Properties of Real Numbers and Equality

3(w + 4) = 3w + 12 is an example of...

• Inverse Property

• Distributive Property

• Multiplicative Inverse

• Associative Property

Answer explanation

The equation 3(w + 4) = 3w + 12 demonstrates the Distributive Property, which states that a(b + c) = ab + ac. Here, 3 is distributed to both w and 4.

Tags

CCSS.6.EE.A.3

(5 + 3) + 2 = 5 + (3 + 2)

• Commutative  Addition

• Commutative Multiplication

• Associative Addition

• Associative Multiplication

Answer explanation

The equation (5 + 3) + 2 = 5 + (3 + 2) demonstrates the Associative Property of Addition, which states that the way numbers are grouped does not change their sum. Thus, the correct choice is Associative Addition.

Tags

CCSS.1.OA.B.3

3 + (12 + 8) = 3 + (8 + 12) 

• Associative Addition 

• Associative Multiplication 

• Commutative Addition 

• Commutative Multiplication 

Answer explanation

The equation shows that the order of addition does not affect the sum. This is an example of Commutative Addition, where a + b = b + a. Thus, 3 + (12 + 8) equals 3 + (8 + 12) due to the commutative property.

Tags

CCSS.1.OA.B.3

Identify the property you would use to solve this equation:
4x = 72

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve the equation 4x = 72, you would use the Division Property of Equality. This property states that if you divide both sides of the equation by the same non-zero number (in this case, 4), the equality holds.

Tags

CCSS.HSA.REI.A.1

Identify the property you would use to solve this equation:
y – 7 = 28

• Additive Property of Equality

• Subtraction Property of Equality

• Multiplicative Property of Equality

• Division Property of Equality

Answer explanation

To solve y – 7 = 28, you need to isolate y. You can do this by adding 7 to both sides of the equation. This demonstrates the Additive Property of Equality, which states that you can add the same value to both sides of an equation.

Tags

CCSS.HSA.REI.A.1

Name the first property you will use to solve this equation:
3(x – 7) = 42

• Multiplication Property of Equality

• Commutative property

• Associative Property

• Distributive Property

Answer explanation

To solve the equation 3(x – 7) = 42, the first property used is the Distributive Property, which allows us to distribute 3 across the terms in the parentheses.

Tags

CCSS.HSA.REI.A.1

Name the property you will first use to solve this equation:
4x – 5 = 17

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve the equation 4x – 5 = 17, you first need to isolate the variable x. You can do this by adding 5 to both sides, which is the Addition Property of Equality. This property states that if you add the same value to both sides of an equation, the equality remains true.

Tags

CCSS.HSA.REI.A.1

Which equation shows the commutative property of addition?

• m + n = n + m

• a + (b + c) = (a + b) + c

• r + y = m + v

• v + r + p = t

Answer explanation

The equation m + n = n + m demonstrates the commutative property of addition, which states that changing the order of the addends does not change the sum. The other options illustrate different properties.

Tags

CCSS.1.OA.B.3

Which equation shows the associative property of addition?

• m + n = n + m

• a + (b + c) = (a + b) + c

• r + y = m + v

• v + r + p = t

Answer explanation

The associative property of addition states that the way numbers are grouped does not change their sum. The equation a + (b + c) = (a + b) + c illustrates this property, showing that grouping can vary without affecting the result.

Tags

CCSS.1.OA.B.3

If y/4 = 5, then y = 20

• Multiplication Property of Equality

• Division Property of Equality

• Addition Property of Equality

• Subtraction Property of Equality

Answer explanation

To solve y/4 = 5, multiply both sides by 4. This uses the Multiplication Property of Equality, resulting in y = 20.

Tags

CCSS.HSA.REI.A.1