A#17 / 1-5 Homework Worksheet Homework Corrections A#17 / 1-5 Homework Worksheet 1. a) 11 b) 20 c) -10 2. 11 yd 3. a) real number, ; rational number, b) real number, ; rational number, ; integer, 3. c) real number, ; irrational number 4. a) b) c) 5. a) always true b) sometimes true c) always true

Warm Up Simplify. 1. 42 2. -23 3. |5 – 16| 4. |3 – 7| 1. 42 2. -23 3. |5 – 16| 4. |3 – 7| Simplify each fraction. 5. 6.

Lesson Objective: I will be able to … Page 22 Lesson Objective: I will be able to … Use the order of operations to simplify expressions Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

When a numerical or algebraic expression contains more than one operation symbol, the order of operations tells which operation to perform first. Page 22 Order of Operations First: Perform operations inside grouping symbols. Second: Evaluate powers. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

Helpful Hint The first letter of these words can help you Page 22 Helpful Hint The first letter of these words can help you remember the order of operations. Please Excuse My Dear Aunt Sally Parentheses Exponents Multiply and Divide (from left to right) Add and Subtract (from left to right 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.

Example 1: Simplifying Numerical Expressions Page 23 Simplify each expression. A. 15 – 2 · 3 + 1 There are no parentheses or exponents. 15 – 2 · 3 + 1 Multiply. = 15 – 6 + 1 Subtract and add from left to right. = 10 B. 12 – 32 + 10 ÷ 2 There are no parentheses. 12 – 32 + 10 ÷ 2 Evaluate exponents. = 12 – 9 + 10 ÷ 2 Divide. = 12 – 9 + 5 Subtract and add from left to right. = 8

Simplify the expression. Your Turn 1 Page 23 Simplify the expression. 5.4 – 32 + 6.2 There are no parentheses. = 5.4 – 32 + 6.2 Simplify exponents = 5.4 – 9 + 6.2 Subtract and add from left to right. = –3.6 + 6.2 = 2.6

Example 2: Evaluating Algebraic Expressions Page 23 Evaluate the expression for the given value of x. 42(x + 3) for x = –2 = 42(–2 + 3) First substitute –2 for x. = 42(1) Perform the operation inside the parentheses. = 16(1) Evaluate powers. = 16 Multiply.

Evaluate the expression for the given value of x. Your Turn 2 Page 24 Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6 = (6 · 22) ÷ (2 + 6) First substitute 6 for x. = (6 · 4) ÷ (2 + 6) Square two. = (24) ÷ (8) Perform the operations inside the parentheses. = 3 Divide.

Example 3: Simplifying Expressions with Other Grouping Symbols Page 24 2(–4) + 22 42 – 9 Simplify: –8 + 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. 14 7 Add to simplify the numerator. Subtract to simplify the denominator. 2 Divide.

Your Turn 3 Simplify: |4 – 7|2 ÷ (–3) = |–3|2 ÷ –3 = 32 ÷ –3 = 9 ÷ –3 Page 24 Simplify: |4 – 7|2 ÷ (–3) The absolute-value symbols act as grouping symbols. Subtract within the absolute-value symbols. = |–3|2 ÷ –3 = 32 ÷ –3 Write the absolute value of –3. = 9 ÷ –3 Square 3. = –3

Example 4: Translating from Words to Math Page 25 Translate each word phrase into a numerical or algebraic expression. A. The sum of the quotient of 12 and –3 and the square root of 25 Show the quotient being added to . B. The difference of y and the product of 4 and Use parentheses so that the product is evaluated first.

Translate the word phrase into a numerical or algebraic expression: Your Turn 4 Page 25 Translate the word phrase into a numerical or algebraic expression: 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)

Cornell Notes Fill in the Essential Question: “How do I simplify expressions using the order of operations?” Write two or three main ideas from this lesson in the Notes section. Write a Question for each main idea. (The answer to the question should be the main idea.) Summarize the answers to your questions in the Summary section. Page 26

Classwork Ladder Activity: Order of Operations

Homework Assignment #18 Finish 1-6 Homework Worksheet Chapter 1 Quiz Friday!