1. Expressions

2. Order of Operations 2/6/13
• PEMDAS
• “Please Excuse My Dear Aunt Sally“
1. Parentheses
2. Exponents
3. Multiply and Divide
(from left to right)
4. Add and Subtract
(from left to right)

3. Examples:
• 2 + (1 – 6)2 – 5
• 7 + (6 × 52 + 3)

4. You Try!
•6 ÷ 3 + 4 × 2
• 20 - (3 × 22 - 5)

5. Combining Like Terms 2/7/13
• What are “like terms”?
▫ Must have the same variable, or
have no variable.
• Terms without a variable are called
“constants.”
• Remember: Variables are letters!
• The number before the letter is called
the coefficient.

6. • Which are like terms?
2x – 6 + 9y + 2 – 6x + 2y
To combine like terms: Add the coefficients!

7. • Examples:
• Simplify each expression.
• 4x + 2 – 2x + 1
• 8y – 4 + 3y
• -7 + 3m – 4 – m

8. • More Examples:
• 8x – y + 9 – 2y
• a + 2a – 5 + b + 2b

9. You Try!
• Simplify.
• 5x + 3 – 2x + 1
• 4m – 2n + 9 – 4m – 5

10. The Distributive Property 2/8/13
• The distributive property tells us how
to simplify expressions like: 2(x – 1)
• We distribute the outside number to
both inside terms.
• Like this:
• Remember: “ab” means “a times b”

11. Examples:
• Simplify.
• 3(2x + 1)
• -2(4 – 3y)
• -(-m + 4)

12. You Try!
• Simplify.
• 4(3x + 5)
• -6(3 – 2v)
• -(-z + 5)

13. Simplifying Expressions 2/14/13
• First, distribute to get rid of all
parentheses.
• Then, combine like terms.

14. Examples:
• Simplify each expression.
• 3(4n + 2) + n
• 7x – (2x – 3) + 1

15. • 2 – 3(4 – 8b)
• -2(m + 5) + 6m – 1
• 4(x + 7) – 2(1 + 5x)

16. You Try!
• Simplify each expression.
• 5(3x + 1) – 4x
• 4r – 6(1 + r)

17. Expressions vs. Equations 2/15/13
• Let’s compare and contrast:
EXPRESSIONS EQUATIONS
BOTH

18. Examples:
• Expression or Equation?
• 2x -7y + 4
• 6x – 14 = 3
• 9m = 6n – 23
• 8(2x – 4) + 9x

19. Evaluating Expressions 2/20/13
• Remember: Variables stand for
numbers.
• Evaluate means to replace each
variable with a number value and
get a number answer.

20. How to Evaluate Expressions:
• Replace each variable (letter) with
the given value (number).
• Always put the new number in ( )!
• Use ORDER OF OPERATIONS to
find the answer.
• Your answer should be a number
with no variables in it!

21. Examples:
• Evaluate each expression.
• 3(x – y); use x = 7 and y = 4
• m – n ÷ 3; use m = 12 and n = 6

22. • qr – 6; use q = 4 and r = 5
• x + y3; use x = 23 and y = 2

23. You Try!
• Evaluate each expression using the
values given.
• ab + b; use a = 4 and b = 2
• 7(x – y); use x = 9 and y = 5

24. Evaluating Expressions with ( )
2/21/13
• Simplify first.
▫ Distribute
▫ Combine Like Terms
• Replace variables with
numbers, then use Order of
Operations.
• Don’t forget ( ) around new
numbers!

25. Examples:
• Simplify each expression. Then
evaluate for the given value.
• 5(x + 3) – 4x; if x = 2
• -4m – (2 – 3m); if m = -3

26. • -2(3k – 1) + 4k + k; if k = -2
• -w + 4 – 2(5w + 7); if w = 1

27. You Try!
• Simplify, then evaluate.
• -(2t – 3) + t – 5; if t = 3
• 2x – 8 + 3(1 – 3x); if x = -2