Order of Operations Objective: Evaluate numerical and algebraic expressions by using the order of operations.

Evaluate Numerical Expressions To evaluate an expression means to find its value.

Example 1 Evaluate 26. 26 = 2 • 2 • 2 • 2 • 2 • 2 = 64

Check Your Progress Choose the best answer for the following. Evaluate 44. 64 128 192 256

  Order of Operations P Parenthesis E Exponents M Multiply and\or Divide, in order from left to right. Exponents Add and/or Subtract, in order from left to right.  

Example 2 Evaluate 48 ÷ 23 • 3 + 5. 48 ÷ 8 • 3 + 5 6 • 3 + 5 18 + 5 23

Check Your Progress Choose the best answer for the following. Evaluate [(92 – 9) ÷ 12]5. 6 15 30 45 When one or more grouping symbols are used, evaluate within the innermost grouping symbols first. = [(81 – 9) ÷ 12]5 = [72 ÷ 12]5 = [6]5

Example 3 Evaluate each expression. (8 – 3) • 3(3 + 2) 4[12 ÷ (6 – 2)]2 = 5 • 3(5) = 4[12 ÷ 4]2 = 5 • 15 = 4[3]2 = 75 = 4[9] = 36 When dealing with fractions, the numerator and denominator are both groups. Simplify each separately before dividing. = 2

Check Your Progress Choose the best answer for the following. Evaluate the expression 2(4 + 7) • (9 – 5). -60 66 88 68 = 2(11) • 4 = 22 • 4

Check Your Progress Choose the best answer for the following. Evaluate the expression 3[5 – 2 • 2]2. 9 18 108 3 = 3[5 – 4]2 = 3[1]2 = 3[1]

Check Your Progress Choose the best answer for the following. Evaluate 1 69/15 4 5/9

Evaluate Algebraic Expressions To evaluate an algebraic expression, replace the variables with their values. Then find the value of the numerical expression using the order of operations.

Example 4 Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2. 2(42 – 3) + 22 = 2(16 – 3) + 4 = 2(13) + 4 = 26 + 4 = 30

Check Your Progress Choose the best answer for the following. Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5. 6 28 36 10 = 33 – 22 + 5 = 27 – 4 + 5 = 23 + 5

Example 5 Each side of the Great Pyramid of Giza, Egypt, is a triangle. The base of each triangle once measured 230 meters. The height of each triangle once measured 187 meters. The area of a triangle is one-half the product of the base b and its height h. Write an expression that represents the area of one side of the Great Pyramid. ½ bh Find the area of one side of the Great Pyramid. ½ (230)(187) 115(187) 21,505 m2

Check Your Progress Choose the best answer for the following. Find the area of a triangle with a base of 123 feet and a height of 62 feet. 3813 ft2 7626 ft2 15,252 ft2 32 ft2 = ½ (123)(62) = 61.5(62)