Final answer:
To verify the properties: a) Commutative property of addition b) Associative property of addition c) Commutative property of multiplication d) Associative property of multiplication e) Distributive law of multiplication over addition, follow the steps. First, verify that changing the order of addition or multiplication does not change the result. Second, verify that changing the grouping of numbers does not change the result. Finally, verify that multiplying a number by the sum of two other numbers is the same as multiplying the number individually by each of the other numbers and then adding the results.
Step-by-step explanation:
The properties mentioned can be verified as follows:
- Commutative property of addition: To verify the commutative property of addition, we need to show that changing the order of addition does not change the result. For example, if we have two numbers a and b, then a + b = b + a.
- Associative property of addition: To verify the associative property of addition, we need to show that changing the grouping of numbers does not change the result. For example, if we have three numbers a, b, and c, then (a + b) + c = a + (b + c).
- Commutative property of multiplication: To verify the commutative property of multiplication, we need to show that changing the order of multiplication does not change the result. For example, if we have two numbers a and b, then a * b = b * a.
- Associative property of multiplication: To verify the associative property of multiplication, we need to show that changing the grouping of numbers does not change the result. For example, if we have three numbers a, b, and c, then (a * b) * c = a * (b * c).
- Distributive law of multiplication over addition: To verify the distributive law of multiplication over addition, we need to show that a * (b + c) = (a * b) + (a * c). This means that multiplying a number by the sum of two other numbers is the same as multiplying the number individually by each of the other numbers and then adding the results.