Unit 1: Introduction to ALGEBRA

Give an algebraic expression for the perimeter

of each figure.

3x

3x 5x

2x

4x – 3 n

6n – 2

n + 3 n + 3

4x – 3

n

4x + 2 4x + 2

2x – 3

4n + 5 4n + 5

3x – 2 3x – 2

2n – 1

REMEMBER

You cannot ADD or SUBTRACT unlike terms

EXAMPLE: 6x – 4 + 8x

*Bring like terms together 6x + 8x – 4

14x – 4

14x – 4 is the simplified expression, we cannot

subtract 14x & 4 because they are unlike, 14x

is a variable term & 4 is a constant term

[number only]

n

4n + 7

SIMPLIFY each of the following algebraic expressions.

*Remember, you can ONLY + & — LIKE terms!

a + a + a

2b + 5b 4a + 2a + 5

x –x + x + 3

y + y + y + y + 2 + 5 3b + 2 – 2b – 3

–8a + 2a + 5

10b – 9b 3a + 2a + 3x

12a – 6a

15x – 10 2x + 8x

x + 2x + 5x

2a + 5 + 3a 20a + 18 + 2a + 5

–x + –7x

8t – 12t –8a – 12a

–18r – 12r

–7a – 9a –10c + 2c

Translating Words into an Algebra Expressions

Example: the sum of three times a number and eight means 3x + 8

Write an algebraic expression for each statement.

The sum of a number and six ______________

The quotient of fifteen and a number ______________

The difference between a number and twenty ______________

The product of seven and a number ______________

The difference between the square of a number and three _____________

The sum of triple z and double n ______________

One quarter of a number ______________

Three times a number decreased by nine ______________

Double a number less one hundred ______________

Ten less than half a number ____________

Translating Words into an Algebra Expressions

Example: twenty less than triple a number means 3x – 20

Write an algebraic expression for each statement.

The sum of double a number and two ______________

The quotient of twice a number and three ______________

The difference between fifty and a number ______________

The product of ten and a number ______________

The difference between five times a number and seven ___________

The difference of triple x and double z ______________

One third of a number ______________

Six times a number decreased by fifteen ______________

Triple a number less seventy ______________

Nineteen less than one quarter of a number ____________

Translating Words into an Algebra Expressions

Example: Fifteen less double a number means 15 – 2n

Write an algebraic expression for each statement.

The sum of five and seven times a number ______________

Ten more than two times a number ______________

Eight less than five times a number ______________

The product of three times a number and four ______________

Eleven less than four times a number ______________

The square of the sum of six times and two ______________

One fifth of a number ______________

The sum of a number and twice the same number ______________

The sum of an even number & the next even number ______________

The sum of a number & the next two consecutive numbers __________

SIMPLIFY each of the following; SIMPLIFY means to combine LIKE TERMS.

6x + 3x

–6n + –5n 15s + –4s

–7b – –4b 9x – –2x –5n – 8n

1 + 3x – 5x + 7

x – 1+ 4x – 6 7x + 8 + 3x – 3

8 + 2x + x – 3

7x – 10 – 3x + 5 –4x – 6 – 4x + 1

6x + 4 – 3x – 9

–6n + 3 + 9 – 2n

–10 – 4x + 5x +6

3s + 6s – 13 + 5

2t – 10 – 6t 8 – 3x – 7x

Algebraic Expressions in Word Problems The rate for a taxi is $5.00 plus $1.35 for each kilometer traveled. Write a simplified algebraic

expression to represent the cost of a taxi ride for x kilometers.

Jason sold x yearbooks the first week, he sold double that in the second week and during the

third week he sold 5 less than during the second week. Write an algebraic expression for each

week and then write a simplified expression to represent the total number of yearbooks that

Jason sole.

Week #1: ____________ Simplified expression:

Week #2: ____________

Week #3: ____________ Pencils cost p¢ each [taxes included]. How many pencils can be purchased for $d?

If a represents a person’s age in years, give an expression to represent the person’s age:

a) in months? b) in days?

If a student has x classes in n days, how many classes does the student have per day?

Todd weighed x kg and lost n kg in each of four consecutive weeks. Give an algebraic

expression to represent Todd’s weight after four weeks.

If there are x boys and n dogs in the park, write an algebraic expression to represent the total

number of feet in the park.

Write an algebraic expression to represent your average on math tests where you scored, x %,

n % and y %.

SIMPLIFY each of the following:

(2x + 4) + 6 (3x + 1) + 3x

(4x – 2) + 4

x + 3 – 2x 8x + 5x + 5 – 2

(x + 3) + (4x + 2)

(5x + 4) – (2x + 2) (6x – 5) + (x – 2)

11x – (9x – 4)

(8x + 7) – (9x + 3) (8x – 10) – (7x – 12)

STEPS to REMEMBER

EXAMPLE: (6x – 4) – (8x + 3)

*Notice minus sign between brackets

Step 6x – 4 – 8x – 3 Remove brackets & make necessary changes

Step 6x – 8x – 4 – 3

*Bring LIKE TERMS together Step -2x – 7

*Simplified, cannot subtract unlike terms!

(2x – 5) – (9 – 7x) 14x – (20x + 3)

(3x – 1) + (5x – 4) (x + 3) – (3x + 1)

(x + 1) + (2x + 4) (x – 2) – (2x – 3)

2x 4 + 3x + 8 5x (4x – 7) – (8x – 9)

12x 9 + 7x + 15 15x (6x – 3) – (11x – 10)

Simplifying Algebraic Expressions

MULTIPLICATION & DIVISION Remember: You can MULTIPLY or DIVIDE unlike terms!

7 • –6s

–5x • –9

4 • –3x

15n ÷ –5

16

64

m

–84x ÷ 12

6 • 2x

–3x • 5 –8 • –9x

–2(4x + 3)

–1(5x – 9)

4(4x – 2)

(15x + 9) 3

5

)1025( x

(–21 – 14x) 7

REMEMBER: You CAN multiply &

divide unlike terms

EXAMPLE : 9 15x

135x

*Multiply the integers, then include

variable & you have the expression

EXAMPLE : -56x 8

-7x

*Divide the integers, then include variable

& you have the expression

9 • –15s

–3n • –12 –8 • 7x

24n ÷ –8

10

60

m

–81x ÷ 9

9 • 6x

–3x • 14 –12 • –9x

–4(5x + 6)

–7(2x – 9) 8(3x – 2)

–3(7x + 4)

–1(8x – 7) –5(9x – 12)

3

)3312( x

(20x – 35) 5

9

)1854( x

2(x – 8) – 3(4x – 2)

2(4x + 5) – 3(x + 2)

3(2x – 5) + 4(x + 1)

7(3x + 2) + 4(5x – 5)

9(2x – 3) – 8(4 – 5x)

4(6 + 8x) – 3(5 – 7x)

5(2x + 1) – 4(x – 3) + 8(2 – 3x) – 4(3 – 5x)

Algebraic Expressions in Word Problems A repairman earns $x per hour plus $30 for traveling expenses. Write an algebraic expression

to represent a bill for 7 hours of work (excluding taxes).

Sophie buys x packages of graph paper for $2.55 each (tax included). She pays with a $20

bill. Write an algebraic expression to represent the amount of change the cashier should give

back to Sophie.

Jasmine pays $x for one dozen multigrain bagels. Write an algebraic expression to represent

the cost of 5 bagels.

Sam sells tickets for the Hadley Junior High School Fall Talent Show, he sells (3x – 4) $3

tickets and (2x + 5) $4 tickets. Write a simplified algebraic expression to represent the

money Sam made.

Simplify each of the following expressions. *Remember: The minus sign between the brackets means the sign inside the brackets changes to the opposite of

what is was, + to — or — to +

(5x + 4) – (x – 2) (6 – 3x) + (x – 5x)

(4x + 5) – (3x – 2) – 6 9x + 5 – 7x

2 • –7x 3(2x – 6)

7x – 4(x + 2) (12x – 6) 3

2

)8610( x

2(3x – 2) + 3(x + 5)

Find the simplified algebraic expression for the perimeter of this polygon.

3x + 4

2x – 5

6 – x

4x + 1

8 – 6x

B I N G O

ALGEBRA

BINGO

On the next page are a series of Algebraic Expressions and Phrases.

1. Cut out each of the expressions and phrases;

2. Match each phrase to an expression;

3. Glue 24 of the algebraic expressions to the above BINGO card;

4. Get some bingo chips & you are ready to play ALGEBRA BINGO!

Algebra

Bingo

Card

Cut out each of these rectangles, there are 52 expressions and phrases in total.

After you cut them out, match the expression with the phrase. Once your teacher

has checked your matches you will glue JUST the expressions onto your BINGO card!

5 + x Double a number

decreased by 5 6 – x Six times a number less

one

6(x + 1) The quotient of

three and a

number less two

4x – 2 Product of six and a

number decreased by

1

2x – 5 Six less a number 9 + x Five times a number

plus 1

4x + 3 Nine minus five

times a number (x – 2)2 The square of a

number minus three

6x – 1 Five more than a

number 8 – x Four times a number

decreased by 2

x + 6 Nine increased by

a number 2 – 3x A number divided by

six

5 – 2x Eight decreased by

a number 2(x + 5) Seven decreased by

two times a number

)2(

3

x

Two less than

three times

number 6

x

Three times a number

plus two

2x - 6 The difference

between triple x

and double n

9 – 5x Three more than

quadruple a number

x – 5 Two times five

more than a

number

7 – 2x Eight less than the

cube of a number

3x – 2 Five minus double

a number 3(x + 2) Five less than a

number

3x – 2n Six less than

double a number x2 – 3 The square of a

number decreased by

two

5x + 1 A number

increased by six x3 – 8 Two decreased by

three times a number

This pages needs to be torn

out and cut up to make your

ALGEBRA

BINGO

CARD

Unit 1 Extra Practice

10x – 8x + 7x + 2 (3y + 5) + (7y – 8)

(12a + 6) – (8a – 4) 11n + 5 – 9n + – (7n + 4)

7u – 2(u + 5) 3(y – 2) + 5(6 + y)

(4x + 10) – 2(3x – 5) (24n – 16) ÷ 4

y + (y + 4) + (y – 4) 5(2x) + 3(3x – 4) – 6(7x)

(8x – 6) – (3x – 6) (4s – 5) – (4s – 5)

(8 – n) + (n – 8) + 4n 3(5 – 2x) – 6(x + 8)