algebra 1 ch 1.1 – evaluate a variable expression

Algebra 1

Ch 1.1 – Evaluate a Variable Expression

Objective Students will evaluate variable

expressions

Vocabulary A variable is a letter that is used to

represent a number. The numbers are the values of the

variable. A variable expression is a collection of

numbers, variables and operations Replacing each variable in an expression

and simplifying is called evaluating the expression

Examples of Variable Expressions

Variable Expression

Meaning Operation

8y 8●y 8(y) 8 times y Multiplication

16 b 16 b

16 divided by b Division

4 + s 4 plus s Addition

9 – x 9 minus x Subtraction

Comments In algebra you do not use the “x” symbol to

represent multiplication – the reason is that the multiplication symbol “x” can be confused with the variable x.

Multiplication in algebra is represented these three ways:

8y 8 ● y 8(y) Also, the letters “I” and “O” are not used as

variables because they can be confused with the number 1 and 0 respectively

Evaluating Expressions Use the following process to evaluate expressions:

1. Write the expression2. Substitute

3. SimplifyNote: We will be using this process for many concepts

that we cover in this course. This process minimizes errors and demonstrates

your understanding of the concept. At the 8th grade level you are required to

demonstrate your understanding of concepts…this is how you do that!

Example # 1 Evaluate the expression when y = 2

8y

8(2)

16

1. Write the expression

2. Substitute

3. Simplify

Answer: The value of the expression when y = 2 is 16

Example #2 Evaluate the expression when y = 2

y + 3

2 + 3

5

1. Write the expression

2. Substitute

3. Simplify

Answer: The value of the expression when y = 2 is 5

Example #3 Evaluate the expression when y = 2

14 – y

14 – 2

12

1. Write the expression

2. Substitute

3. Simplify

Answer: The value of the expression when y = 2 is 12

Comments As you can see the examples were pretty

simple and you can probably do them in your head…

However, the purpose of the lesson is for you to work with the process for evaluating variable expressions

Therefore, the examples are simple so that you focus on working with the process and not on calculating the numbers…

This process can be applied to real-life situations as follows:

Example # 4 Average speed is given by the following formula:

Average Speed =Distance

Time

You can find the average speed of a car that traveled 180 miles from Boise, Idaho, to the Minidoka National Wildlife Refuge in 3 hours by using the process as shown in the next slide

=d

t

Example #4

Average Speed

180

3

1. Write the expression

2. Substitute

3. Simplify

Average Speed

d

t

Average Speed 60

=

=

=

Answer: The average speed was 60 miles per hour

Your Turn In the following slides you will have the opportunity

to practice what this lesson is about, which is evaluating variable expressions.

Make no mistake about it…the only way that you will become proficient with this process is by working with it…

It’s ok if you make a mistake…the solutions will be on the last page…If you don’t get the same answer you have to question what you did…Check your work and see if you can find where the error is (this is where the real learning and understanding take place)

If you still don’t understand after you have checked your work…bring your work to me and I will help

Your TurnEvaluate theexpressionwhen y = 6

1. 5y2. 24

y3. y + 19 4. y – 25. y 3

Evaluate the expressionFor the given value ofthe variable:6. 12x when x = 57. 9 + p when p = 118. 6.3 when x = 3

x 9. d when d = 60

1210. r(10) when r= 8.2

Your Turn11. You invest $80 at a simple annual

interest rate of 2%. How much simple interest would you earn in 1.5 years? Use the formula I = prt where I is simple interest, p is principal, r is rate, and t is time.

Your Turn Calculate average speed using the formula

Average Speed

d

t=

12. A train travels 75 miles in 55 minutes

13. In 5 seconds an athlete runs 40 feet

14. A horse gallops 4 kilometers in 30 minutes

Your Turn Solutions1. 302. 43. 254. 45. 26. 607. 20

8. 2.19. 510. 8211. $2.4012. 1.3 miles per minute13. 8 ft per second14. 7.5 km per minute

Summary A key tool in making learning effective is

being able to summarize what you learned in a lesson in your own words…

In this lesson we talked about evaluating expressions…Therefore, in your own words summarize this lesson…be sure to include key concepts that the lesson covered as well as any points that are still not clear to you…

I will give you credit for doing this lesson…please see the next slide…

Credit I will add 25 points as an assignment grade for

you working on this lesson… To receive the full 25 points you must do the

following: Have your name, date and period as well a lesson

number as a heading. Do each of the your turn problems showing all work Have a 1 paragraph summary of the lesson in your own

words Please be advised – I will not give any credit

for work submitted: Without a complete heading Without showing work for the your turn problems Without a summary in your own words…