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Order or Operations/Properties of Numbers 1-1/1-2

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Vocabulary 1-1 Numerical expression- made up of numbers and operations. Order of operations- When simplifying a numerical expression, rules that must be followed so that everyone gets the same answer.

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Vocabulary 1-2 Commutative Property- you can add numbers in any order and multiply numbers in any order. Associative Property- When you add or multiply, you can group the numbers together in any combination. Identity Property- the sum of 0 and any number is the number and the product of 1 and any number is the number. Distributive Property- multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

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ORDER OF OPERATIONS 1. Perform operations within grouping symbols. 2. Evaluate powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. Remember: PEMDAS Please Excuse My Dear Aunt Sally

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Simplify the expression. Use the order of operations to justify your answer. Additional Example 1A: Using the Order of Operations 3 + 15 ÷ 5 3 + 3 6 Divide. Add.

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Additional Example 1B: Using the Order of Operations 44 – 14 ÷ 2 · 4 + 6 Divide and multiply from left to right. Subtract and add from left to right. Simplify the expression. Use the order of operations to justify your answer.

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Additional Example 1C: Using the Order of Operations 3 + 2 3 · 5 Evaluate the power. Multiply. Add. Simplify the expression. Use the order of operations to justify your answer.

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Simplify the expression. Additional Example 2A: Using the Order of Operations with Grouping Symbols 42 – (3 · 4) ÷ 6 Perform the operation inside the parentheses. Divide. Subtract.

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When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. Helpful Hint

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Additional Example 2B: Using the Order of Operations with Grouping Symbols [(26 – 4 · 5) + 6] 2 [(26 – 20) + 6] 2 [6 + 6] 2 12 2 144 The parentheses are inside the brackets, so perform the operations inside the parentheses first. Simplify the expression.

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You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

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Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2 6) 1 = 2 (6 1) B. 3 + 0 = 3 C. 7 + 9 = 9 + 7 (2 6) 1 = 2 (6 1) The numbers are regrouped. Associative Property 3 + 0 = 3 One of the factors is 0. Identity Property 7 + 9 = 9 + 7 The order of the numbers is switched. Commutative Property

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Check It Out: Example 1 Tell which property is represented. A. 7 1 = 7 B. 3 + 4 = 4 + 3 C. (5 1) 2 = 5 (1 2)

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Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20 9 5 21 + 16 + 9 = 16 + 9 + 21 Commutative Property. = 16 + (9 + 21) = 16 + 30 Associative Property. = 46 Add. 20 9 5 = 20 5 9 Commutative Property. = 20 (5 9) = 20 45 Associative Property. = 900 Multiply.

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Check It Out: Example 2A & B Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12 3 5 17 + 14 + 3 = 14 + 17 + 3 12 3 5 = 3 5 12

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Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: = (6 50) + (6 4) Rewrite 54 as 50 + 4. = 300 + 24 = 324 Use the Distributive Property. Multiply. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6 60) – (6 6) = 360 - 36 Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

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Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: 8(19) = 8(20 – 1) 8(19) = 8(10 + 9)

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