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Simplifying Expressions Using Order of Operations

Learn how to simplify expressions by following the order of operations, including evaluating powers, grouping symbols, and more. Practice problems with step-by-step solutions provided.

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Simplifying Expressions Using Order of Operations

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  1. Warm Up 8/12/09

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

  3. Vocabulary order of operations

  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. Directions: Simplify using the Order of Operations Copy Each Problem and EACH Step

  6. Example 1 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. 8 ÷ · 3 1 2 1 2 Example 2 8 ÷ · 3 There are no grouping symbols. 16· 3 Divide. 48 Multiply.

  8. Example 3 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.

  9. Example 4 –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.

  10. Directions: Evaluate each Expression Using the Order of Operations Copy each problem and each step.

  11. Example 5 10 – x · 6 for x = 3 First substitute 3 for x. 10 –x · 6 10 – 3 · 6 Multiply. Subtract. 10 – 18 –8

  12. Example 6 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.

  13. Example 7 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.

  14. Example 8 (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. Perform the operations inside the parentheses. (24) ÷ (8) 3 Divide.

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

  16. 2(–4) + 22 42 – 9 –8 + 22 42 – 9 Example 9 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

  17. 5 + 2(–8) (–2) – 3 3 5 + 2(–8) –8 – 3 5 + (–16) – 8 – 3 –11 –11 Example 10 Simplify. 5 + 2(–8) (–2) – 3 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 3 Evaluate the power in the denominator. Multiply to simplify the numerator. Add. Divide. 1

  18. Translate From Words To Math Copy each problem and solution.

  19. Example 11 The quotient of -2 and the sum of -4 and x Use parentheses to show that the sum of -4 and x is evaluated first.

  20. Example 12 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)

  21. 52 – (5 + 4) 2. |4 – 8| Lesson Summary Simply each expression. 1. 2[5 ÷ (–6 – 4)] –1 4 3. 5  8 – 4 + 16 ÷ 22 40 Translate each word phrase into a numerical or algebraic expression. 3(–5 + n) 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

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