Holt Algebra Order of Operations Warm Up Simplify |5 – 16| 3. – |3 – 7| 16 –8 4 Translate each word phrase into a numerical or algebraic expression. 5. the product of 8 and 6 6. the difference of 10y and 4 8  6 10y – 4 11 Simplify each fraction

Holt Algebra Order of Operations Use the order of operations to simplify expressions. Objective

Holt Algebra 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. First: Second: Third: Fourth: Perform operations inside grouping symbols. Evaluate powers. Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Order of Operations

Holt Algebra Order of Operations Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.

Holt Algebra Order of Operations 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

Holt Algebra Order of Operations Simplify each expression. A. 15 – 2 · – 2 · – There are no grouping symbols. Multiply. Subtract and add from left to right. B. 12 – ÷ 2 12 – ÷ 2 12 – ÷ 2 12 – There are no grouping symbols. Evaluate powers. The exponent applies only to the 3. Divide. Subtract and add from left to right. Example 1: Translating from Algebra to Words

Holt Algebra Order of Operations 8 ÷ · 3 There are no grouping symbols. Divide. 48 Multiply. Check It Out! Example 1a Simplify the expression ÷ · · 3

Holt Algebra Order of Operations 5.4 – There are no grouping symbols. 5.4 – Simplify powers. – Subtract Add. Check It Out! Example 1b Simplify the expression.

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

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

Holt Algebra Order of Operations Evaluate the expression for the given value of x. 4 2 (x + 3) for x = –2 4 2 (x + 3) 4 2 (–2 + 3) 42(1)42(1) 16(1) 16 First substitute –2 for x. Perform the operation inside the parentheses. Evaluate powers. Multiply. Example 2B: Evaluating Algebraic Expressions

Holt Algebra Order of Operations Evaluate the expression for the given value of x x 2 ÷ 4 for x = 2 Check It Out! Example 2a 14 + x 2 ÷ ÷ ÷ First substitute 2 for x. Square 2. Divide. Add.15

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

Holt Algebra Order of Operations Simplify. 2(–4) – 9 2(–4) – 9 – – 9 – – Example 3A: Simplifying Expressions with Other Grouping Symbols The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. Multiply to simplify the numerator. Evaluate the power in the denominator. Add to simplify the numerator. Subtract to simplify the denominator. Divide.

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

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

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

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

Holt Algebra Order of Operations 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

Holt Algebra Order of Operations 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.

Holt Algebra Order of Operations 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 ( ) Use parentheses to show that the sum of 9.4 and 8 is evaluated first.

Holt Algebra Order of Operations 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 (7) + 3(39) First substitute values for each variable. Multiply. 400 Add. Hank Aaron ’ s total number of bases for 1959 was 400.