Properties and Like Terms

If x and y are integers, then 3(x+y)=3x+3y is an example of which property?

• distributive property

• identity property of addition

• associative property of addition

• commutative property of addition

Which equation illustrates the commutative property of addition?

• a+b=a+b

• m+2n=2n+m

• 3(x−1)=3x−3

• x(3−y)=x(y−3)

Which of the following statements illustrates the identity property of addition?

• m + 0 = m

• x + y = y + x

• g(h + j) = gh + gj

• (p + q) + r = p + (q + r)

Which expression is equivalent to 2+y+y+y+y+y+3?

• 5y

• 5y+5

• y⁵+5

• 2y⁵+3

Brad’s scores on three math tests are three consecutive even integers. The sum of his test scores is represented by the expression below, where m represents his first test score.

(m)+(m+2)+(m+4)

Which expression is equivalent to the sum of Brad’s test scores?

• 7m

• 9m

• 3m+6

• 7m+3

What property is illustrated by the statement?

(a + b) + c = a + (b + c)

• Additive Identity Property

• Additive Inverse Property

• Associative Property of Addition

• Commutative Property of Addition

Which property of operations could be used as the next step in simplifying the expression?

12.6 + 3.2 + (-5.6) + 9.8 = 12.6 + (-5.6) + 3.2 + 9.8

• Use the Additive Inverse Property to add the addends.

• Use the Associative Property of Addition to group the addends.

• Use the Commutative Property of Addition to group the addends.

• Use the Additive Identity Property to add the addends.

The expression c + 0.07c gives the cost of an item including the tax of 7%. Which is the simplified expression?

• 1.07

• c + 0.07

• 1.07c

• (c + 0.07)1

The expression is equivalent to (r - 6)(4)?

• r - 2

• r - 24

• 4r - 6

• 4r - 24

Determine which property of multiplication is shown?

6(10 + 7) = (6 x 10) + (6 x 7)

• Associative

• Identity

• Distributive

• Commutative