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Objective Use the order of operations to simplify expressions.

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**Helpful Hint Please Parentheses Excuse Exponents My Multiply Dear**

order of operations tells which operation to perform first. 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 B. 12 – ÷ 2

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**Simplify the expression.**

Check It Out! Example 1a Simplify the expression. 1 2 8 ÷ · 3

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Check It Out! Example 1b Simplify the expression. 5.4 –

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Check It Out! Example 1c Simplify the expression. –20 ÷ [–2(4 + 1)]

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**Example 2A: Evaluating Algebraic Expressions**

Evaluate the expression for the given value of x. 10 – x · 6 for x = 3

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**Example 2B: Evaluating Algebraic Expressions**

Evaluate the expression for the given value of x. 42(x + 3) for x = –2

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Check It Out! Example 2a Evaluate the expression for the given value of x. 14 + x2 ÷ 4 for x = 2

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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

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**HW p43 (24-41, 55, 56) 2 ? Lesson Check Last 5 minutes**

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Lesson Check Day 1 Simply each expression. 1. 2[5 ÷ (–6 – 4)] 2. 5 8 – ÷ 22

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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

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

3| ÷ 2|

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Check It Out! Example 3a Simplify. 5 + 2(–8) (–2) – 3 3

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Check It Out! Example 3b Simplify. |4 – 7|2 ÷ –3

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Check It Out! Example 3c Simplify.

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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 B. the difference of y and the product of 4 and

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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.

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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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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.

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**HW p43 (42-54, 60, 66, 68-70) 2 ? Lesson Check Last 5 minutes**

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Lesson Check Day 2 Simply each expression. 1. 52 – (5 + 4) |4 – 8| Translate each word phrase into a numerical or algebraic expression. 2. 3 three times the sum of –5 and n

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Order of Operations with Exponents and Integers

Order of Operations with Exponents and Integers

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