Which property was used to simplify the expression?
$3 c+9+4 c=3 c+4 c+9$
A. distributive property
B. commutative property
C. associative property
D. inverse property
Answer (1)
The expression 3 c + 9 + 4 c = 3 c + 4 c + 9 was simplified using the commutative property, which allows changing the order of terms in addition without affecting the result. The commutative property states that a + b = b + a . In this case, 9 + 4 c = 4 c + 9 . Therefore, the correct answer is the commutative property. $\boxed{corrmutative property}
Explanation
Understanding the Problem The given equation is 3 c + 9 + 4 c = 3 c + 4 c + 9 . We need to identify which property was used to simplify the expression. The options are distributive property, commutative property, associative property, and inverse property.
Identifying the Change Let's analyze the change in the expression. On the left side, we have 3 c + 9 + 4 c , and on the right side, we have 3 c + 4 c + 9 . Notice that the order of the terms 9 and 4 c has been changed.
Applying the Commutative Property The commutative property states that a + b = b + a . In our case, we can think of a as 9 and b as 4 c . So, 9 + 4 c = 4 c + 9 . This is exactly what happened in the given expression.
Checking the Associative Property The associative property states that ( a + b ) + c = a + ( b + c ) . This property involves grouping terms, which is not what happened in the given expression.
Checking the Distributive Property The distributive property states that a ( b + c ) = ab + a c . This property involves multiplying a term by a sum, which is not what happened in the given expression.
Checking the Inverse Property The inverse property states that a + ( − a ) = 0 . This property involves adding a number to its inverse, which is not what happened in the given expression.
Conclusion Therefore, the property used to simplify the expression 3 c + 9 + 4 c = 3 c + 4 c + 9 is the commutative property.
Examples
The commutative property is useful in everyday situations. For example, if you are buying items at a store, the order in which the cashier rings up the items doesn't change the total amount you owe. Similarly, when calculating the area of a rectangle, multiplying the length by the width gives the same result as multiplying the width by the length. This property ensures that the order of operations doesn't affect the outcome in addition and multiplication.
