Answer:
28 and 30 are equivalent
Explanation:
Let's analyze each pair of expressions to determine if they are equivalent or not, and if any properties are applied.
27. 48 - 6 and 6 - 48:
These expressions are not equivalent. The property being applied here is the commutative property of subtraction. The commutative property states that changing the order of the numbers being subtracted does not change the result. However, in this case, the order of the numbers being subtracted is different, resulting in different values.
Example:
48 - 6 = 42
6 - 48 = -42
28. 8 + (5 + 9) and (8 + 5) + 9:
These expressions are equivalent. The property being applied here is the associative property of addition. The associative property states that changing the grouping of numbers being added does not change the result. In both expressions, the numbers being added are the same, so the sum will be the same regardless of how we group them.
Example:
8 + (5 + 9) = 8 + 14 = 22
(8 + 5) + 9 = 13 + 9 = 22
29. 17 • 1 and 1:
These expressions are not equivalent. The property being applied here is the identity property of multiplication. The identity property states that multiplying any number by 1 does not change its value. In the first expression, 17 is multiplied by 1, resulting in 17. However, in the second expression, only 1 is present, so the value is simply 1.
Example:
17 • 1 = 17
1 = 1
30. 0 + 14 and 14:
These expressions are equivalent. The property being applied here is the identity property of addition. The identity property states that adding 0 to any number does not change its value. In both expressions, the number being added is 14, so the sum will be the same regardless of whether we add 0 or not.
Example:
0 + 14 = 14
14 = 14
To summarize:
27. Not equivalent; commutative property of subtraction does not hold.
28. Equivalent; associative property of addition is applied.
29. Not equivalent; identity property of multiplication does not hold.
30. Equivalent; identity property of addition is applied.