1-1 Variables and Expressions

You would be wise to listen carefully and take notes! Copy

material that is highlighted the same

color as the above title.

In this section we are going to learn about

mathematical expressions and how to “translate” verbal

expressions into mathematical expressions.

Algebra 1A by Gregory HaucaGlencoe adapted from presentations by Linda Stamper

Pre Quiz

1) increase2) decrease3) more than4) less than

5) product

7) difference8) quotient

9) sum

6) plus+

−

+

−

x

+

−

÷+

10) times x

Write and translate each word into an operation symbol.

Write and answer the following problems.

1)2)3)

4)

5)

7)

8)

9)

6)

10)

In Algebra, an expression is a mathematical phrase that contains operations, numbers, and/or variables..

An expression that represents a particular number is called a numerical expression.

A variable expression consists of numbers, variables and operations.numbers- ex. 2,-3,

πvariables – letters ex. a,x,yoperations - addition, subtraction,

multiplication and division +, -, •, ÷

Ex. 3 + 6 ÷ 3

Ex. 3x2 + 2x - 1

You can use letters to represent one or more numbers. When a letter is used to represent a value that can change or vary, it is called a variable.

In variable expressions, a raised dot or parentheses are often used to indicate multiplication as the symbol x can be easily mistaken for the variable x. Here are some ways to represent the product of x and y.

In general, good algebraic form is the xy version!

In each expression, the quantities being multiplied are called factors, and the result is called the product.

xyyx yx yx yx

Multiplication Symbols

Examples. 2y, 3xy

Example. the product of x and y

Powers.

43base

exponent

word description: four to the third power or

four cubed

factored form: 4 • 4 • 4

evaluated form: 64

Powers consist of a base and an exponent

A power is a short way of writing a

repeating multiplication.

Example:

1. Write problem. 72

2. Write word description.

or seven squared

3. Write factored form.

7 • 7

Ex.1 Express the power 72 in words. Then write the factored form and evaluate

it.

seven to the second power

Ex.1

4. Evaluate. 49

Writing expressions in exponential or power form.

y4

y • y • y • y

Ex.2 Ex.3

53

5 • 5 • 5 (3x)

4

3x • 3x • 3x • 3x

Ex.4

Must have parentheses!

Evaluating expressions.

16

2 • 2 • 2 • 2

Ex.5 Ex.6

125

5 • 5 • 5

-9

-32

Ex.7

Remember! An exponent applies only to what is directly in front of it.

(-3)2

9

-(3 • 3) -3 • -3

In English there is a difference between a phrase and a sentence. Sentences have verbs and phrases do not.

In this section we are only going to translate phrases into expressions.

PhrasesPhrases are translated into expressions.

SentencesSentences are translated into equations and inequalities.

Remember! A numeric expression is made up of

numbers and operations (ex. 5 – 3).

A variable expression is made up of variables,

numbers and operations. (ex. 3 + 2x).

Words representing operations.

add

plus

sum

increased by

total

more than

added to

subtract

minus

difference

decreased by

diminished by

less than

subtracted from

less

multiply

times

product

of

twice 2

divide

quotient

Translating phrases into variable expressions.

2. 11 greater than a number

n + 11

1. The sum of a number and 30

n + 30

3. A number decreased by 75

n – 75 Note that translation of this phrase “switches”

the order of what is read. The expression 11 + n would NOT be

correct.

4. a number subtracted from 15

15 – n

The translation of this phrase also “switches” the

order of what is read.

5. The product of 5 and a number

5n

Not 5·n or 5(n) or (5)(n)

6. The product of a number and 4 4n

In products of numbers and variables the number is always placed first. Do not

write “ n4 ”.

7. The quotient of a number and 6

n 6

Use a fraction bar in algebra to designate division! Not a ÷

symbol. The first number is always

the numerator (on top)

n ÷ 6

1. Twice a number plus 7

2n + 7

3. The difference of 8 and three times a number

8 -

2. 5 more than the product of a number and 4

4n + 5

Multiple Operation PhrasesSome phrases require more than one operation or variable when translating them. In some you will need grouping symbols to show the correct order of operations.

2 • n + 7

4 • n

+ 5

3 • n

8 – 3n

4. A number cubed divided by 2

3 n2

Class Practice

Translate:

n - 12

six times a number

6n

a number divided by 8

n8

a number minus 12

the sum of 15 and a number

15 + n

the difference of a number and 6.7

n – 6.7

the quotient of 17 and a number

17n

Translate: n + 15

the product of a number and 6

6n

5.2 less than a number

n 5.2

not n6

15 more than a number

the product of 6 and a number, subtract 10 6n - 10

the quotient of a number and 10, plus 2

n 10 + 2

twice the sum of a number and 15

2(n + 15)

not 2n + 15

the difference of a number and 6, divided by 4

n 6

4

HW1–A2 Pages 8-9 #13-22,26,28,30-33,46.

Teacher Contact Information: I can be reached at school by phone at

805-498-3617 x1602 or by email at ghauca@conejousd.comChapter assignment guides showing homework assignments and powerpoint lessons can be downloaded from my website at: www.myteacherpages.com/webpages/ghauca Powerpoints Password - studentStudent individual test/class grades can also be accessed at my website. Click on Student Grades Find class Enter login name – student’s last name Enter password – student’s school ID number

Whiteboard PracticeTranslate: A number minus 12

n - 12

Translate: six times a number

6n

Translate: a number divided by 8

n8

Translate: the sum of 15 and a number

15 + n

Translate: the difference of a number and 6.7

n – 6.7

Translate: The quotient of 17 and a number

17n

Translate: 15 more than a number

n + 15

Translate: the product of a number and 6

6n

Translate: 5.2 less than a number

n 5.2

not n6

The product of 6 and a number, subtract 10

6n - 10

The quotient of a number and 10, plus 2 n

10

+ 2

Twice the sum of a number and 15

2(n + 15)

The difference of a number and 6, divided by 4

n 6

4

not 2n + 15

Did you use a fraction

bar to designate division?

a. 11 greater than a numbern +

11b. a number subtracted from 15 15 –

nc. The sum of a number and 30 n + 30

Ex.1.

d. Maria’s age minus 27 a – 27 e. The quotient of 18 and a number

18 n

f. The sum of a number and ten, divided by two.

210n

a. The difference of a number and 7

n – 7

b. 32 increased by a number

32 + n

c. 25 less than a number

–

Writing word phrases as algebraic expressions.

d. The quotient of a number and six.

n 6

Use a fraction bar to

designate division!

25 n

e. The product of a number and five 5n

The number always comes

before the variable?

f. 10 less the product of 5 and a number cubed 10 –

5n3

Remember! Use a fraction

bar to designate division?

a. 11 greater than a numbern +

11b. a number subtracted from 15 15 –

nc. The sum of a number and 30 n + 30

Ex.1

d. Maria’s age minus 27 a – 27

e. The quotient of 18 and a number18 n

f. The sum of a number and ten, divided by two.

210n

a. eight more than a number

n + 8

b. seven less the product of 4 and a number x7 – 4x

c. n cubed divided by 2

Ex.2

d. 9 more than the quotient of b and 5

e. one third the original area of a

f. thirteen less than a number

n - 13

2n3

95b

3a

ora31

c. 32 increased by a number

32 + x

Translating phrases into variable expressions.

d. 11 greater than a number

p + 11

a. The sum of a number and 30

n + 30

Addition phrases :

e. 7 more than a number

y + 7

b. 12 plus a number

12 + a

Note that translation of this phrase “switches”

the order of what is read. The expression 11 + p would NOT be

correct.

The translation of this phrase also “switches” the order of what is read. The

word “than” often indicates you may need to switch.

a. The difference between a number and 7

n – 7

d. 25 less than a number

y – 25

c. A number decreased by 75

a – 75

e. a number subtracted from 15

15 – p

b. A number minus 27

x – 27

Subtraction phrases :

Note that translation of this phrase “switches”

the order of what is read. The expression 25 - y would NOT be

correct.

The translation of this phrase also “switches” the

order of what is read.

Multiplication phrases :

c. Twice a number

2p

a. The product of 5 and a number

5n

b. The product of a number and 5 5n

In products of numbers and variables the number is always placed first. Do not

write “ n5 ”.

d. 300 times a number

300x

e. A number times 7 7aTwice means 2

times.

Remember in products the number always comes before the

variable.

Not 5·n or 5(n) or (5)(n)

a. The quotient of a number and 6

n 6

Use a fraction bar in algebra to designate

division! Not a ÷ symbol.

The first number is always the numerator

(on top)

Division phrases:

b. The quotient of 18 and a number

18 x

c. A number divided by 12

a 12

n ÷ 6