Warm Up Evaluate. 1. 4 2

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

2. Vocabulary order of operations terms like terms coefficient

3. When an expression contains more than one operation, the order of operations tells you which operation to perform first.

4. Order of Operations First: Perform operations inside grouping symbols. Second: Evaluate powers. Third: Perform multiplication and division from left to right. Fourth: Perform addition and subtraction from left to right.

5. Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, begin with the innermost set. Follow the order of operations within that set of grouping symbols and then work outward.

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

7. Additional Example 1: Simplifying Numerical Expressions Simplify each expression. A. 15 – 2  3 + 1 There are no grouping symbols. 15 – 2  3 + 1 Multiply. 15 – 6 + 1 Subtract. 9 +1 10 Add. B. 12 + 32 + 10 ÷ 2 12 + 32+ 10 ÷ 2 There are no grouping symbols. 12 + 9 + 10 ÷ 2 Evaluate powers. The exponent applies only to the 3. 12 + 9 + 5 Divide. 26 Add.

8. Additional Example 1: Simplifying Numerical Expressions Simplify each expression. C. The fraction bar is a grouping symbol. Evaluate powers. The exponent applies only to the 4. Multiply above the bar and subtract below the bar. Add above the bar and then divide.

9. Partner Share! Example 1a Simplify the expression. There are no grouping symbols. Rewrite division as multiplication. Multiply. 48

10. Partner Share! Example 1b Simplify the expression. The square root sign acts as a grouping symbol. Subtract. 3  7 Take the square root. 21 Multiply.

11. Partner Share! Example 1c Simplify the expression. The division bar acts as a grouping symbol. Add and evaluate the power. Multiply, subtract and simplify.

12. Additional Example 2: 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 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. 2B + 4S +7D 2(10) + 4(6) + 7(5) Substitute values for variables. 20 + 24 + 35 Multiply. 79 Add. A total of $79 was collected on Friday.

13. Partner Share! Example 2 A 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 223 + 46 + 2(7) + 3(39) Substitute values for variables. 223 + 46 + 14 + 117 Multiply. 400 Add. Hank Aaron’s total number of bases for 1959 was 400.

14. The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x – 3x + 2

15. A coefficientis a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x

16. Distributive Property Example 7x – 4x = (7 – 4)x ax – bx = (a – b)x = 3x Like terms can be combined. To combine like terms, use the Distributive Property. Notice that you can combine like terms by adding or subtracting the coefficients. Keep the variables and exponents the same.

18. Additional Example 1: Identifying Properties Name the property that is illustrated in each equation. A. 7(mn) = (7m)n The grouping is different. Associative Property of Multiplication B. (a + 3) + b = a + (3 + b) The grouping is different. Associative Property of Addition C. x + (y + z) = x + (z + y) The order is different. Commutative Property of Addition

19. Partner Share! Example 1 Name the property that is illustrated in each equation. The order is different. a. n + (–7) = –7 + n Commutative Property of Addition b. 1.5 + (g + 2.3) = (1.5 + g) + 2.3 The grouping is different. Associative Property of Addition The order is different. c. (xy)z = (yx)z Commutative Property of Multiplication

20. Additional Example 3: Combining Like Terms Simplify the expression by combining like terms. A. 72p – 25p 72p –25p 72p and 25p are like terms. 47p Subtract the coefficients.

21. and are like terms. Write 1 as . Additional Example 3: Combining Like Terms Simplify the expression by combining like terms. B. A variable without a coefficient has a coefficient of 1. Add the coefficients.

22. Additional Example 3: Combining Like Terms Simplify the expression by combining like terms. C. 0.5m + 2.5n 0.5m+ 2.5n 0.5m and 2.5n are not like terms. 0.5m + 2.5n Do not combine the terms.

23. Caution! Add or subtract only the coefficients. 6.8y² – y² ≠ 6.8

24. 2m2 + m3 Partner Share! Example 3 Simplify by combining like terms. a. 16p + 84p 16p + 84p 16p + 84p are like terms. 100p Add the coefficients. b. –20t – 8.5t –20t – 8.5t 20t and 8.5t are like terms. –28.5t Subtract the coefficients. c. 3m2 + m3 – m2 3m2–m2+ m3 3m2 and – m2are like terms. Subtract coefficients.

25. Additional Example 4: Simplifying Algebraic Expressions Use properties and operations to show that 14x + 4(2 + x) simplifies to 18x + 8. Statements Reasons 1. 14x + 4(2 + x) 2. 14x + 4(2) + 4(x) Distributive Property 3. 14x + 8 + 4x Multiply. 4. 14x + 4x + 8 Commutative Property of Addition 5. (14x + 4x) + 8 Associative Property of Addition 6. 18x + 8 Combine like terms.

26. Partner Share! Example 4 Use properties and operations to show that 6(x – 4) + 9 simplifies to 6x – 15. Statements Reasons 1. 6(x – 4)+ 9 2. 6x – 6(4) + 9 Distributive Property 3. 6x – 24 + 9 Multiply. 4. 6x – 15 Combine like terms.