1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

Objective Use the order of operations to simplify expressions.

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

Grouping symbols include parentheses ( ), brackets [ ], and braces { } 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.

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 Divide Add Subtract

Example 1: Translating from Algebra to Words Simplify each expression. A. 15 – 2 · 3 + 1 15 – 2 · 3 + 1 There are no grouping symbols. 15 – 6 + 1 Multiply. 10 Subtract and add from left to right. 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. Subtract and add from left to right. 8

Simplify the expression. Check It Out! Example 1a Simplify the expression. 1 2 8 ÷ · 3 8 ÷ · 3 1 2 There are no grouping symbols. 16 · 3 Divide. 48 Multiply.

Check It Out! Example 1b Simplify the expression. 5.4 – 32 + 6.2 There are no grouping symbols. 5.4 – 32 + 6.2 5.4 – 9 + 6.2 Simplify powers. –3.6 + 6.2 Subtract 2.6 Add.

Check It Out! Example 1c Simplify the expression. –20 ÷ [–2(4 + 1)] There are two sets of grouping symbols. –20 ÷ [–2(4 + 1)] Perform the operations in the innermost set. –20 ÷ [–2(5)] Perform the operation inside the brackets. –20 ÷ –10 2 Divide.

Check It Out! Example 2b Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6 (x · 22) ÷ (2 + 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.

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

Example 3A: Simplifying Expressions with Other Grouping Symbols 2(–4) + 22 42 – 9 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 2(–4) + 22 42 – 9 –8 + 22 42 – 9 Multiply to simplify the numerator. –8 + 22 16 – 9 Evaluate the power in the denominator. Add to simplify the numerator. Subtract to simplify the denominator. 14 7 2 Divide.

Example 3B: Simplifying Expressions with Other Grouping Symbols 3|42 + 8 ÷ 2| The absolute-value symbols act as grouping symbols. 3|42 + 8 ÷ 2| Evaluate the power. 3|16 + 8 ÷ 2| Divide within the absolute-value symbols. 3|16 + 4| 3|20| Add within the absolute-symbols. 3 · 20 Write the absolute value of 20. 60 Multiply.

Evaluate the power in the denominator. Check It Out! Example 3a Simplify. 5 + 2(–8) (–2) – 3 3 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 5 + 2(–8) (–2) – 3 3 5 + 2(–8) –8 – 3 Evaluate the power in the denominator. 5 + (–16) – 8 – 3 Multiply to simplify the numerator. –11 Add. 1 Divide.

Check It Out! Example 3c Simplify. The radical symbol acts as a grouping symbol. Subtract. 3 · 7 Take the square root of 49. 21 Multiply.

Lesson Quiz Simply each expression. 2. 52 – (5 + 4) |4 – 8| 1. 2[5 ÷ (–6 – 4)] –1 4 3. 5  8 – 4 + 16 ÷ 22 40 Translate each word phrase into a numerical or algebraic expression. 4. 3 three times the sum of –5 and n 3(–5 + n) 5. the quotient of the difference of 34 and 9 and the square root of 25 6. the volume of a storage box can be found using the expression l · w(w + 2). Find the volume of the box if l = 3 feet and w = 2 feet. 24 cubic feet

Assignment: p. 43, #’s 24-49 Vocabulary from p. 40 into notebook