Download 1.2 Evaluate and Simplify Algebraic Expressions

1.2 Evaluate and Simplify Algebraic Expressions
Vocabulary
Numerical Expression ­ an expression consisting of numbers, operators and grouping symbols.
Given 25: Base ­ 2 is the base
Exponent ­ 5 is the exponent
Power ­ the repeated multiplication of the same factor.
Simplify the following.
1.
53
2. ­34
st
3. (­3)4
Order of Operations
1 Perform operations within grouping symbols
2nd Evaluate powers
3rd Multiply and divide from left to right
4th Add and subtract from left to right
Simplify the following.
4.
24 ­ 8 ∙ 12 ÷ 4
5. ­18 + 35 ∙ (3 ­ ­ 23)
Vocabulary
Variable ­ a letter used to represent one or more numbers.
Algebraic Expression ­ any expression involving variables, for example, x2 ­ 4x ­ 5.
Mathematical Model ­ an expression that represents a real­life situation.
1
Evaluate the following expressions when x = ­1.
6.
25(x ­ 4)
7. x2 + 5 ­ x
8.
You have $50 and are buying some movies on DVD that cost $15 each. Write an expression that shows how much money you have left after buying n movies. Evaluate the expression when n = 2 and n = 3.
Start with a verbal model:
Write your labels:
Write an algebraic model:
Now solve for n = 2 and n = 3.
Simplifying Algebraic Expressions
Vocabulary
Term ­ the individual parts in an expression, separated by addition or subtraction if there is more than one. In 5x ­ 17, 5x and 17 are terms.
Coefficient ­ the number in front of the variable. If there is no number, than the coefficient is 1. In the term 12c, 12 is the coefficient. In x7, the coefficient is 1.
Like Terms ­ terms that have the same variable and exponent. 4x9 and 2x9 are like terms. Only like terms can be combined using addition or subtraction.
Constant Terms ­ terms without variables, such as 2 and ­17. (They are also like terms.)
2
Simplify the following by combining like terms.
9.
7x2 + 12x ­ x2 ­ 40x
10. 8(y ­ x) ­ 2(x ­ y)
11.
You want to buy either a CD or a cassette as a gift for each of 10 people. CD’s cost $13 and cassettes cost $8. Write an expression for the total amount you must spend. Then evaluate the expression when 4 of the people get CD’s.
Start with a verbal model:
Write your labels:
Write an algebraic model:
Simplify the expression:
Now solve for n = 4.
3
Assignment: Pg 13, #1­3, 5­19 odd, 25­49 odd, 57­60, 62.
4