Algebra I in Simple English/Introduction to Basic Algebra Ideas/Variables and Expressions

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Contents 1 Vocabulary 2 Lesson 3 Example Problems 4 Practice Games 5 Practice Problems

[edit] Vocabulary

Variable

Term

Operation

Expression

Evaluate

Substitute

[edit] Lesson

A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are a, x, y, θ, and λ. The letters x and y are commonly used, but remember that any other symbols would work just as well.

Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.

Some examples of variables in use:

• 3x - three times x
• 5 - y - five minus y
• 2 / s - 2 divided by s

A term is a number or a variable or a cluster of numbers and variables multiplied and or divided separated by addition and subtraction.

Examples of terms:

• 3 + 5 The terms are 3 and 5.
• 6 / x The term is 6/x, 6 over x is one term, because the operation is division.
• 6x + 5 The terms are 6x and 5, 6x and 5 are separate terms because they are separated by a addition or subtraction.

An operation is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like +, -, *, or / for operations.

An expression is two or more terms, with operations between all terms.

Examples of expressions:

• 3 / 4
• 8 * x
• x * 6 + y
• a * b * c * d

To evaluate an expression, you do the operations to the terms of an expression.

Examples of evaluating expressions:

• 3 + 4 evaluates to 7.
• 18 / 3 evaluates to 6.
• 4 * 5 - 3 evaluates to 17.

To evaluate an expression with variables, you substitute (put a thing in the place of an other thing) numbers for the variables.

Examples of substituting: (Substitute 3 for x in these examples.)

• x + 4 is 3 + 4.
• 18 / x is 18 / 3.
• 4 * 5 - x is 4 * 5 - 3.

[edit] Example Problems

Evaluate 5*x when x is 2.

Substitute 2 for x to get 5*2.

Evaluate 5*2 to get the answer 10.

Evaluate x / 3 + y when x is 9 and y is 4.

Substitute 9 for x and substitute 4 for y is to get 9 / 3 + 4.

Evaluate 9 / 3 + 4 to get the answer 7.

[edit] Practice Games

http://www.quia.com/cm/29771.html (evaluating expressions)

Advanced Expression Evaluator at http://analysischamp.com/eex/expeval.asp

[edit] Practice Problems

(Note: put answer in parentheses after each problem you write)

Evaluate each expression if a = 1, b = 2, c = 3, and d = 5.

1. 5*b (10)
2. 9*c (27)
3. c-2 (1)
4. d-5 (0)
5. b/2 (1)
6. 36/c (12)
7. b*c + 2 (8)
8. b*c*d - 5 (25)

Evaluate each expression if x = 4, y = 2, and z = 3.

1. x+y (6)
2. 2*z (6)
3. x*z (12)
4. x+y+z (9)
5. x*y+z (11)
6. y*z-x (2)