1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

Warm Up Simplify. 1. 42 2. |5 – 16| 3. –23 4. |3 – 7| 16 11 –8 4 1. 42 2. |5 – 16| 3. –23 4. |3 – 7| 16 11 –8 4 Translate each word phrase into a numerical or algebraic expression. 5. the product of 8 and 6 8  6 6. the difference of 10y and 4 10y – 4 Simplify each fraction. 16 2 8 56 1 7 7. 8. 8

Objective Use the order of operations to simplify expressions.

Vocabulary order of operations

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 grouping symbols. First: Second: Simplify powers and roots. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

Grouping symbols include parentheses ( ), brackets [ ], and braces { } Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, simplify the expression inside the innermost set first. Follow the order of operations within that set of grouping symbols and then work outward.

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 15 – 2 · 3 + 1 There are no grouping symbols. 15 – 6 + 1 Multiply. 10 Subtract and add from left to right. B. 12 – 32 + 10 ÷ 2 12 – 32 + 10 ÷ 2 There are no grouping symbols. 12 – 9 + 10 ÷ 2 Evaluate powers. The exponent applies only to the 3. 12 – 9 + 5 Divide. Subtract and add from left to right. 8

Simplify the expression. Check It Out! Example 1a Simplify the expression. 1 2 8 ÷ · 3 8 ÷ · 3 1 2 There are no grouping symbols. 16 · 3 Divide. 48 Multiply.

Check It Out! Example 1b Simplify the expression. 5.4 – 32 + 6.2 There are no grouping symbols. 5.4 – 32 + 6.2 5.4 – 9 + 6.2 Simplify powers. –3.6 + 6.2 Subtract 2.6 Add.

Check It Out! Example 1c Simplify the expression. –20 ÷ [–2(4 + 1)] There are two sets of grouping symbols. –20 ÷ [–2(4 + 1)] Perform the operations in the innermost set. –20 ÷ [–2(5)] Perform the operation inside the brackets. –20 ÷ –10 2 Divide.

Example 2A: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 10 – x · 6 for x = 3 10 – x · 6 First substitute 3 for x. 10 – 3 · 6 Multiply. 10 – 18 Subtract. –8

Example 2B: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 42(x + 3) for x = –2 42(x + 3) First substitute –2 for x. 42(–2 + 3) Perform the operation inside the parentheses. 42(1) 16(1) Evaluate powers. 16 Multiply.

Check It Out! Example 2a Evaluate the expression for the given value of x. 14 + x2 ÷ 4 for x = 2 14 + x2 ÷ 4 14 + 22 ÷ 4 First substitute 2 for x. 14 + 4 ÷ 4 Square 2. 14 + 1 Divide. 15 Add.

Check It Out! Example 2b Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6 (x · 22) ÷ (2 + 6) (6 · 22) ÷ (2 + 6) First substitute 6 for x. (6 · 4) ÷ (2 + 6) Square two. (24) ÷ (8) Perform the operations inside the parentheses. 3 Divide.

Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.

Example 3A: Simplifying Expressions with Other Grouping Symbols 2(–4) + 22 42 – 9 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 2(–4) + 22 42 – 9 –8 + 22 42 – 9 Multiply to simplify the numerator. –8 + 22 16 – 9 Evaluate the power in the denominator. Add to simplify the numerator. Subtract to simplify the denominator. 14 7 2 Divide.

Example 3B: Simplifying Expressions with Other Grouping Symbols 3|42 + 8 ÷ 2| The absolute-value symbols act as grouping symbols. 3|42 + 8 ÷ 2| Evaluate the power. 3|16 + 8 ÷ 2| Divide within the absolute-value symbols. 3|16 + 4| 3|20| Add within the absolute-symbols. 3 · 20 Write the absolute value of 20. 60 Multiply.

Evaluate the power in the denominator. Check It Out! Example 3a Simplify. 5 + 2(–8) (–2) – 3 3 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 5 + 2(–8) (–2) – 3 3 5 + 2(–8) –8 – 3 Evaluate the power in the denominator. 5 + (–16) – 8 – 3 Multiply to simplify the numerator. –11 Add. 1 Divide.

Check It Out! Example 3b Simplify. |4 – 7|2 ÷ –3 The absolute-value symbols act as grouping symbols. |4 – 7|2 ÷ –3 |–3|2 ÷ –3 Subtract within the absolute-value symbols. 32 ÷ –3 Write the absolute value of –3. 9 ÷ –3 Square 3. –3 Divide.

Check It Out! Example 3c Simplify. The radical symbol acts as a grouping symbol. Subtract. 3 · 7 Take the square root of 49. 21 Multiply.

You may need grouping symbols when translating from words to numerical expressions. Remember! Look for words that imply mathematical operations. difference subtract sum add product multiply quotient divide

Example 4: Translating from Words to Math Translate each word phrase into a numerical or algebraic expression. A. the sum of the quotient of 12 and –3 and the square root of 25 Show the quotient being added to . B. the difference of y and the product of 4 and Use parentheses so that the product is evaluated first.

Check It Out! Example 4 Translate the word phrase into a numerical or algebraic expression: the product of 6.2 and the sum of 9.4 and 8. Use parentheses to show that the sum of 9.4 and 8 is evaluated first. 6.2(9.4 + 8)

Example 5: Retail Application A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the expression 2B + 4S + 7D. On Friday the shop wrapped 10 Basic packages B, 6 Super packages S, and 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday.

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

First substitute values for each variable. Check It Out! Example 5 Another formula for a player's total number of bases is Hits + D + 2T + 3H. Use this expression to find Hank Aaron's total bases for 1959, when he had 223 hits, 46 doubles, 7 triples, and 39 home runs. Hits + D + 2T + 3H = total number of bases First substitute values for each variable. 223 + 46 + 2(7) + 3(39) 223 + 46 + 14 + 117 Multiply. 400 Add. Hank Aaron’s total number of bases for 1959 was 400.

Lesson Quiz Simplify each expression. 2. 52 – (5 + 4) |4 – 8| 1. 2[5 ÷ (–6 – 4)] –1 4 3. 5  8 – 4 + 16 ÷ 22 40 Translate each word phrase into a numerical or algebraic expression. 4. 3 three times the sum of –5 and n 3(–5 + n) 5. the quotient of the difference of 34 and 9 and the square root of 25 6. the volume of a storage box can be found using the expression l · w(w + 2). Find the volume of the box if l = 3 feet and w = 2 feet. 24 cubic feet