decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
-14+(15+7)=(15+7)+(-14)
This statement is an example of the associative property of addition.
The statement "-14+(15+7)=(15+7)+(-14)" is an example of the associative property. Specifically, it demonstrates the associative property of addition. This property states that when adding three or more numbers, the grouping of the numbers does not affect the sum. In this case, no matter whether we add -14 to (15+7) or (15+7) to -14, the result will be the same.
To decide which property is being demonstrated in the given statement, let's quickly review the properties you mentioned:
1. The commutative property states that changing the order of the numbers being added or multiplied does not change the result. For addition, it can be written as: a + b = b + a. For multiplication, it can be written as: a * b = b * a.
2. The associative property states that the grouping of numbers being added or multiplied does not change the result. For addition, it can be written as: (a + b) + c = a + (b + c). For multiplication, it can be written as: (a * b) * c = a * (b * c).
3. The identity property states that adding or multiplying a number with an identity element does not change the value. For addition, the identity element is 0, so a + 0 = a. For multiplication, the identity element is 1, so a * 1 = a.
4. The inverse property states that for any number, there exists an additive inverse and a multiplicative inverse. For addition, the additive inverse of a number a is -a, such that a + (-a) = 0. For multiplication, the multiplicative inverse of a number a is 1/a, such that a * (1/a) = 1.
5. The distributive property states that you can distribute a number being multiplied to other numbers being added or subtracted. It can be written as: a * (b + c) = (a * b) + (a * c).
Now, let's analyze the given statement:
-14 + (15 + 7) = (15 + 7) + (-14)
This statement shows the associative property of addition. According to the associative property, the grouping of numbers being added does not affect the result. Therefore, we can rearrange the numbers without changing the value. In this case, we can shift the grouping from the left side to the right side, or vice versa, and still get the same result.
So, the given statement is an example of the associative property of addition.