To solve the problem, we need to identify which property (Commutative, Associative, or Distributive) is being used in each computation. Let's analyze each equation step by step:
1. \( 57 \times (85 + 13) = 57 \times 85 + 57 \times 13 \)
- This equation shows that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
-
Property:
Distributive Property
2. \( (13 + 84) + 53 = 13 + (84 + 53) \)
- This equation shows that the way numbers are grouped when adding does not change the result.
-
Property:
Associative Property of Addition
3. \( 6 \times (19 + 12) = 6 \times 19 + 6 \times 12 \)
- This equation shows that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
-
Property:
Distributive Property
4. \( 41 + 77 = 77 + 41 \)
- This equation shows that the order of addition does not change the result.
-
Property:
Commutative Property of Addition
5. \( (10 + 20) + 30 = 10 + (20 + 30) \)
- This equation shows that the way numbers are grouped when adding does not change the result.
-
Property:
Associative Property of Addition
6. \( 23 + 42 = 42 + 23 \)
- This equation shows that the order of addition does not change the result.
-
Property:
Commutative Property of Addition
7. \( (12 + 55) + 61 = 12 + (55 + 61) \)
- This equation shows that the way numbers are grouped when adding does not change the result.
-
Property:
Associative Property of Addition
8. \( (73 + 32) + 57 = 73 + (32 + 57) \)
- This equation shows that the way numbers are grouped when adding does not change the result.
-
Property:
Associative Property of Addition
9. \( 62 \times (94 + 5) = 62 \times 94 + 62 \times 5 \)
- This equation shows that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
-
Property:
Distributive Property
10. \( 81 + 9 = 9 + 81 \)
- This equation shows that the order of addition does not change the result.
-
Property:
Commutative Property of Addition
Final Answer:
\[
\boxed{
\begin{array}{|c|l|l|}
\hline
1 & 57 \times (85 + 13) = 57 \times 85 + 57 \times 13 & \text{Distributive} \\
\hline
2 & (13 + 84) + 53 = 13 + (84 + 53) & \text{Associative} \\
\hline
3 & 6 \times (19 + 12) = 6 \times 19 + 6 \times 12 & \text{Distributive} \\
\hline
4 & 41 + 77 = 77 + 41 & \text{Commutative} \\
\hline
5 & (10 + 20) + 30 = 10 + (20 + 30) & \text{Associative} \\
\hline
6 & 23 + 42 = 42 + 23 & \text{Commutative} \\
\hline
7 & (12 + 55) + 61 = 12 + (55 + 61) & \text{Associative} \\
\hline
8 & (73 + 32) + 57 = 73 + (32 + 57) & \text{Associative} \\
\hline
9 & 62 \times (94 + 5) = 62 \times 94 + 62 \times 5 & \text{Distributive} \\
\hline
10 & 81 + 9 = 9 + 81 & \text{Commutative} \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of commutative associative and distributive properties worksheet.
