# 6th Grade - Do Operations In The Correct Order

 Grade Level: 6th Skill: Algebra Topic: Do Operations in the Correct Order Goal: Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. Skill Description: Follow the order of operations rules to solve problems with multiple operations. Use the Commutative Property of Addition or Multiplication to evaluate expressions. This property states that the order of the numbers can be changed and not change the sum or product [Ex. 7 + 3 = 3 + 7 or 7 x 3 = 3 x 7]. Use the Associative Property to evaluate expressions with addition or multiplication operations. The Associative Property states that the way numbers are grouped does not affect the sum or product [Ex. 7 + (4+5) = (7 + 4) + 5 or 6 x (4 x 5) = (6 x 4) x 5]. Evaluate expressions using the Distributive Property of Multiplication over Addition. The Distributive Property says that it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results [Ex. 5 (2 + 3) = (5 x 2) + (5 x 3)]. Explain why each property was used or why each operation was performed in a particular order.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Evaluate the expression. 25/(4 + 1) – 3 (50) (2) Find the missing number. Tell which property is shown. 30 + (5 + 8) = (__ + 5) + 8 (30, Associative) (3) Find the missing number. Tell which property is shown. 8 x 7 x 10 = 10 x ___ x 7 (8, Commutative) (4) Use the commutative property and solve the expression with mental math. 142 + 56 + 8 (142 + 8 + 56 = 106) (5) Use the Distributive Property to solve the problem. 6 (29) (6(20)+6(9)= 120 + 54 = 174)

### Online Resources

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### Extra Help Problems

 (1) Find each missing number. Write the name of the property that is shown. 15 x (13 x 6) = (15 x 13) x ___ (6, Associative) (2) Find each missing number. Write the name of the property that is shown. 14 + 9 + 11 = 9 + ___ + 14 (11, Commutative) (3) Find each missing number. Write the name of the property that is shown. 75 x 55 = ___ x 75 (55, Commutative) (4) Find each missing number. Write the name of the property that is shown. (___ + 11) + 8 = 17 + (11+ 8) (17, Associative) (5) Find each missing number. Write the name of the properties that are shown. (53 x 22) x (7 x 15) = (22 x ___) x (53 x 15) (7, Associative, Commutative) (6) Find each missing number. Write the name of the property that is shown. 4(82) = 4(80) + 4 (___) (2, Distributive) (7) Find each missing number. Write the name of the property that is shown. 5 (48) – 5 (8) = __(48 – 8) (5, Distributive) (8) Use the distributive property and mental math to solve. 7 (32) (7(30) + 7(2)= 240 + 14 = 224) (9) Use the commutative property and mental math to solve. 17 + 9 + 33 (17 + 33 + 9 = 59) (10) Use the associative property and mental math to solve. (42 + 9) + 8 (42 + 8 = 50 + 9 = 59) (11) Use the distributive property and mental math to solve. 9 (43) + 9 (7) (9(40)+9(3) + 9(7) = 450) (12) Use the commutative property and mental math to solve. 8 x 54 x 10 (4,320) (13) Use the associative property and mental math to solve. (99 x 4) x 5 (1,980) (14) In the problem 47 + 19 + 3, the commutative problem could be used to perform the operations using only mental math. Which numbers should be moved to make the operations easier to compute mentally? Rewrite the problem using the commutative property and explain why you moved the numbers you moved. (47 + 3 + 19) (15) When solving the expression (8 x 17) x 5, Carley used to associative and commutative properties to rewrite the problem as (8 x 5) x 17. Explain why she would do this. (She could move 8 x 5 to mentally get 40. Next, she would be able to mentally multiply 40 x 17 to get 680.) (16) (6 + 18) 23 (192) (17) 9/3 + 7 • 4 (40) (18) 56(11) – (14 – 8 x 2) (618) (19) 59 + 9 – 7 x 6 + 1 (27) (20) 175 – 5 x 52÷2 (112.50) (21) 18 + 2 x 11 – 14 (26) (22) (79 + 44) x (55 ÷ 11) (615) (23) (16 + 2 x 5) – 42 (10) (24) (15 – 9 + 11) x 4 (99 ÷ 11 x 2) (1,224) (25) [(4 + 5) x (15 ÷ 5) – 7 + 125] x 72 (6,145)