Sort the equations according to the property they illustrate.

Question

You have 14 cards in this activity.
0 are sorted correctly.

3(5x−2)=15x−6

communative

associtavie

not a property

identify

or dirbutive

Answer 1

To help you sort your given equation \(3(5x - 2) = 15x - 6\) according to the properties it illustrates, let's analyze each option you've listed:

1. Communative (Commutative): This property states that the order in which numbers are added or multiplied does not change the result. This equation does not illustrate the commutative property.

2. Associtavie (Associative): This property states that how numbers are grouped in addition or multiplication does not change their sum or product. This equation does not illustrate the associative property.

3. not a property: This option implies that the equation does not illustrate a specific mathematical property at all, which may seem appropriate, but let's analyze further.

4. identify (Identity): The identity property refers to adding 0 or multiplying by 1 without changing the original value. This equation does not illustrate the identity property.

5. or dirbutive (Distributive): The distributive property states that \(a(b + c) = ab + ac\). The left side of the equation, \(3(5x - 2)\), applies the distributive property. Thus, this equation illustrates the distributive property.

Based on this analysis, the sorting would be:

• Distributive: \(3(5x - 2) = 15x - 6\) demonstrates the application of the distributive property.
• Not a property: Since the equation doesn’t specifically illustrate commutative, associative, or identity properties.

Please note that your current options contain a few typographical errors ("associtavie" for associative and "or dirbutive" for distributive). It would also be advisable to clarify if you meant to include other equations or examples to generate a more comprehensive sorting activity.

Answer 2

99+0=99

Answer 3

The equation \(99 + 0 = 99\) illustrates the Identity Property of Addition. The identity property states that when you add zero to any number, that number remains unchanged.

Here's the breakdown according to the properties you mentioned earlier:

• Identity: Correct, as it exemplifies the identity property.
• Commutative: Incorrect; this equation does not illustrate the commutative property.
• Associative: Incorrect; this equation does not illustrate the associative property.
• Distributive: Incorrect; this equation does not illustrate the distributive property.
• Not a property: Not applicable in this case, as the equation indeed illustrates a valid property.

So, you'd sort the equation \(99 + 0 = 99\) under the Identity property.

Answer 4

1(-99)=99

Answer 5

The equation \(1 \times (-99) = -99\) appears to contain an error in the interpretation of the multiplication with the identity property.

When you multiply one by any number, the result is that number itself (this is known as the Identity Property of Multiplication).

To correctly analyze:

• The left side of the equation \(1 \times (-99)\) equals \(-99\), not \(99\).
• Therefore, \(1 \times (-99) = -99\) is correct, but the equation as presented \(1(-99) = 99\) is incorrect.

So, if we restate the equation correctly as \(1(-99) = -99\):

1. Identity Property of Multiplication: This demonstrates the identity property because multiplying any number by 1 yields the original number.

In conclusion, the correct description for the equation is:

• Identity: This reflects the identity property of multiplication.

If you need to sort your equations, this would go under the Identity property.