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distributive property to evaluate the expressions

by kaila
(alliance, ohio us)











































Use the distributive property to evaluate the expressions. 5(30 + 4)
I need help with this becuase i dont know how to do it. Everytime i try to ask the teacher she yells at me and tells me to sit down and be quiet.
I just moved here to alliance, and at my old school we was not even learning this, and i had told my teacher that and she said o well.! so will someone please help me?

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Dec 10, 2010
Distributive Property
by: Staff

The question:


by Kaila
(Alliance, Ohio US)


Use the distributive property to evaluate the expressions. 5(30 + 4)

I need help with this becuase i dont know how to do it. Everytime i try to ask the teacher she yells at me and tells me to sit down and be quiet.

I just moved here to alliance, and at my old school we was not even learning this, and i had told my teacher that and she said o well.! so will someone please help me?


The answer:

I’m going to work this problem out for you.

But first, I’m going to try to give you a way of thinking about the distributive law which should help to understand it.


THE DISTRIBUTIVE LAW

Suppose you are going to give ONE FRIEND two items: 1 dime and 1 nickel

That’s straightforward enough, you just need 1 dime and 1 nickel – nothing more.


Now suppose you are going to give TWO FRIENDS the same thing: each is to be given 1 dime and 1 nickel.

Since you have two friends, you will need: 2 dimes and 2 nickels.


Now suppose you are going to give FIVE FRIENDS the same thing: each is to be given 1 dime and 1 nickel.

Since you have five friends, you will need: 5 dimes and 5 nickels.


That is exactly how the distributive law works:

You need: 5 friends times 1 dime and 5 friends times 1 nickel

= 5 friends * (1 dime + 1 nickel)

= 5(1 dime + 1 nickel)

= 5 times 1 dime + 5 times 1 nickel

= 5 * 1 dime + 5 * 1 nickel

= 5 dimes + 5 nickels


The distributive law formulizes the reasoning we just used:

5(1 dime + 1 nickel)

Instead of adding the value of the dime and value of the nickel together before you multiply, you can multiply the 5 times the dime by itself, then multiply 5 times the nickel by itself. Then you can add the two results.

5(1 dime + 1 nickel) = 5 * 1 dime + 5 * 1 nickel

= 5 dimes + 5 nickels

= 50 cents + 25 cents

= 75 cents


DISTRIBUTIVE LAW - YOUR PROBLEM

5(30 + 4)

= 5 * 30 + 5 * 4

= 150 + 20

= 170

The final answer is: 170


WHY ? WHY? WHY EVEN BOTHER TO LEARN ABOUT THE DISTRIBUTIVE LAW?

WHAT’S THE POINT?

Isn’t it easier to add the two numbers together first, then multiply by 5? That way, you don’t have to bother with the distributive law at all.


If you are only dealing with numbers, it is easier to add the numbers before you multiply.


However, your teacher is not teaching you some interesting, obscure facts about numbers that you will never use your entire life.

Your teacher is leading up to equations such as this one:

5(X + 3) = 20

You cannot add the X and 3 because you don’t know the value of X. You would be stuck, except for the distributive law.


There are some other examples of how to use the distributive law here:

http://www.solving-math-problems.com/distributive-property.html




Thanks for writing.


Staff
www.solving-math-problems.com



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