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### Variables and Expressions

- A
*variable*is used to represent an unknown number or value. - An
*algebraic expression*combines numbers and variables with arithmetic operations. - Review these terms: product, factor, power, base, exponent
- Practice translating verbal expressions into algebraic expressions. This is an essential skill you will need to solve word problems throughout this course.
*Evaluating an expression*means to find the value of the expression.

### Variables and Expressions

Write an algebraic expression for:

Five less than the sum of x and y

Five less than the sum of x and y

- 5 less than x + y

**x**

**+**

**y**âˆ’

**5**

Write an algebraic expression for:

The product of the square of a and the cube of b

The product of the square of a and the cube of b

**a**

^{2}Â·

**b**

^{3}

Write an algebraic expression for:

The sum of four times and seven, divided by the difference of 2 minus the square of

The sum of four times and seven, divided by the difference of 2 minus the square of

- 4g + 7
- 2 âˆ’ x
^{2}

[(

**4****g****+****7**)/(**2**âˆ’**x**^{2})]Write an algebraic expression for:

The sum of six times m and eight minus n

The sum of six times m and eight minus n

- 6 Â·m
- 6m
- 8 – n

(

**6****m**)**+**(**8**âˆ’**n**)Write an algebraic expression for:

The difference of nine times s and three less than r, divided by the product of the square of t

The difference of nine times s and three less than r, divided by the product of the square of t

- 9s âˆ’ ( r âˆ’ 3 )
- t
^{2}

[(

**9****s**âˆ’ (**r**âˆ’**3**))/(**t**^{2})]Write an algebraic expression for:

The product of seven times the difference of two and c

The product of seven times the difference of two and c

- 2 – c

**7**Â·(

**2**âˆ’

**c**)

Write an algebraic expression for:

The product of sixteen times u, divided by the difference of v and twenty three

The product of sixteen times u, divided by the difference of v and twenty three

- 16 Â·u
- 16u
- v âˆ’ 23

[(

**16****u**)/(**v**âˆ’**23**)]Write an algebraic expression for:

The square of twenty divided by x

The square of twenty divided by x

- [20/x]

( [(

**20**)/(**x**)] )^{2}Write an algebraic expression for:

The product of eighteen times eleven less than the cube of r

The product of eighteen times eleven less than the cube of r

- r
^{3}âˆ’ 11

**18**Â·(

**r**

^{3}âˆ’

**11**)

Write an algebraic expression for:

The difference of five times d and the cube of e

The difference of five times d and the cube of e

- 5 Â·d
- 5d
- e
^{3}

**5**

**d**âˆ’

**e**

^{3}

*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

### Variables and 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 0:00
- History of Algebra
- Origin of Word
- Real World Problems
- Definitions 0:58
- Variable
- Algebraic Expression
- Operations
- Example 1: Words into Expressions 3:02
- Example 2: Words into Expressions 5:20
- Example 3: Words into Expressions 6:45
- Example 4: Words into Expressions 9:46

0 answers

Post by Mohamed E Sowaileh on July 10 at 08:35:00 AM

Hello Dr. Carleen Eaton,

I hope you are very well.

I am a student who is extremely weak in math. In order to be very strong in math, specially for engineering field, could you provide me with sequential order of mathematical topics and textbooks. With what should I begin so that I can master big topics like calculus, statistics, probability ... etc.

Your guidance is precious to me.

Thank you so much.

0 answers

Post by Michael Romanov on October 25, 2016

al-gabr closely means completion - "This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi."

Just to put it all in one place:

The idea is to balance out or complete something: a shape or equation or expression.

A Variable is a letter or symbol that represents a number or group of numbers.

An Expression is a mathematical phrase that combines numbers and or variables with arithmetic operations. Â

An Equation is a mathematical statement that two Expressions are equal.

That last part is important because if you do not understand arithmetic operations, you will struggle when trying to balance out / complete an expression or equation.

3 answers

Last reply by: Dr Carleen Eaton

Mon Feb 1, 2016 3:55 PM

Post by Jessie Carrillo on January 24, 2016

Greetings Professor Eaton, I was wondering if the related books on your Algebra 1 and Algebra 2 courses are books you based off the lectures. If yes, do you recommend acquiring those books and working with them in conjuction with your lessons. If not, what book or books do your recommend to get a good handle on Algebra 1 and Algebra 2.

1 answer

Last reply by: Dr Carleen Eaton

Mon May 13, 2013 12:19 AM

Post by Shoshana C on May 11, 2013

How do you know that m and n are equal?

2 answers

Last reply by: Elena Doskalovich

Mon Jun 10, 2013 9:13 AM

Post by Leilani Greenwood on January 5, 2013

Will there be any practice problems?

1 answer

Last reply by: Dr Carleen Eaton

Thu Dec 27, 2012 12:21 AM

Post by Mary Galanopoulos on December 26, 2012

Would you put parenthesis around the m and n?