1-1 Expressions and Formulas

Order of Operations● What is the Order of Operations?

It is a set of rules to find the exact value of a numerical expression.

● Why do we use the Order of Operations?

A long time ago, people just decided on an order in which operations should be performed. It has nothing to do with magic or logic. It makes communication easier, and everyone comes up with the same answer. (MathForum.org/Dr.Math)

Order of Operations

● Use the phrase . . .

“Please Excuse My Dear Aunt Sally” to help remember the order in which to evaluate the expression.

● PEMDAS

P ● The P stands for parentheses and represents all grouping symbols.

● ( ), [ ], { }

● Simplify within the grouping symbols first.

● If there is more than one grouping symbol, simplify within the innermost symbol first.

E

● The E stands for exponents.

● Evaluate all powers.

M & D

● M & D stand for multiplication and division.

● You must simplify whichever comes first in the expression from left to right.

A & S● A & S stand for Addition and Subtraction

● You must simplify whichever comes first in the expression from left to right.

Example: Simplify

● P First, work inside the brackets.

Evaluate inside the parentheses first: 4 + 2 = 6.

Then raise 6 to the second power: 36.

Now perform addition and subtraction from left to right: 36 - 8 = 28, now 28 +3 = 31.

Brackets are done.

● M Multiply 31 by 4. ● Final answer is 124.

4 2 2 8 3 4

Algebraic Expressions

● An algebraic expression is an expression that contains at least one variable.

● You can evaluate an algebraic expression by replacing each variable with a value and then applying the Order of Operations.

Example: Evaluate a(5a + 2b) if a=3 and b=-2● Substitute the values into the expression.

● 3[5(3) + 2(-2)]

● Now apply the Order of Operations:

Inside the brackets, perform multiplication and division before addition and subtraction

● 5(3) = 15 and 2(-2)= -4

● 3[15 + -4] then 15 + -4 = 11

● 3[11] = 33

Formulas● Formula is a mathematical sentence that expresses

the relationship between certain quantities.

● If you know a value for every variable in the formula except one, you can find the value of the remaining variable.

● Examples of common formulas: A = lw

V= lwh

Example: Find the area of a rectangle if the length is 5 cm and the width is 9 cm.

● Apply the formula A = lw

● Substitute the values of the variables

● A = (5 cm)(9 cm)

● A = 45 cm squared