This document discusses order of operations and simplifying expressions through combining like terms and using the distributive property. It provides examples and practice problems for readers to try. Order of operations is explained using PEMDAS ("Please Excuse My Dear Aunt Sally") to remember the steps: 1) Parentheses 2) Exponents 3) Multiply/Divide 4) Add/Subtract. Combining like terms means adding coefficients of terms with the same variables. The distributive property distributes numbers outside parentheses to terms inside.

1. Simplifying 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 2/13/13
• 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 2/14/13
• 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