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Use the order of operations to simplify expressions.

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.

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Use the order of operations to simplify expressions.

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  1. Objective Use the order of operations to simplify expressions.

  2. Vocabulary order of operations

  3. 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. Perform multiplication and division from left to right. Third: Perform addition and subtraction from left to right. Fourth:

  4. 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.

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

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

  7. 1 2 Check It Out! Example 1a Simplify the expression. 8 ÷ · 3

  8. Check It Out! Example 1b Simplify the expression. 5.4 – 32 + 6.2

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

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

  11. 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.

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

  13. Check It Out! Example 2b Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6

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

  15. 2(–4) + 22 42 – 9 –8 + 22 42 – 9 Example 3A: Simplifying Expressions with Other Grouping Symbols Simplify. 2(–4) + 22 42 – 9 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 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 Divide. 2

  16. Example 3B: Simplifying Expressions with Other Grouping Symbols Simplify. 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| Add within the absolute-symbols. 3|20| Write the absolute value of 20. 3 · 20 Multiply. 60

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

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

  19. Check It Out! Example 3c Simplify.

  20. 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

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 52 – (5 + 4) 2. |4 – 8| Lesson Quiz Simply each expression. 1. 2[5 ÷ (–6 – 4)] 3. 5  8 – 4 + 16 ÷ 22 Translate each word phrase into a numerical or algebraic expression. 4. 3 three times the sum of –5 and 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.

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