Module 1 Topic 2

Variables and Expressions

Variable: an unknown that is usually represented by a letter; used in writing

expressions

Expressions are different from equations because expressions do not have an

“equals” sign

Writing an Algebraic Expression

EX: Write the algebraic expression that represents the sum of a number and 3

X + 3

Write this down:

sum + difference –

product x quotient /

Writing an Algebraic Expression

EX: Juan has 40 different plants that he wants to plant into r rows. Write an algebraic expression that represents how many plants will be in each row.

40/r

Order of Operations

Never goes away!

1. Parenthesis and Exponents

2. Multiplication and Division

3. Addition and Subtraction

Order of Operations

EX: 23 – 4(-7 + 10) + 6

8 – 4(3) + 6

8 – 12 + 6

-4 + 6

2

Simplifying Algebraic Expressions

EX: Simplify 3x*22 + 5x – 8/2

3x*4 + 5x – 8/2

12x + 5x – 4

17x - 4

EX: Simplify (-3)2 – 6y + 2y(5) -10 YOU TRY!

9 – 6y + 2y(5) – 10

9 – 6y + 10y – 10

4y – 1 (Did you get it? )

The Distributive Property

Allows us to simplify expressions when you can’t use order of operations.

EX: Distribute the expression

5(r + 12)

5r + 5*12

5r + 60

Let’s Put it All Together!

EX: Simplify 2 – 3(t + 5) + 43 - 60t/5

2 – 3(t + 5) + 64 – 60t/5

2 – 3t – 15 + 64 – 12t

-15t + 51

Let’s Try a Word Problem

Sharon has $125 in a savings account and is spending $8 each week on lunch at school.

a. How much will she have left after w weeks? A: $125 - $8w

b. How much will she have after 5 weeks?

A: $125 - $8(5) = $125 - $40 = $85

c. What equation can be written to find out how many weeks it will take for her to have $45 left?

A: $45 = $125 - $8w