why can you simplify 5(50+3) using the distributive property? why can't you simplify 5(50)+ 3 using the Distributive property?
Why can’t you simplify 5(50+3) using the distributive property? Why can’t you simplify 5(50)+3 using the distributive property?
To understand why you can simplify 5(50+3) using the distributive property but not 5(50) + 3, let's review the distributive property first.
The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
In other words, you can multiply a number (a) with the sum of two other numbers (b and c) by distributing the multiplication to each term within the parentheses.
Now, let's apply this property to the expressions you mentioned:
1. 5(50+3):
Here, we have the expression 50+3 enclosed in parentheses and multiplied by 5. Using the distributive property, we can distribute the multiplication to each term inside the parentheses.
5(50) + 5(3) = 250 + 15 = 265
So, by applying the distributive property, we simplified 5(50+3) to 265.
2. 5(50) + 3:
In this expression, we have two separate terms: 5 multiplied by 50 and 3. However, there is no addition or subtraction operation between these two terms, so we cannot use the distributive property because there is nothing to distribute. Instead, we evaluate each term separately.
5(50) + 3 = 250 + 3 = 253
In summary, you can simplify 5(50+3) using the distributive property because there is a sum of terms inside the parentheses that can be distributed. However, you cannot use the distributive property with 5(50) + 3 because there is no operation between the two terms, and they should be evaluated separately.