Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions
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.
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.
Evaluate each expression if a = 1, b = 2, c = 3, and d = 5. remember order of operations
- b*c + 2
- b*c*d – 5
Evaluate each expression if x = 4, y = 2, and z = 3.