Lesson 1 1 Core Focus on Linear Equations

Lesson 1. 1 Core Focus on Linear Equations Order of Operations

Warm-Up Write each power in expanded form. Find its value. 1. 92 9 × 9 = 81 2. 23 2× 2× 2=8 3. 15 1× 1× 1=1 4. (– 7)2 (– 7) = 49 5. (− 3)3 (– 3) = – 27

Lesson 1. 1 Order of Operations Find the value of expressions using the order of operations.

Vocabulary Order of Operations A set of rules which are followed when evaluating an expression with more than one operation. Absolute Value The distance a number is from zero. The absolute value of a number is always positive. Good to Know! The notation for absolute value is | x |, which says “the absolute value of x. ”

Order of Operations 1. Find the value of expressions inside grouping symbols such as parentheses, absolute value bars and fraction bars. 2. Find the value of all powers. 3. Multiply and divide from left to right. 4. Add and subtract from left to right.

Example 1 Find the value of the expression. a. 8(− 3+7) – 2 ∙ 5 Add the integers inside the parentheses. 8(– 3+7) – 2 ∙ 5 = 8(4) – 2 ∙ 5 Multiply from left to right. = 32 – 10 Subtract. = 22

Example 1 Find the value of the expression. b. 52 + |3 – 8| ÷ 5 Subtract inside the absolute value bars. 52 + |3 – 8| ÷ 5 = 52 + |– 5| ÷ 5 Make the value inside the bars positive. = 52 + 5 ÷ 5 Find the value of the power. = 25 + 5 ÷ 5 Divide. = 25 + 1 Add. = 26

Example 2 Find the value of the expression . Perform operation inside the parentheses. Find the value of (– 8)2. The fraction bar is a type of grouping symbol. Subtract in the denominator before dividing. Dividing numerator by denominator. Subtract.

Example 3 Jakim’s family took a vacation to California. The plane tickets cost a total of $840, the hotel cost $250 and gas cost $130. There are 5 people in Jakim’s family. a. Write an expression that could be used to find the cost person. The numbers must be added before dividing by the number of people. Use parentheses or the fraction bar to group the numbers that must be added. OR

Example 3 Continued… Jakim’s family took a vacation to California. The plane tickets cost a total of $840, the hotel cost $250 and gas cost $130. There are 5 people in Jakim’s family. b. Find the cost person. Add the numerators. Divide. The vacation cost $244 person.

Communication Prompt Why is there an order of operations in mathematics?

Exit Problems Find the value of each expression. 1. 9 + 7(2 + 1) 30 2. 4 3. 5| – 1 – 5| – 40 – 10