Unit 4 Review-Order of Operations and Properties

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

• 9m + 15

• 18m + 9

• 18m + 54

• 3(6m +12)

Completely factor the following expression using the distributive property: 28 + 36.

• 2(15+18)

• 4(7+9)

• 6(4+6)

• 14(2+3)

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.

Which of the following correctly shows the associative property of multiplication?

• ax b = b x a

• a x (b x c) = (a x b) x c

• ax0=0

• a(b + c) = (a x b) + (ax c)

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

Amy drove at a rate of x miles per hour. Uma drove half the rate of speed that Amy drove. Which expression represents the rate of speed at which Uma drove?

• ½ + x

• x - ¹₂

• 2x

• x/2

Sunday brunch at a local restaurant costs $12.94 per person. Let n represent the total number of people eating brunch together. Which expression could be used to find the cost of brunch for an entire group?

• 12.94 + n

• 12.94 ÷ n

• 12.94 - n

• 12.94n

Emma had 8 pennies and Tana had 6 pennies. Each girl found a strategy for finding the number of pennies they had together. Emma used 8 + 6. Tana used 6 + 8. Which statement is true about the strategies the girls used?

• Only Emma is correct because of the zero property.

• Only Tana is correct because of the identity property of addition.

• Both Emma and Rana are correct because of the commutative property of addition.

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

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

• 8(5x + 4)

• 4(8 + 10x)

• 5(6 + 8x)

• 2(16 + 20x)

Evaluate the following expression: (1/3)³

(a)