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### Expressions and Variables

• Variable: A letter or symbol that can stand for one or more numbers.
• Expression: A mathematical phrase that includes numbers and variables. These do not have equal signs. Different types of expressions include numerical expressions, algebraic expressions, and word expressions.

### Expressions and Variables

Evaluate each expression:
13 × 30 =
390
Evaluate each expression:
14 × 20 =
280
Evaluate each expression:
n - 9, for n = 12
• 12 − 9 =
3
Evaluate each expression:
x + 5, for x = 6
• 6 + 5 =
11
Evaluate each expression:
12 - m, for m = 3
• 12 − 3 =
9
Evaluate each expression:
s ÷ t, for s = 21 and t = 3
• 21 ÷3 =
7
Evaluate each expression:
x ÷ y, for x = 42 and y = 6
• 42 ÷6 =
7
Evaluate each expression:
m ÷ n, for m = 81 and n = 9
• 81 ÷9 =
9
Evaluate each expression:
cd, for c = 4 and d = 8
• (4)(8) =
32
Evaluate each expression:
xy,for x = 9 and y = 8
• (9)(8) =
72

*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.

### Expressions and Variables

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
• Vocabulary 0:06
• Variable
• Expression
• Numerical Expression
• Algebraic Expression
• Word Expression
• Extra Example 1: Evaluate the Expression 2:27
• Extra Example 2: Evaluate the Expression 3:16
• Extra Example 3: Evaluate the Expression 4:04
• Extra Example 4: Evaluate the Expression 4:59

### Transcription: Expressions and Variables

Hi, welcome to Educator.com.0000

This lesson is on expressions and variables; let's begin.0002

First thing we have to go over--variable; variable.0009

A variable is a letter or symbol that can stand for or represent one or more numbers.0014

In place of numbers, I have usually letters.0021

If I use A or B... I can use X, Y... those are all considered variables.0026

I can also use symbols.0033

Sometimes in math, we use Greek symbols; or I can use star as a symbol.0035

Anything that represents numbers would be considered a variable.0043

Expressions; expressions are numbers or mathematical phrases that includes numbers and variables.0049

Keep in mind that expressions do not have equal signs.0058

If it does have an equal sign, then it would be called something else.0063

It would be called an equation.0066

We have different types of expressions.0069

The first type is a numerical expression; numerical means numbers.0072

If we have a numerical expression, it would be an expression, mathematical phrase, that has only numbers.0077

Here is an example, 30 plus 5; this is considered a numerical expression.0086

There is no variables; we only have numbers.0092

The next one--algebraic expression--is the most common type of expression.0096

That is when you have both numbers and variables.0102

6 plus A is an example of an algebraic expression.0107

2X minus 10 is also another example.0112

We have A; that is a variable; X is a variable here too.0115

2X minus 10 is an algebraic expression.0120

The other type is a word expression.0125

Word expression is when you use words to express your expression.0128

Or you write out your expression using words.0134

P divided by 9 would be considered a word expression0136

because instead of writing the symbol out, you would write just--divided by--the words.0140

Let's do a few examples of evaluating expressions.0147

Evaluating just means to solve or simplify the expression.0150

If I have a numerical expression, 12 times 20, this is a numerical expression.0157

I can actually simplify this out; I can multiply 12 and 20 together.0164

12 times 20; 2 times 0 is 0.0171

Because it is 0, I can just move on.0180

2 times 2 is 4; 2 times 1 is 2.0182

When I evaluate this expression, I get 240.0188

This next one, M minus 8, that is my expression.0197

They want me to evaluate this expression when they tell me that M is equal to 8.0203

Here is the expression; let me use black.0210

M minus 8 is my expression; they told me that m is 8.0214

Remember variables; this is a variable that represents a number.0220

The number that it represents is 8.0224

This is the same thing as 8 minus 8; my answer is 0.0228

When I evaluate the expression M minus 8 when M is equal to 8, then my answer would be 0.0237

The next example, I am evaluating the expression, S divided by T.0245

S divided by T can also be written like this, as a fraction, S divided by T.0252

They are telling me that S is 28 and T is 4; S is 28.0259

Instead of writing S, I am going to write out 280267

because S is a variable that represents the number 28 and T represents the number 4.0270

I can write it like this; or I can write it just 28 divided by 4.0281

It is the same thing; 28 divided by 4 is 7.0286

When I evaluate the expression, I get 7 as my answer.0294

The final example, example four, evaluate the expression CD.0300

When I have two variables next to each other like that, CD, this means C times D; C times D.0306

C represents the number 3; it is 3; D represents the number 200.0316

If CD means C times D, then it means 3 times 200.0325

When I multiply 3 times 200, I get 600.0332

When you evaluate the expression CD, when you are given the numbers that they represent, then the answer will be 600.0342

That is it for this lesson on Educator.com.0353

We will see you next time; thank you.0356