# Using “Expressions” and “Variables”

### What is a “numerical expression”?

A mathematical expression that represents a particular number – it consists of numbers and the operations of mathematics to be performed

EX:   2 + 4 – 3 +3*4 – 2/3

### What are the “Basic Operations of Arithmetic”?

A sum equals the value of two or more terms or addends (numbers) separated by the plus symbol (+)

EX:  3 + 5 forms the sum 8

Subtraction – Difference

A difference equals two or more terms (numbers) separated by the minus symbol. (-)

EX:  10 – 5 forms the difference 5

Multiplication – Product

A product equals two or more terms called number factors separated by the product operation symbol. (*)

EX: 3*5 forms the product 15

Division – Quotient

A quotient equals a term called the dividend divided by a term called the divisor separated by the divided by symbol. (:) or (/)

EX:  15/3 forms the quotient 5

### What is a “variable”?

A letter that is used to represent one or more numbers

EX: Leters a, b, c, … could represent 2, 5 and 7 in a specific situation

### What is the “value of a variable”?

The number(s) represented by the variable

EX: The letter “a” may represent 2 in a specific situation

### What is a “variable” or “algebraic expression”?

A mathematical expression consisting of numbers, variables and the mathematical operations to be performed

EX:  We can form an expression in which we take the variable “a” (it must be a specific number but it can be any one we choose) multiply it by 5, adding that to 3 and then subtracting from it the number given as the quotient of the numbers “6” and “4” — or more simply:  3 +5a – 6/4

### How do we “evaluate” a “variable expression”?

We use a process of substituting the number for each variable in the expression and then forming the basic operations of arithmetic – resulting in a numerical expression that is then evaluated

EX:  So, if “a” represents 2 in 5a + 3 then we have 5*2 +3 or 13 as the evaluation of the expression 5a + 3

### What then is “Algebra”?

“Generalized arithmetic” with letters used to stand for numbers. Some letters represent known values – other letters stand for unknown values

EX:  x = ax + b  x represents an unknown and a” and “b” known