For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

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### Algebraic Expressions

- An algebraic expression differs from an open sentence or equation in that it has no equal sign.
- The value of an algebraic expression can vary depending on the value of the variable.
- Within a single problem, the value of the variable remains the same.
- A variable is a symbol that represents one or more numbers. A mathematical expression with one or more variables is an algebraic expression. To evaluate an algebraic expression, replace each variable with a number and then simplify.

### Algebraic Expressions

Evaluate the expression 5 × (81 ÷ x) for x = 9.

- 5 ×(81 ÷9) =
- 5 ×9 =

45

Evaluate the expression 72 ÷ (y - 62) for x = 70.

- 72 ÷(70 − 62) =
- 72 ÷8 =

9

Evaluate the expression 10m - 4 when m = 3.

- 10(3) − 4 =
- 30 − 4 =

26

Evaluate the expression n ÷ 4 + 9 when n = 24.

- 24 ÷4 + 9 =
- 6 + 9 =

15

Evaluate the expression x × 2 + (17 - y) for x = 5 and y = 15.

- 5 ×2 + (17 − 15)=
- 10 + 2 =

12

The formula A = l × w ÷ 2 gives the area of a right triangle with length l and width w. Find the area of a right triangle with a length of 9 in and a width of 8 in.

- A = 8in ×9in ÷2
- A = 72in
^{2}÷2

A = 36in

^{2}Solve for Q if Q = 63 ÷ j + 7 × k and j = 7,k = 4.

- Q = 63 ÷7 + 7 ×4
- Q = 9 + 28

Q = 37

Eric's store charges $ 5 for a shake and $ 4 for a smoothie. How much does he make when a customer buys 3 shakes and 5 smoothies?

- Let x = number of shakes bought. Let y = number of smoothies bought.

- Total = $5x + $4y, and x = 3, y = 5.
- Total = $5(3) + $4(5)

- Total = $15 + $20

Total = $35

Tiffany uses the formula $ 7m + $ 3n to calculate her son Jason's allowance, with m = number of As on his report card, and n = number of Bs on his report card. What is Jason's allowance if he received 2 As and 4 Bs?

- $7m + $3n, and m = 2, n = 4
- $ 7(2) + $ 3(4) =
- $ 14 + $ 12 =

$26

R = 10a - 13b + 5c. Find R if a = 10, b = 2, and c = 3.

- R = 10(10) − 13(2) + 5(3)
- R = 100 − 26 + 15

- R = 74 + 15

R = 89

Let a = number of apples, b = number of bananas, and c = number of carrots. An apple costs 50 cents, a banana costs 85 cents, and a carrot costs 30 cents.

a) Find the formula for the total cost of apples, bananas, and carrots.

b) How much does 2 apples, 1 banana, and 3 carrots cost?

a) Find the formula for the total cost of apples, bananas, and carrots.

b) How much does 2 apples, 1 banana, and 3 carrots cost?

- a) 50a + 85b + 30c

- b) 50(2) + 85(1) + 30(3) =

- 100 + 85 + 90 =
- 185 + 90 =

275 cents, or $2.75

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Algebraic Expressions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Modeling an Algebraic Expression
- Evaluating an Algebraic Expression
- Evaluating an Algebraic Expression
- Using a Table to Evaluate an Expression
- Extra Example 1: Evaluate the Expression
- Extra Example 2: Evaluate the Expression
- Extra Example 3: Perimeter of a Rectangle
- Extra Example 4: Finding Income

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:16
- Variable
- Algebraic Expression
- Evaluate
- Modeling an Algebraic Expression 1:16
- Model the Expression 2x + 4
- Evaluating an Algebraic Expression 1:47
- Evaluate 3x - 7 for x = 8.2
- Evaluating an Algebraic Expression 2:45
- Evaluate (3.7 + x) ÷ 2 for x = 9.6
- Using a Table to Evaluate an Expression 4:10
- Example: Pairs of Shoes
- Extra Example 1: Evaluate the Expression 5:46
- Extra Example 2: Evaluate the Expression 6:06
- Extra Example 3: Perimeter of a Rectangle 6:46
- Extra Example 4: Finding Income 7:40

0 answers

Post by Shaun Donovan on May 25 at 09:20:49 AM

I love your teaching style. Reminds me of my high school teacher in Massachusetts. Thanks.

2 answers

Last reply by: Lindsey Sutfin

Mon Apr 13, 2015 3:07 PM

Post by Victor Arellano on June 10, 2014

I like how you teach just going too fast sometimes

2.5 times 9 is 22.5 and you wrote 22.4

2 answers

Last reply by: Ruby Zhang

Wed Jun 14, 2017 10:58 PM

Post by Mohamed Elnaklawi on March 30, 2014

In extra example IV, you said a dog WASHER, in the end, you said how much does she earn WALKING each dog. Please go back to check the mistake.

0 answers

Post by Mark Andrews on August 20, 2013

Just realised I misread the question above

It was X = 8.2

Sorry

1 answer

Last reply by: Professor Fung

Sat Aug 31, 2013 2:36 AM

Post by Mark Andrews on August 16, 2013

3x - 7 =8.2

I thought we add 7 to both sides

3x - 0 = 15.2

To get X on its own

Divide by 3 therefore what you do to one side you do to the other.

x = 15.2 / 3

Therefore X = 5.066666

1 answer

Last reply by: Professor Fung

Sat Jul 6, 2013 6:31 AM

Post by Eric Klein on July 1, 2013

@8:22 The answer is zero or unknown, lol, because the question asks how much does she earn for WALKING each group... not WASHING like originally stated... I win. Jk, but thats twice in the same video the questions were wrong... Hmmmmm??

3 answers

Last reply by: Professor Fung

Tue Jun 25, 2013 10:31 PM

Post by Giliana Levis on April 13, 2013

Can anyone help me with the practice question (10)

when I did the problem I wrote towards the end a=100-26+15 equaling 100-41, were do you get the 74 from?

I had the same answer 89 but I was wondering if the 74 came from doing 100-26 then adding 15. Is my way wrong or should I use the other way instead?

1 answer

Last reply by: Professor Fung

Sat Feb 16, 2013 4:36 AM

Post by Magdy Mettias on February 10, 2013

Dear Ms. Fung

Keep up the good work!

0 answers

Post by James Sommers on November 17, 2011

Dear Ms. Fung,

I LOVE your teaching style!! You make learning easy. I'm glad that you leave your corrections/erasures in your presentations. This holds our attention - making it seem we are live with you, rather then a boring, edited seminar. Thanks much!

2 answers

Last reply by: Patricia Wiggins

Thu Jun 7, 2012 12:18 PM

Post by javier mancha on August 15, 2011

you talk very fast, slow down , so you can check your own work .So that you dont confuse us , with your fast talking

4 answers

Last reply by: Victor Castillo

Fri Jan 25, 2013 8:41 AM

Post by John Welch on September 28, 2010

Example 4 - The formula gives us the charges for washing the dogs, there is no mention of the charges for walking the dogs.

5 answers

Last reply by: Giliana Levis

Sat Apr 13, 2013 5:32 PM

Post by John Welch on September 28, 2010

Example II, correct answer should be 16.5 not 16.4

2.5

x 9

------

22.5 22.5 - 6 = 16.5