Objective Use the order of operations to simplify expressions.

When a numerical or algebraic expression contains more than one operation symbol, the order of operations tells which operation to perform first. Order of Operations Perform operations inside parentheses. First: Second: Evaluate powers/exponents. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

Helpful Hint The first letter of these words can help you remember the order of operations. Please Excuse My Dear Aunt Sally Parentheses Exponents Multiply Divide Add Subtract

Example 1: Translating from Algebra to Words Simplify each expression. A. 15 – 2 · 3 + 1 There are no parentheses or exponents. 15 – 2 · 3 + 1 15 – 6 + 1 Multiply before you add/subtract. 9 + 1 = 10 Subtract and add from left to right. B. 12 + 32 - 10 ÷ 2 12 + 32 - 10 ÷ 2 There are no parentheses. 12 + 9 - 10 ÷ 2 Do exponents. Only to the 3. 12 + 9 - 5 Divide before you add/subtract. 21 – 5 = 16 Add and subtract from left to right.

Check It Out! Example 1c Simplify the expression. There are two sets of parentheses –20 ÷ [–2(4 + 1)] Do what is in the innermost parentheses first Next do what is in the remaining set of parentheses –20 ÷ [–2(4 + 1)] –20 ÷ [–2(5)] –20 ÷ –10 Divide. 2

Example 3A: Simplifying Expressions with Other Grouping Symbols When there is a fraction bar, do everything on the top and then everything on the bottom. 2(–4) + 22 42 – 9 2(–4) + 22 42 – 9 Multiply, then add to simplify the numerator. –8 + 22 42 – 9 14 42 – 9 Do the exponent, then subtract to simplify the numerator. 14 16 – 9 14 7 = 2 Divide.

Check It Out! Example 3b Simplify. |4 – 7|2 ÷ –3 The absolute-value symbols act like parentheses (do what is inside them first). |4 – 7|2 ÷ –3 |–3|2 ÷ –3 Now perform the operation of absolute value. 32 ÷ –3 Next do the exponent 9 ÷ –3 Divide. –3

Check It Out! Example 3c Simplify. Square roots act like parentheses too (Do what is inside it first) Then find the square root. 3 · 7 Multiply. 21

Example 5: Retail Application A store offers gift-wrapping at three price levels. The amount of money made from wrapping gifts each day can be found using 2B + 4S + 7D. On Friday the store wrapped 10 Basic (B) packages, 6 Super (S) packages, and 5 Deluxe (D) packages. Use the expression to find how much money the store made from gift wrapping on Friday. (Plug in the values for B, S, and D to solve.)

Example 5 Continued 2B + 4S + 7D First substitute the value for each variable. 2(10) + 4(6) + 7(5) 20 + 24 + 35 Multiply the three pieces. 44 + 35 Add from left to right. 79 The store made $79 from gift wrapping on Friday.