Distributive Property of Rational Numbers

Which of the following is true for the rational numbers a, b and c ?

• a × (b + c) = (a × b) + (b × c)

• a × (b + c) = (a + b) × (a + b)

• a + (b × c) = (a × b) + (a × c)

• a × (b + c) = (a × b) + (a × c)

Answer explanation

For rational numbers the distributive property of multiplication over addition can be expressed in general form as shown in option 4. Other options are incorrect representations of distributive property.

Tags

CCSS.7.NS.A.2C

(-¾) × (⅚ - ⅞) = (-¾ × ⅚) - _______

• {-3/4 × (-7/8)}

• (-3/4 × 7/8)

• (3/4 × 7/8)

• (-3/4 - 7/8)

Answer explanation

According to the distributivity of multiplication over subtraction a × (b - c)= (a × b) - (a × c) where a, b and c are rational numbers. Therefore, (-¾) × (⅚ - ⅞) = (-¾ × ⅚) - (-¾ × ⅞)

Tags

CCSS.7.NS.A.2C

What property is this?
9(b + 0.5) = 9b + 4.5

• Commutative

• Associative

• Distributive

• Additive Inverse

Tags

CCSS.6.EE.A.3

Fill in the blank to properly solve the DISTRIBUTIVE PROPERTY:
7(12 - 4) = 84  -  ____

• 3

• 4

• 7

• 28

Tags

CCSS.6.NS.B.4

The ​ (a)   Property can be used to state that (x + 2)7 + 3x is equivalent to 7x + 14 + 3x.

• Distributive

• Commutative

• Associative

Tags

CCSS.6.EE.A.3

The Property can be used to state that (x + 2)7 + 3x is equivalent to 7x + 14 + 3x.

• Distributive

• Commutative

• Associative

Tags

CCSS.6.EE.A.3

Find the equivalent expression for5(a + 6)

• 5a+6

• 5a+30

• a+30

• 5a-30

Tags

CCSS.6.EE.A.4

7(x + 4)

Tags

CCSS.6.EE.A.3

Answer explanation

To simplify the expression, distribute the 2 to both terms inside the parentheses: 2(3x) + 2(4) + x = 6x + 8 + x = 7x + 8. Therefore, the correct choice is 7x + 8.

Tags

CCSS.6.EE.A.3

Fill in the blank:
2(x + 7) = 2x + __

• 7

• 14

• 7x

• 14x

Tags

CCSS.6.EE.A.3