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This pdf includes the following topics:-

Expressions

What is a variable?

Algebraic Expressions

What are coefficients?

What is a term?

What are constants?

Writing Algebraic Expressions

Expressions

What is a variable?

Algebraic Expressions

What are coefficients?

What is a term?

What are constants?

Writing Algebraic Expressions

1.
Algebraic Expressions and

Terms

Unit 1

Terms

Unit 1

2.
Expressions

You are familiar with the following type of

numerical expressions:

12 + 6

3 (12)

6 (3 + 2)

15 - 4 (6)

You are familiar with the following type of

numerical expressions:

12 + 6

3 (12)

6 (3 + 2)

15 - 4 (6)

3.
What is a variable?

In the expression 12 + B, the letter “B” is a

variable.

A variable is a letter or symbol that

represents an unknown value.

In the expression 12 + B, the letter “B” is a

variable.

A variable is a letter or symbol that

represents an unknown value.

4.
Algebraic Expressions

When variables are used with other

numbers, parentheses, or operations, they

create an algebraic expression.

a + 2

(a) (b)

3m + 6n - 6

When variables are used with other

numbers, parentheses, or operations, they

create an algebraic expression.

a + 2

(a) (b)

3m + 6n - 6

5.
What are coefficients?

A coefficient is the number multiplied by the

variable in an algebraic expression.

Algebraic Expression Coefficient

6m + 5 6

8r + 7m + 4 8, 7

14b - 8 14

A coefficient is the number multiplied by the

variable in an algebraic expression.

Algebraic Expression Coefficient

6m + 5 6

8r + 7m + 4 8, 7

14b - 8 14

6.
What is a term?

A term is the name given to a number, a

variable, or a number and a variable

combined by multiplication or division.

Algebraic Expressions Terms

a + 2 a, 2

3m + 6n - 6 3m, 6n, - 6

A term is the name given to a number, a

variable, or a number and a variable

combined by multiplication or division.

Algebraic Expressions Terms

a + 2 a, 2

3m + 6n - 6 3m, 6n, - 6

7.
What are constants?

A constant is a number that cannot

change its value.

In the expression: 5x + 7y - 2

the constant is - 2.

A constant is a number that cannot

change its value.

In the expression: 5x + 7y - 2

the constant is - 2.

8.
Figure it out!

Identify the terms, coefficients, and constants.

1. 12a - 6b + 4

2. 4x - 2y

3. c - 32

4. 3x + 2

Identify the terms, coefficients, and constants.

1. 12a - 6b + 4

2. 4x - 2y

3. c - 32

4. 3x + 2

9.
Writing Algebraic Expressions

You can translate word phrases into variable

expressions.

Examples:

1. Three more than a number =

2. The quotient of a number and 8 =

3. Six times a number =

4. 15 less than a number =

5. The quotient of 30 and a number plus 10 =

You can translate word phrases into variable

expressions.

Examples:

1. Three more than a number =

2. The quotient of a number and 8 =

3. Six times a number =

4. 15 less than a number =

5. The quotient of 30 and a number plus 10 =

10.
Key words to look for:

Addition: Subtraction:

Add Minus

Plus Difference

Sum Subtract

Total Less than

Increased by Decreased by

More than less

Addition: Subtraction:

Add Minus

Plus Difference

Sum Subtract

Total Less than

Increased by Decreased by

More than less

11.
Cont…

Multiplication Division

Product Quotient

Times divide

multiply

Multiplication Division

Product Quotient

Times divide

multiply

12.
Write algebraic expressions for

these word phrases

1. Four more than s

2. The product of 7 and c

3. Nine less than x

4. A number divided by the sum of 4 and 7.

5. Twice the sum of a number plus 4.

6. The sum of ¾ of a number and 7.

7. Ten times a number increased by 150.

these word phrases

1. Four more than s

2. The product of 7 and c

3. Nine less than x

4. A number divided by the sum of 4 and 7.

5. Twice the sum of a number plus 4.

6. The sum of ¾ of a number and 7.

7. Ten times a number increased by 150.

13.
Write an algebraic phrase for these

situations

1. A car was traveling 35 miles per hour

for a number of hours.

2. Bob ran 7 times a week for a number of

weeks.

3. The plumber added an extra $35 to her

bill.

4. Thirty-five fewer people came than the

number expected.

situations

1. A car was traveling 35 miles per hour

for a number of hours.

2. Bob ran 7 times a week for a number of

weeks.

3. The plumber added an extra $35 to her

bill.

4. Thirty-five fewer people came than the

number expected.

14.
How do you describe a

variable expression?

Variable Meaning Operation

5x, 5·x, (5)(x) 5 times x Multiplication

(same as x·5)

5÷ x 5 divided by Division

5/x x

5 + x (same as x + 5 plus x Addition

5–x 5 minus x subtraction

variable expression?

Variable Meaning Operation

5x, 5·x, (5)(x) 5 times x Multiplication

(same as x·5)

5÷ x 5 divided by Division

5/x x

5 + x (same as x + 5 plus x Addition

5–x 5 minus x subtraction

15.
Evaluate a Variable Expression

Example 1: Evaluate each expression

when n = 4. Simplify

Simplify(means

(meansto tosolve

solvethe

theproblem

problemor

orperform

perform

as many of the indicated operations as possible.)

as many of the indicated operations as possible.)

a. n + 3

Solution: n + 3 = 4 + 3Substitute 4 for n. Simplify

=7

b. n – 3

Solution: n – 3 = 4 – 3 Substitute 4 for n. Simplify

=1

Example 1: Evaluate each expression

when n = 4. Simplify

Simplify(means

(meansto tosolve

solvethe

theproblem

problemor

orperform

perform

as many of the indicated operations as possible.)

as many of the indicated operations as possible.)

a. n + 3

Solution: n + 3 = 4 + 3Substitute 4 for n. Simplify

=7

b. n – 3

Solution: n – 3 = 4 – 3 Substitute 4 for n. Simplify

=1

16.
Evaluate an Algebraic

Expression

Example 2: Evaluate each expression if x = 8.

a. 5x

Substitute 8 for x. Simplify

5x = 5(8)

Solution: Using

Usingparenthesis

parenthesisisisthe

thepreferred

preferredmethod

methodtotoshow

show

Solution: = 40 multiplication.

multiplication.Additional

Additionalways

waystotoshow

showmultiplication

multiplicationare

are

55· ·88and 5 x 8.

and 5 x 8.

b. x÷4

Substitute 8 for x.

x÷4=8÷4

Simplify

Solution:

=2 x 8

Recall

Recallthat

thatdivision

divisionproblems

problemsare

arealso

also 4 4

fractions – this problem could be

fractions – this problem could be 2;

written

writtenas:

as: because

x

x 4

4

Expression

Example 2: Evaluate each expression if x = 8.

a. 5x

Substitute 8 for x. Simplify

5x = 5(8)

Solution: Using

Usingparenthesis

parenthesisisisthe

thepreferred

preferredmethod

methodtotoshow

show

Solution: = 40 multiplication.

multiplication.Additional

Additionalways

waystotoshow

showmultiplication

multiplicationare

are

55· ·88and 5 x 8.

and 5 x 8.

b. x÷4

Substitute 8 for x.

x÷4=8÷4

Simplify

Solution:

=2 x 8

Recall

Recallthat

thatdivision

divisionproblems

problemsare

arealso

also 4 4

fractions – this problem could be

fractions – this problem could be 2;

written

writtenas:

as: because

x

x 4

4

17.
Evaluating More Expressions

Example 3: Evaluate each expression if x

= 4, y = 6, and z = 24.

a. 5xy Substitute 4 for x; 6 for y. simplify

Solution: 5xy = 5(4)(6)

= 120

b. z Substitute 24 for z; 6 for y. Simplify.

y

Solution:

z 24

y 6

=4

Example 3: Evaluate each expression if x

= 4, y = 6, and z = 24.

a. 5xy Substitute 4 for x; 6 for y. simplify

Solution: 5xy = 5(4)(6)

= 120

b. z Substitute 24 for z; 6 for y. Simplify.

y

Solution:

z 24

y 6

=4

18.
Now You Try…

Evaluate each expression given that a = 6, b =

12, and c = 3.

1. 4ac A

2. a÷c A

3. a+b+c A

4. ba A

5. b–c A

6. c÷b

A

Evaluate each expression given that a = 6, b =

12, and c = 3.

1. 4ac A

2. a÷c A

3. a+b+c A

4. ba A

5. b–c A

6. c÷b

A

19.
You Try #1

Evaluate each expression given that a = 6, b

= 12, and c = 3.

1. 4ac Substitute

Substitutethe

thevalue

valuefor

foraa==66and

andcc==33

into

intothe

theproblem

problemand

andmultiply

multiply

4ac = 4(6)(3)

= (24)(3)

= 72

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

1. 4ac Substitute

Substitutethe

thevalue

valuefor

foraa==66and

andcc==33

into

intothe

theproblem

problemand

andmultiply

multiply

4ac = 4(6)(3)

= (24)(3)

= 72

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

20.
You Try #2

Evaluate each expression given that a = 6, b

= 12, and c = 3.

2.a ÷ c Substitute

Substitutethe

thevalue

valuefor

foraa==66and

andcc==33

into

intothe

theproblem

problemand

anddivide

divide

a÷c=6÷3

=2

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

2.a ÷ c Substitute

Substitutethe

thevalue

valuefor

foraa==66and

andcc==33

into

intothe

theproblem

problemand

anddivide

divide

a÷c=6÷3

=2

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

21.
You Try #3

Evaluate each expression given that a = 6, b

= 12, and c = 3.

3. a + b + c Substitute

Substitutethe

thevalue

valuefor

foraa==6,6,b=12,

b=12,

and

and c = 3 into the problem, thenadd.

c = 3 into the problem, then add.

a + b + c = 6 + 12 + 3

= 18 + 3

= 21

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

3. a + b + c Substitute

Substitutethe

thevalue

valuefor

foraa==6,6,b=12,

b=12,

and

and c = 3 into the problem, thenadd.

c = 3 into the problem, then add.

a + b + c = 6 + 12 + 3

= 18 + 3

= 21

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

22.
You Try #4

Evaluate each expression given that a = 6, b

= 12, and c = 3.

4.ba Substitute

Substitutethe

thevalue

valuefor

forb=12

b=12and

andaa==66

into

intothe

theproblem,

problem, then

thenmultiply.

multiply.

ba = (12)(6)

= 72

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

4.ba Substitute

Substitutethe

thevalue

valuefor

forb=12

b=12and

andaa==66

into

intothe

theproblem,

problem, then

thenmultiply.

multiply.

ba = (12)(6)

= 72

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

23.
You Try #5

Evaluate each expression given that a = 6, b

= 12, and c = 3.

5.b - c Substitute

Substitutethe

thevalue

valuefor

forb=12

b=12and

andaa==33

into

intothe

theproblem,

problem, then

thensubtract.

subtract.

b – c = 12 – 3

=9

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

5.b - c Substitute

Substitutethe

thevalue

valuefor

forb=12

b=12and

andaa==33

into

intothe

theproblem,

problem, then

thensubtract.

subtract.

b – c = 12 – 3

=9

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

24.
You Try #6

Evaluate each expression given that a = 6, b

= 12, and c = 3.

6.c ÷ b Substitute

Substitutethe

thevalue

valuefor

forc=3

c=3and

andbb==12

12into

into

the

theproblem,

problem, then thenDivide

Divide

c 3 Note:

Note:ItItisisbetter

betterto

torewrite

rewritethis

thisdivision

Divideboth

both

numeratorand

c b problem as a fraction.

problem as a fraction.

division

and

denominatorby by

b 12 This Thisfraction

fractioncan

cannow

nowbebereduced

reducedto

toits

its

the GCF = (3) to simplest form.

the GCF = (3) to

reducethis

this 3 3 1 simplest form.

fraction. ItItisisOK

OKtotohave

haveaafraction

12 3 4 asasanananswer.

answer.

fraction

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide

Evaluate each expression given that a = 6, b

= 12, and c = 3.

6.c ÷ b Substitute

Substitutethe

thevalue

valuefor

forc=3

c=3and

andbb==12

12into

into

the

theproblem,

problem, then thenDivide

Divide

c 3 Note:

Note:ItItisisbetter

betterto

torewrite

rewritethis

thisdivision

Divideboth

both

numeratorand

c b problem as a fraction.

problem as a fraction.

division

and

denominatorby by

b 12 This Thisfraction

fractioncan

cannow

nowbebereduced

reducedto

toits

its

the GCF = (3) to simplest form.

the GCF = (3) to

reducethis

this 3 3 1 simplest form.

fraction. ItItisisOK

OKtotohave

haveaafraction

12 3 4 asasanananswer.

answer.

fraction

Click

Clickto

toreturn

returntoto

“You try it” slide

“You try it” slide