Rules of Mathematical Operations

Simplest Form

A fraction is in simplest form when Greatest Common Factor (GCF) of the numerator and denominator is 1.

Expression

A mathematical phrase that contains operations, numbers, and/or variables and doesn't have an equal sign. For example, 4x+7

Equation

A mathematical sentence that contains an equal sign. For example, 4x+5=2

Terms

A number, a variable, or a product of numbers and variables.

Variable

A placeholder for a piece of information that can change. Usually represented by a letter. For example in the expression 3x+2, the variable is x.

Solution

A value for a variable that makes an equation true. For example, m=9

Like Terms

Expressions that contain the same variables. For example 2x and 4x are like terms. 3y and 7y are also like terms

Inverse Operations

Operations that undo each other. + (addition) undoes - (subtraction) and x (multiplication) undoes / (division)

Evaluate

Replacing the variables with numbers and finding numerical value of the expression

Parentheses

Used in mathematics as grouping symbols for operations. When simplifying an expression, the operations within the parentheses are performed first. For example, (7+9) x 3, first you add 7+9...

Commutative Property of Addition and Multiplication

a math rule that says that the order in which we add or multiply numbers does not change the product. For example, 3+4 is the same as 4+3 and 3x4 is the same as 4x3

Identity Property of multiplication

any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. For example, 32x1=32.

Distributive Property of Multiplication OVER Addition or Subtraction

is applied when you multiply a value by a sum. For example, you want to solve 5(10+3). The multiplication of 5(10) and 5(3) will be performed before you add. 5(10) + 5(3) = 50 + 15 = 65

Multiplicative Property of Zero

says that the product of 0 and any number is 0. For example, 2x0=0

Identity Property of Addition

says that the sum of 0 and any number is that number. For example, 2+0=2

Order of Operations or PEMDAS

the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponents 3. multiplication and division 4. addition and subtraction (PEMDAS)

Associative Property of Addition

the sum of three or more numbers remains the same regardless of how the numbers are grouped, for example 2+3+4 is the same as 3+2+4

Associative Property of Multiplication

the way in which factors are grouped in a multiplication problem does not change the product, for example 3x2x4 is the same as 2x3x4