Week+8

=Pre/Alg=

10/9

In the last lesson, we learned how to evaluate an arithmetic expression with more than one operation according to the following rules: > || **Rule 1:** || Simplify all operations inside parentheses. || > || **Rule 2:** || Perform all multiplications and divisions, working from left to right. || > || **Rule 3:** || Perform all additions and subtractions, working from left to right. || However, the problem above includes an exponent, so we cannot solve it without revising our rules. > || **Rule 1:** || Simplify all operations inside parentheses. || > || **Rule 2:** || Simplify all exponents, working from left to right. || > || **Rule 3:** || Perform all multiplications and divisions, working from left to right. || > || **Rule 4:** || Perform all additions and subtractions, working from left to right. || We can solve the problem above using our revised order of operations. Let's look at some other examples that involve our new rules for order of operations.
 * Problem: || Evaluate this arithmetic expression: 18 + 36 ** ÷ ** 3 2 ||
 * Problem: || Evaluate this arithmetic expression 18 + 36 ** ÷ ** 3 2 ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Solution: || || 18 + 36 ** ÷ ** **3 2 ** || = 18 + 36 ** ÷ ** 9 || Simplify all exponents (Rule 2) ||
 * 18 + **36 ** ÷ ** 9** || = 18 + 4 || Division (Rule 3) ||
 * 18 + 4 || = 22 || Addition (Rule 4) || ||
 * Example 1: || Evaluate 5 2 x 2 4 ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Solution: || || **5 2 ** x 2 4 || = 25 x 2 4 || Simplify all exponents, working from left to right (Rule 2) ||
 * 25 x **2 4 ** || = 25 x 16 ||^  ||
 * 25 x 16 || = 400 || Multiplication (Rule 3) || ||


 * Example 2: || Evaluate 289 - (3 x 5) 2 ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Solution: || || 289 - **(3 x 5)** 2 || = 289 - 15 2 || Simplify all operations inside parentheses (Rule 1) ||
 * 289 - **15 2 ** || = 289 - 225 || Simplify all exponents (Rule 2) ||
 * 289 - 225 || = 64 || Subtraction (Rule 4) || ||


 * Example 3: || Evaluate 8 + (2 x 5) x 3 4 ** ÷ ** 9 ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Solution: || || 8 + **(2 x 5)** x 3 4 ** ÷ ** 9 || = 8 + 10 x 3 4 ** ÷ ** 9 || Simplify all operations inside parentheses (Rule 1) ||
 * 8 + 10 x **3 4 ** ** ÷ ** 9 || = 8 + 10 x 81 ** ÷ ** 9 || Simplify all exponents (Rule 2) ||
 * 8 + **10 x 81** ** ÷ ** 9 || = 8 + 810 ** ÷ ** 9 || Perform all multiplications and divisions, working from left to right (Rule 3) ||
 * 8 + **810 ** ÷ ** 9** || = 8 + 90 ||^  ||
 * 8 + 90 || = 98 || Addition (Rule 4) || ||


 * Example 4: || An interior decorator charges $15 per square foot to lay a carpet, and an installation fee of $150. If the room is square and each side measures 12 feet, how much will it cost to carpet it? ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Solution: || If one side of the square-shaped room is 12 feet, then the area of the room is (12 feet) 2 . ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * || || 15 x **12** 2 + 150 || = 15 x 144 + 150 || Simplify all exponents (Rule 2) ||
 * **15 x 144** + 150 || = 2,160 + 150 || Multiplication (Rule 3) ||
 * 2,160 + 150 || = 2,310 || Addition (Rule 4) || ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * Answer: || It will cost $2,310 to carpet this room. ||


 * Summary: || To help us remember the order of operations, we can use the mnemonic **PEMDAS**, which stands for: ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * || || **P**lease || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **E**xcuse || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **M**y || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **D**ear || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **A**unt || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **S**ally || ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * || [[image:http://www.mathgoodies.com/lessons/vol7/images/aunt_sally.gif width="100" height="80"]] ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * || || **P**arentheses, || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] || **E**xponents, || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] |||| **M**ultiplication & **D**ivision, || [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="2" caption=" "]] |||| **A**ddition & **S**ubtraction || ||
 * [[image:http://www.mathgoodies.com/lessons/vol7/images/tab.gif width="10" height="3" caption=" "]] ||
 * || Note that although there are six words, they correspond to four rules. ||

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Work Sheet #3

10/11