why can you simplify 5(50+3) using the distributive property? why can't you simplify 5(50)+ 3 using the Distributive property?
With 5(50+3), both terms within the parenthesis are multiplied by 5.
5(50+3) = 5*53 = 265
Another way to look at it is:
5(50+3) = 5*50 + 5*3 = 250 + 15 = 265
To understand why we can simplify 5(50+3) using the distributive property but not 5(50)+3, let's first review what the distributive property is.
The distributive property states that for any real numbers a, b, and c, a(b+c) is equal to ab + ac. In other words, when you multiply a number (a) by the sum of two other numbers (b and c), you can distribute the multiplication to each term inside the parentheses.
Now, let's apply this understanding to the two expressions you mentioned:
1. 5(50+3):
We can multiply 5 by each term inside the parentheses using the distributive property:
5(50+3) = 5(50) + 5(3)
= 250 + 15
= 265
2. 5(50)+3:
This expression does not use the distributive property because there are no parentheses indicating a sum or difference of terms. Instead, it is a simple multiplication followed by an addition:
5(50) + 3
= 250 + 3
= 253
Therefore, even though both expressions involve multiplication, only the first expression (5(50+3)) can be simplified using the distributive property because it has a sum within the parentheses. The second expression (5(50)+3) does not involve any such sum, so we cannot apply the distributive property to simplify it.