ________.variables

In algebra, variables are symbols used to represent unspecified numbers or values.

NOTE: Any letter may be used as a variable.

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 x

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

In algebraic expressions, we often use a dot or parentheses to indicate multiplication.This is so we don’t mistake the symbol X for the letter (variable) x.

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

In algebraic expressions, we often use a dot or parentheses to indicate multiplication.This is so we don’t mistake the symbol X for the letter (variable) x.

Examples:

xy yx yx yx

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

In algebraic expressions, we often use a dot or parentheses to indicate multiplication.This is so we don’t mistake the symbol X for the letter (variable) x.

Examples:

xy yx yx yx

In each expression, the quantities being multiplied are called _______,

and the result is called the _______.

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

In algebraic expressions, we often use a dot or parentheses to indicate multiplication.This is so we don’t mistake the symbol X for the letter (variable) x.

Examples:

xy yx yx yx

In each expression, the quantities being multiplied are called _______,factors

and the result is called the _______.

Variables and Expressions Variables and Expressions

An algebraic expression consists of one or more numbers and variables along withone or more arithmetic operations.

Examples:

x5 73 xq

p4 cdab 53

In algebraic expressions, we often use a dot or parentheses to indicate multiplication.This is so we don’t mistake the symbol X for the letter (variable) x.

Examples:

xy yx yx yx

In each expression, the quantities being multiplied are called _______,factors

and the result is called the _______.product

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than addition

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

addition

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

addition

subtraction

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient division

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

a) Eight more than a number n. translates to

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

a) Eight more than a number n. 8 + ntranslates to

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

a) Eight more than a number n. 8 + ntranslates to

b) Seven less the product of 4 and a number x. translates to

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

a) Eight more than a number n. 8 + ntranslates to

b) Seven less the product of 4 and a number x. 7 – 4xtranslates to

c) One third of the size of the area a. translates to

Variables and Expressions Variables and Expressions

It is often necessary to translate verbal expressions into algebraic expressions.

English word(s) Math Translation

more than

less than

product

addition

subtraction

multiplication

of multiplication

quotient divisionWrite an algebraic expression for eachverbal expression:

a) Eight more than a number n. 8 + ntranslates to

b) Seven less the product of 4 and a number x. 7 – 4xtranslates to

c) One third of the size of the area a. translates to or a3

1

3

a

Variables and Expressions Variables and Expressions

An expression like xn is called a ______, and is read, “x to the nth power.”

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

The exponent indicates the number of times the _____ is used as a ______.

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

The exponent indicates the number of times the _____ is used as a ______.base factor

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

The exponent indicates the number of times the _____ is used as a ______.base factor

exponent

base 46

power

4 4 4 4 4 4 6 factors of 4

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

The exponent indicates the number of times the _____ is used as a ______.base factor

exponent

base 46

power

4 4 4 4 4 4 6 factors of 4

NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of).

Variables and Expressions Variables and Expressions

An expression like xn is called a ______,power and is read, “x to the nth power.”

The variable x is called the ____, and n is called the ________.base exponent

The exponent indicates the number of times the _____ is used as a ______.base factor

exponent

base 46

power

4 4 4 4 4 4 6 factors of 4

NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of).

2 25 (5 )x x5 (5 ) (5 )x x x x

2 25 25x x

base is only the x base is the ( ) and everything in it.

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power 4

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power

4 to the second power or 4 squared

4

44

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power

4 to the second power or 4 squared

4 to the third power or 4 cubed

4

44

444

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power

4 to the second power or 4 squared

4 to the third power or 4 cubed

4 to the fourth power

4

44

444

4444

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power

4 to the second power or 4 squared

4 to the third power or 4 cubed

4 to the fourth power

3 times b to the fifth power

4

44

444

4444

bbbbb 3

Variables and Expressions Variables and Expressions

Symbols Words Meaning

41

42

43

44

3b5

xn

4 to the first power

4 to the second power or 4 squared

4 to the third power or 4 cubed

4 to the fourth power

3 times b to the fifth power

x to the nth power

4

44

444

4444

bbbbb 3

xxxx . . .

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 25 55 28 88 211 1111

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 = 4

25 55= 25

28 88= 64

211 1111= 121

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 = 4

23 33

25 55= 25

26 66

28 88= 64

29 99

211 1111= 121

212 1212

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 = 4

23 33= 9

25 55= 25

26 66= 36

28 88= 64

29 99 = 81

211 1111= 121

212 1212= 144

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 = 4

23 33= 9

24 44

25 55= 25

26 66= 36

27 77

28 88= 64

29 99 = 81

210 1010

211 1111= 121

212 1212= 144

213 1313

Variables and Expressions Variables and Expressions

To evaluate an expression means to ____________.find its value

Evaluate each expression:

24 = 2222

= 16

53 = 555

= 125

22 22 = 4

23 33= 9

24 44 = 16

25 55= 25

26 66= 36

27 77 = 49

28 88= 64

29 99 = 81

210 1010 = 100

211 1111= 121

212 1212= 144

213 1313= 169

Variables and Expressions Variables and Expressions

Find the perimeter of the triangle.The dimensions are in feet.

a b

c

= 8

= 17

= 15

Variables and Expressions Variables and Expressions

Find the perimeter of the triangle.The dimensions are in feet.

a b

c

Perimeter = a + b + c Write the expression.

= 8

= 17

= 15

Variables and Expressions Variables and Expressions

Find the perimeter of the triangle.The dimensions are in feet.

a b

c

Perimeter = a + b + c Write the expression.

= 8 + 15 + 17 Substitute values.

= 8

= 17

= 15

Variables and Expressions Variables and Expressions

Find the perimeter of the triangle.The dimensions are in feet.

a b

c

Perimeter = a + b + c Write the expression.

= 8 + 15 + 17 Substitute values.

= 40 Simplify.

= 8

= 17

= 15

Variables and Expressions Variables and Expressions

Find the perimeter of the triangle.The dimensions are in feet.

a b

c

Perimeter = a + b + c Write the expression.

= 8 + 15 + 17 Substitute values.

= 40 Simplify.

The triangle has a perimeter of 40 feet.

= 8

= 17

= 15

Variables and Expressions Variables and Expressions

Exponents often are used in the formula for area and volume. In fact, the wordsquared comes from the formula for the area of a square.

s

s

Area of a square: A = s2

The word cubed comes from the formula for the volume of a cube.

ss

s

Volume of Cube: V = s3

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

16444 1643

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

16444 1643 1646

08

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

Each dimension of the cubical storage space inside a fireproofsafe is 12 inches. What is the volume of the storage space?

12 in

12 in

12 in

16444 1643 1646

08

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

Each dimension of the cubical storage space inside a fireproofsafe is 12 inches. What is the volume of the storage space?

12 in

12 in

12 in

16444 1643 1646

08

312 inV

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

Each dimension of the cubical storage space inside a fireproofsafe is 12 inches. What is the volume of the storage space?

12 in

12 in

12 in

16444 1643 1646

08

312 inV

ininin 121212

Variables and Expressions Variables and Expressions

Evaluate the expression for the given values of the variables.

c3 + d when c = 4 and d = 16

Each dimension of the cubical storage space inside a fireproofsafe is 12 inches. What is the volume of the storage space?

12 in

12 in

12 in

16444 1643 1646

08

312 inV

ininin 121212 3in 1728

Variables and Expressions Variables and Expressions