5(3 + 2) = 15 + 10 is an example of the associative property for addition.
False.
The given equation is an example of the distributive property, not the associative property. The associative property states that the grouping of numbers in an addition or multiplication expression does not affect the result.
Actually, the given equation is an example of the distributive property, not the associative property. The distributive property states that multiplying a number by the sum of two other numbers is the same as multiplying the number separately by each of the two numbers and then adding the results. Let's break down the equation step by step to show how the distributive property applies:
Step 1: Simplify the expression within the parentheses.
3 + 2 = 5
Step 2: Multiply the result from Step 1 by 5.
5 * 5 = 25
Step 3: Simplify the right side of the equation.
15 + 10 = 25
Therefore, both sides of the equation are equal, demonstrating the distributive property.
Actually, the equation you provided is an example of the distributive property, not the associative property. The associative property for addition states that changing the grouping of the numbers being added does not change the sum. On the other hand, the distributive property allows you to multiply a number by the sum of two or more numbers, and it can be written as:
a(b + c) = ab + ac
In your equation, you have 5(3 + 2) on the left side, which means you are multiplying 5 by the sum of 3 and 2. To solve this, you can distribute the 5 to both terms inside the parentheses:
5(3 + 2) = 5 * 3 + 5 * 2
This gives you:
15 + 10 = 25
So, the equation holds true as 15 + 10 does indeed equal 25. This demonstrates the distributive property, not the associative property.