Associative Property

The addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parentheses indicates the terms that are considered one unit.The groupings (Associative Property) are within the parentheses. Hence, the numbers are 'associated' together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations.

Addition Example:

When we change the groupings of addends, the sum does not change:
(2 + 5) + 4 = 11 or 2 + (5 + 4) = 11
(9 + 3) + 4 = 16 or 9 + (3 + 4) = 16
Just remember that when the grouping of addends changes, the sum remains the same.

Multiplication Example:

When we change the groupings of factors, the product does not change:
(3 x 2) x 4 = 24 or 3 x (2 x 4) = 24.
Just remember that when the grouping of factors changes, the product remains the same.

Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product.

Equation

A mathematical statement that two expressions are equal.

Solution

The number that makes the equation true.

Single Step Equations

• Make sure both expressions are equal to each other, what you do to one side you must do to the other side
• You want to get "x" (the variable) all by itself,  i.e. x = ?
• Undo what has been done to the variable, i.e. dividing with multiplication, addition with subtraction and vice versa

Algebraic Expressions

13x   → x multiplied by 13 (multiplication)

5 - y → the difference of 5 and y (subtraction)  

 ^x/₃    → the quotient of x and 3 (division, addition)

(x + 9) / x → the ratio of 9 more than x to x (division, addition)

(n + 2) – 9 → nine less than the total of a number and two (subtraction)

 x-4   → 4 less than x (subtraction)

8+y   → the sum of 8 and y (addition)

Addition                           Subtraction                   Multiplication                 Division  

plus                                  minus                             times                              divide

sum                                  difference                      product                          quotient

more than                        less than                        twice                              ratio

increased by                    decreased by                 multiplied by                 divided by

Two Step Equations

• Order of Operations (PEMDAS)
  • Perform all operations within grouping symbols, i.e. parentheses
  • Do all multiplication in order which they occur, left to right
  • Do all additions and subtractions in order which they occur, left to right
• Make sure both expressions are equal to each other, what you do to one side you must do to the other side
• You want to get "x" (the variable) all by itself,  i.e. x = ?
• Undo what has been done to the variable, i.e. dividing with multiplication, addition with subtraction and vice versa