Actions with Algebraic Expressions

 Order  of Operations.

1. If the expression contains brackets, first calculate whatever is within the brackets and then work outward.

  2.  Working from left to right, do multiplication and division before addition and subtraction.

   To remember the order of operations, simply remember:

Multiplication, Division, Addition, Subtraction  or  "My Dear Aunt Sally"

    1) Properties of addition.

Commutative property: changing the order of addends does not change the sum.

Formula: a + c = c + a
Example: 2 + 4 = 4 + 2 = 6

Associative property: changing the grouping of addends does not change the sum.

Formula: (a + b) + c = a + (b + c)
Example: (3 + 6)+ 5 = 9 + 5=14; 3 + (6 + 5) = 3 + 11= 14  $$\Rightarrow$$(3 + 6) + 5 = 3 + (6 + 5)


2) Properties of multiplication.

Commutative property: changing the order of factors does not change the product.

Formula: a  c = c a
Example: 2 4 = 4 2 = 8; 3 7 = 7 3 = 21

Associative property: changing the grouping of factors does not change the product.

Formula: (a b) c = a (b c)
Example: (3 6) 5 = 18 5 = 90; 3 (6 5) = 3 30= 90 $$\Rightarrow$$(3 6) 5 = 3 (6 5)

Distributive property of multiplication over addition:

sum of two numbers times a third number equals product of the first

and third numbers plus product of the second and third numbers.

Formula: (a + b) c = a c + b c
Example: (2 + 3) 5 = 5 5 = 25; 2 5 + 3 5 = 10+15 = 25 $$\Rightarrow$$ (2 + 3) 5 = 2 5 + 3 5

Distributive property of multiplication over subtraction:

difference of two numbers times a third number equals product of the first

and third numbers minus product of the second and third numbers.

Formula: (a - b) c = a c - b c
Example: (6 - 3) 5 = 3 5 = 15 ; 6 5 - 3 5 = 30 - 15 = 15 $$\Rightarrow$$ (6 - 3) 5 = 6 5 - 3 5

Combined properties of addition and subtraction:

1)  a-b-c=(a-b)-c=(a-c)-b=a-(b+c)

2)  a+b-c=(a+b)-c=a+(b-c)=b+(a-c)