Consider the following equation: 4(3+5)=12+20. This is an application of which property of operations?(1 point)
Responses
Associative Property of Addition
Distributive Property
Commutative Property of Addition
Associative Property of Multiplication
Distributive Property
To determine which property of operations is being applied in the equation 4(3+5)=12+20, we need to understand the properties of operations.
1. The Associative Property of Addition states that changing the grouping of numbers being added does not change the sum. In other words, (a + b) + c = a + (b + c).
2. The Distributive Property states that multiplying a number by a sum is the same as multiplying each addend by that number and then adding the products together. In other words, a(b + c) = ab + ac.
3. The Commutative Property of Addition states that changing the order of addends or factors does not change the sum or product. In other words, a + b = b + a.
4. The Associative Property of Multiplication states that changing the grouping of numbers being multiplied does not change the product. In other words, (ab)c = a(bc).
Now, let's analyze the given equation: 4(3+5) = 12+20.
The equation can be simplified as follows:
4(8) = 12+20.
We see that the expression inside the parentheses is being multiplied by 4, which means we are using the Distributive Property.
Therefore, the correct answer is: Distributive Property.