Lesson 1-2 Glencoe Algebra 1 Order of operations Lesson 1-2 Glencoe Algebra 1

Learning Goal You expressed algebraic expressions verbally. Evaluate numerical expressions and algebraic expressions by using the order of operations. Then/Now

Vocabulary evaluate – to find the value of order of operations – the rule which lets you know which operation to perform first. Vocabulary

26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 Use 2 as a factor 6 times. = 64 Multiply. Evaluate Expressions Evaluate 26. 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 Use 2 as a factor 6 times. = 64 Multiply. Answer: 64 Example 1

Evaluate 44. A. 64 B. 128 C. 192 D. 256 Example 1

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48 ÷ 23 ● 3 + 5 = 48 ÷ 8 ● 3 + 5 Evaluate powers. Use Order of Operations Evaluate 48 ÷ 23 ● 3 + 5. 48 ÷ 23 ● 3 + 5 = 48 ÷ 8 ● 3 + 5 Evaluate powers. = 6 ● 3 + 5 Divide 48 by 8. = 18 + 5 Multiply 6 and 3. = 23 Add 18 and 5. Answer: 23 Example 2

Evaluate [(92 – 9) ÷ 12]5. A. 6 B. 15 C. 30 D. 45 Example 2

(8 – 3) ● 3(3 + 2) = 5 ● 3(5) Evaluate inside parentheses. Expressions with Grouping Symbols A. Evaluate (8 – 3) ● 3(3 + 2). (8 – 3) ● 3(3 + 2) = 5 ● 3(5) Evaluate inside parentheses. = 5 ● 15 Multiply 3 by 5. = 75 Multiply 5 by 15. Answer: 75 Example 3

4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first. Expressions with Grouping Symbols B. Evaluate 4[12 ÷ (6 – 2)]2. 4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first. = 4(3)2 Evaluate expression in grouping symbol. = 4(9) Evaluate power. = 36 Multiply. Answer: 36 Example 3

Evaluate the power in the numerator. Expressions with Grouping Symbols C. Evaluate the power in the numerator. Multiply 6 and 2 in the numerator. Subtract 32 and 12 in the numerator. Example 3

Evaluate the power in the denominator. Expressions with Grouping Symbols Evaluate the power in the denominator. Multiply 5 and 3 in the denominator. Subtract from left to right in the denominator. Answer: 2 Example 3

A. Evaluate the expression 2(4 + 7) ● (9 – 5). B. 66 C. 88 D. 68 Example 3

B. Evaluate the expression 3[5 – 2 ● 2]2. C. 108 D. 3 Example 3

C. A. 1 B. C. 4 D. Example 3

Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2. Evaluate an Algebraic Expression Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2. 2(x2 – y) +z2 = 2(42 – 3) + 22 Replace x with 4, y with 3 and z with 2. = 2(16 – 3) + 22 Evaluate 42. = 2(13) + 22 Subtract 3 from 16. = 2(13) + 4 Evaluate 22. = 26 + 4 Multiply 2 and 13. = 30 Add. Answer: 30 Example 4

Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5. B. 28 C. 36 D. 10 Example 4

Write and Evaluate an Expression ARCHITECTURE Each side of the Great Pyramid at 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. Example 5

Write and Evaluate an Expression A. Write an expression that represents the area of one side of the Great Pyramid. Example 5

B. Find the area of one side of the Great Pyramid. Write and Evaluate an Expression B. Find the area of one side of the Great Pyramid. Replace b with 230 and h with 187. Multiply 230 by 187. Multiply by 43,010. Answer: The area of one side of the Great Pyramid is 21,505 m2. Example 5

Find the area of a triangle with a base of 123 feet and a height of 62 feet. A. 3813 ft2 B. 7626 ft2 C. 15,252 ft2 D. 32 ft2 Example 5

End of the Lesson

Homework p 13 #15-35 odd; #36-38; #39-53 odd; #65-68 Mixed Review 1