1. Holt Algebra 1 1-6 Order of Operations Warm Up 8/12/09

2. Holt Algebra 1 1-6 Order of Operations Use the order of operations to simplify expressions. Objective

3. Holt Algebra 1 1-6 Order of Operations order of operations Vocabulary

4. Holt Algebra 1 1-6 Order of Operations

5. Holt Algebra 1 1-6 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.

6. Holt Algebra 1 1-6 Order of Operations Directions: Simplify using the Order of Operations Copy Each Problem and EACH Step

7. Holt Algebra 1 1-6 Order of Operations 12 – 3 2 + 10 ÷ 2 12 – 9 + 10 ÷ 2 12 – 9 + 5 8 There are no grouping symbols. Evaluate powers. The exponent applies only to the 3. Divide. Subtract and add from left to right. Example 1

8. Holt Algebra 1 1-6 Order of Operations 8 ÷ · 3 There are no grouping symbols. Divide. 48 Multiply. Example 2 1212 8 ÷ · 3 1212 16 · 3

9. Holt Algebra 1 1-6 Order of Operations 5.4 – 3 2 + 6.2 There are no grouping symbols. 5.4 – 9 + 6.2 Simplify powers. –3.6 + 6.2 2.6 Subtract Add. Example 3

10. Holt Algebra 1 1-6 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. Example 4

11. Holt Algebra 1 1-6 Order of Operations Directions: Evaluate each Expression Using the Order of Operations Copy each problem and each step.

12. Holt Algebra 1 1-6 Order of Operations Example 5 10 – x · 6 for x = 3 10 – x · 6 10 – 3 · 6 10 – 18 –8 First substitute 3 for x. Multiply. Subtract.

13. Holt Algebra 1 1-6 Order of Operations 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 6

14. Holt Algebra 1 1-6 Order of Operations 14 + x 2 ÷ 4 for x = 2 Example 7 14 + x 2 ÷ 4 14 + 2 2 ÷ 4 14 + 4 ÷ 4 14 + 1 First substitute 2 for x. Square 2. Divide. Add.15

15. Holt Algebra 1 1-6 Order of Operations (x · 2 2 ) ÷ (2 + 6) for x = 6 Example 8 (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.

16. Holt Algebra 1 1-6 Order of Operations Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.

17. Holt Algebra 1 1-6 Order of Operations Simplify. 2(–4) + 22 4 2 – 9 2(–4) + 22 4 2 – 9 –8 + 22 4 2 – 9 –8 + 22 16 – 9 14 7 2 Example 9 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.

18. Holt Algebra 1 1-6 Order of Operations Example 10 Simplify. 5 + 2(–8) (–2) – 3 3 5 + 2(–8) –8 – 3 5 + 2(–8) (–2) – 3 3 5 + (–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.

19. Holt Algebra 1 1-6 Order of Operations Translate From Words To Math Copy each problem and solution.

20. Holt Algebra 1 1-6 Order of Operations 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.

21. Holt Algebra 1 1-6 Order of Operations Example 12 The product of 6.2 and the sum of 9.4 and 8. 6.2(9.4 + 8) Use parentheses to show that the sum of 9.4 and 8 is evaluated first.

22. Holt Algebra 1 1-6 Order of Operations Lesson Summary Simply each expression. 1. 2[5 ÷ (–6 – 4)] 2. 5 2 – (5 + 4) |4 – 8| 3. 5  8 – 4 + 16 ÷ 2 2 –14 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