Finding Equivalent Expressions Using Properties of Operations

Which property says that the grouping of terms in multiplication and addition problems does not affect the outcome? 

• Inverse

• Identity

• Associative

• Distributive

Which property says that the value outside the parentheses should be applied to all values inside the parentheses? 

• Associative

• Distributative

• Commutative

• Inverse

Use properties of operations to find an equivalent expression for 4(2 + y) - (3y + 3). What is the equivalent expression? (7.EE.A.1)

• -2y + 11

• y + 11

• y + 5

• 7y + 11

Which of the following is equivalent to -36? Choose all that apply. (7.NS.A.2.c)

• - 9 ● (-4)

• - 12 ● 3

Sal was finding the perimeter of the given rectangle. He wrote this expression: (3x + 3x) + (4x + 4x) + (3 + 3). Which expressions are equivalent?

• 2(3x) + 2(4x + 3)

• 3x + 3x + 4x + 3 + 4x + 3

• 4(3x) + 2(4x)

• 3 + 3 + x (3 + 3 + 4 + 4)

• 20x

Given this equation, select all expressions that make the following equation true. (7.NS.A.c)

Select the expression that is equivalent to 6(3m + 9).

• 9m + 15

• 18m + 9

• 18m + 54

• 3(6m +12)

Mrs. Black wrote the following algebraic expression on the board: 3 + (9+f). She asked the students to come up with an equivalent expression and justify why. Brook: The correct answer is f + (3+9) and the distributive property justifies that since the order of numbers changed. Shawn: No its not, the correct answer is (3+9)f and the associative property justifies this since the groupings changed. Which statement best describes the situation?

• Shawn is correct because the groupings of the numbers changed.

• Shawn is incorrect because it should be the distributive property not the associative property. Brook's answer is correct because the order of the numbers changed.

• Brook is incorrect because it should be the commutative property not the distributive.

• Neither Emma nor Tana is correct because of the associative property of addition.

Use the expression below to answer the following question: 6x - 12. If the coefficient is multiplied by 3, what is the new expression?

• 6x - 36

• 12x - 12

• 18x - 24

• 18x - 12

Select all expressions equivalent to 32 + 40x using the distributive property.

• 8(5x + 4)

• 4(8 + 10x)

• 5(6 + 8x)

• 2(16 + 20x)