Algebra I

1.1 Evaluate Expressions

Question: How do you evaluate algebraic expressions and powers?

Answer: By substituting numbers in for the variable and performing the indicated operation(s)

Vocabulary• Variable — a letter used to

represent one or more numbers

• Expression--numbers, variable, and operations (ex: mn)

• Algebraic Expression — an expression that includes at least one variable

Section 1.1 EVALUATING AN EXPRESSION WITH

ONE OR MORE VARIABLES

Please look at the handy chart below & let’s talk it out:

Algebraic Algebraic ExpressionExpression

Real MeaningReal Meaning Operation Operation UsedUsed

5(n) 5·n 5n 5 times n Multiplication

14/y 14÷y 14 divided by y Division

6 + c 6 plus c Addition

8 – x 8 minus x Subtraction

a. 13 •n =13 •3 Substitute 3 for n. =39 Multiply.

b. 9/n =9/3 Substitute 3 for n. =3 Divide.

c. n -1 = 3 - 1 Substitute 3 for n. =2 Subtract.

d. n + 8 = 3 + 8 Substitute 3 for n. = 11 Add.

Evaluate algebraic expressions

Evaluate the expression when n = 3.

Let’s Practice

Let y = 21. 6y

2. 8 divided by y

3. y + 4

4. 11 take away y

If you know how much it costs ($360) and how much you earn each week, you can determine how many weeks it will take you to save enough $$$.

You earn about $64/week, how many weeks will it take you to buy your iPhone?

Here’s the situation:

You’re saving money to buy an iPhone…

$399$399

You can do this by EVALUATING AN EXPRESSION THAT

INVOLVES A VARIABLE: 64w = ?

Section 1.1EVALUATING AN EXPRESSION WITH

ONE OR MORE VARIABLES

Evaluate the expression BELOW when:

w = 2, w = 3, w = 4… until you get an answer.

64w = ?

64(2) = 12864(3) = 19264(4) = 25664(5) = 32064(6) = 384

Section 1.1 EVALUATING AN EXPRESSION WITH

ONE OR MORE VARIABLES

The total cost of seeing a movie at a theater can be represented by the expression a + r where a equals the cost of admission (in dollars) and r is the cost (in dollars) of refreshments. Let’s say you pay $7.25 for admission and $7.50 for refreshments. Find the total cost.

total cost = a + r

= 7.25 + 7.50

= 14.75

Vocab• Power — an expression that

represents repeated multiplication of the same factor

• Exponent — the number of times the base gets repeated

• Base — the number that is multiplied as many times as the exponent

Power Words Product

71

Seven to the first power 7

52

Five to the second power 5 • 5

(1/2)3

One half to the third power -OR-

one half cubed ½ • ½ • ½

Z5 Z to the fifth power z•z•z•z•z

More Practice…

Write in words and expand using numbers1. 95

2. 28

3. N4

4. x3 when x = 8

5. k2 when k = 2.5

Section 1.1 EVALUATING AN EXPRESSION WITH

ONE OR MORE VARIABLES

Each edge or side of a medium sized pop-up storage cube is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube.

14 in.

V = s3

= 143

= 2,744

The volume of the storage cube is 2,744 cubic inches.

Closer

How do you evaluate an expression that contains variables?

• You substitute the values of the variable in the expression and simplify the resulting numerical expression.