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**1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz**

Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

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**Warm Up Simplify. 1. 42 2. |5 – 16| 3. –23 4. |3 – 7| 16 11 –8 4**

|5 – 16| – |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

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Objective Use the order of operations to simplify expressions.

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Vocabulary order of operations

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**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: Evaluate powers. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

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**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, evaluate the expression from the innermost set first.

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**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

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**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 – ÷ 2 12 – ÷ 2 There are no grouping symbols. 12 – ÷ 2 Evaluate powers. The exponent applies only to the 3. 12 – 9 + 5 Divide. Subtract and add from left to right. 8

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**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.

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

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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.

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**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

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**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.

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

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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.

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

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**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.

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**Example 3B: Simplifying Expressions with Other Grouping Symbols**

3| ÷ 2| The absolute-value symbols act as grouping symbols. 3| ÷ 2| Evaluate the power. 3| ÷ 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.

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**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.

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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.

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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.

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**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

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**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.

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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( )

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**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.

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

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**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. (7) + 3(39) Multiply. 400 Add. Hank Aaron’s total number of bases for 1959 was 400.

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Lesson Quiz Simply each expression. 2. 52 – (5 + 4) |4 – 8| 1. 2[5 ÷ (–6 – 4)] –1 4 3. 5 8 – ÷ 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

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