more-properties-worksheets.pdf - Name Date Topic: Commutative ... - Free Printable

I can see questions 9 and 10 now:

Question 9: "The ________ property multiplies the value outside the brackets with each of the terms in the brackets." - As I noted previously, this is describing the Distributive Property.

Question 10: "8 × (6 + 2) = 8 × 6 + 8 × 2" - This is a correct example of the Distributive Property, showing that multiplying a number by a sum equals the sum of that number multiplied by each addend.

Now I have analyzed all the questions. Let me provide the complete solution.

Based on my analysis of all questions on the worksheet about Commutative, Associative, and Distributive Properties:

1. 3 + 5 = 5 + 3 - This is an example of the Commutative property (specifically, Commutative Property of Addition).

2. 2 × 7 × 6 = 2 × 6 × 7 - This is an example of the Commutative property (specifically, Commutative Property of Multiplication).

3. 14 + 21 = 21 + 14 - This is an example of the Commutative property (Commutative Property of Addition).

4. The Associative property means the numbers can be regrouped.

5. The rule that refers to grouping is Associative property.

6. For this property says that, changing the GROUPING of the numbers that are being added or multiplied does NOT change the value of it. - This describes the Associative property.

7. 12 × 3 + 4 = 12 × (3 + 4) - This is intended to be an example of the Distributive property (though the equation as written is mathematically incorrect; it should be 12 × (3 + 4) = 12 × 3 + 12 × 4).

8. The Distributive property multiplies the value outside the brackets with each of the terms in the brackets.

9. The Distributive property multiplies the value outside the brackets with each of the terms in the brackets. (This appears to be a duplicate of question 8)

10. 8 × (6 + 2) = 8 × 6 + 8 × 2 - This is an example of the Distributive property.

In summary:
- The Commutative Property states that the order of numbers doesn't matter in addition or multiplication (a + b = b + a, a × b = b × a).
- The Associative Property states that the grouping of numbers doesn't matter in addition or multiplication ((a + b) + c = a + (b + c), (a × b) × c = a × (b × c)).
- The Distributive Property states that multiplying a number by a sum equals the sum of that number multiplied by each addend (a × (b + c) = a × b + a × c).