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 MeaningOperation 8y 8 ● y 8(y) 8 times yMultiplication 16  b 16 b 16 divided by bDivision 4 + s4 plus sAddition 9 – x9 minus xSubtraction

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: 8y8 ● y8(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 expression 2. Substitute 3. Simplify Note:  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 8 th 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) 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 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 – 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 Write the expression 2. Substitute 3. Simplify Average Speed d t 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 Turn Evaluate the expression when y = y y 3. y y – 2 5. y  3 Evaluate the expression For the given value of the variable: 6. 12x when x = p when p = when x = 3 x 9. d when d = r(10) when r= 8.2

Your Turn 11. 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 Solutions $ miles per minute ft per second 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…