6.1.3 Order of Operations

Vocabulary Numerical Expression – Only contains numbers and operations. Evaluate – Find the value of (solve) a numerical expression Order of Operations – Steps to follow in solving a numerical expression with multiple operations “Evaluate” and “find the value of” mean the same thing and are used interchangeably.

PEMDAS PEMDAS, or Please Excuse My Dear Aunt Sally P = Parentheses IMPORTANT! Multiplication and division are evaluated LEFT to RIGHT when not in parentheses. Same goes for addition and subtraction. So think of PEMDAS like this: PE[MD][AS] Multiplication and division still come before addition and subtraction but within MD do whichever one you see first in reading the problem left to right. PEMDAS, or Please Excuse My Dear Aunt Sally P = Parentheses E = Exponents M = Multiplication D = Division A = Addition S = Subtraction

Why It’s Important Let’s say you received $20 for your birthday from your Aunt Ruby. And then your Aunt Mary wanted to show off so she gave you twice as much. Then, you spent $10 to go to the movies. How much money do you have left? Numerical expression: 20 + (20 x 2) – 10 20 + 40 – 10 60 – 10 50 You have $50 left from your birthday money.

Without following the PEMDAS Rules… Let’s say you received $20 for your birthday from your Aunt Ruby. And then your Aunt Mary wanted to show off so she gave you twice as much. Then, you spent $10 to go to the movies. How much money do you have left? Numerical expression: 20 + (20 x 2) – 10 20 + 20 x 2 – 10 20 + 40 – 10 40 x 2 – 10 60 – 10 80 – 10 50 70

Some Practice With PEMDAS Evaluate: 12 – 2 x 4 7 + 60 ÷ (3 x 5) 12 – 8 7 + 60 ÷ 15 4 7 + 4 11

PEMDAS with Exponents Remember to read LEFT to RIGHT when evaluating multiplication and division outside of parenthesis. Same goes for addition and subtraction. Do the operation that comes first. So in this instance when we get to this point, even though M comes before D in PEMDAS, you do the D first because it comes first reading left to right and neither operation is inside parentheses. INCORRECT CORRECT 30 ÷ (7 + 2³) x 6 30 ÷ (7+2³) x 6 30 ÷ (7 + 8) x 6 30 ÷ (7 + 8) x 6 30 ÷ 15 x 6 30 ÷ 15 x 6 30 ÷ 90 2 x 6 .333333 12

Independent Practice Evaluate the following expressions: 7 x 5 + 3 4 x 3² + 18 – 9 6 + 2⁴ - 1 6 x 15 – 10 ÷ 2 (28 – 20) ÷ 4 16 + (5² - 7) ÷ 3

Homework Pg. 20 (#1, 5, 10, 12, 13, 14, 15, 20, 21, 23)