## Introduction

In this topic we will be using the H.C.F or highest common factor with the distributive property to find the sum of two numbers. This is a great way to review both of the topics in one lesson. Good Luck!

## Finding the H.C.F with Distributive Property...

Let's take the two numbers 24+36. Now I know that as a 6th grader, you can just simply add the two numbers together using the simple addition method, but I'm going to be showing you how to use the H.C.F and the distributive property to add the two numbers.

First, list all the factors for each of these numbers:

24= 2 x 2 x 3
36= 2 x 2 x 3 x 3

Next, find the highest common factor for the two numbers.

As you can see the H.C.F is 3.

Now, we will rewrite 24+36 using the distributive property:

24+36
3 ( ) + 3 ( )
Now, fill in the parenthesis with the number you multiplied 3 by to get 24 and 36.

( You can find that number by dividing...)

24/3=8
36/3=12

24+36
3 (8) + 3 (12)

Next, write the two numbers in parenthesis together by an addition sign:

24+36
3 (8) + 3 (12)
3 (8+12)

24+36
3 (8) + 3 (12)
3 (8+12)
3 (20)

Now, just multiply to get your sum!

24+36
3 (8) + 3 (12)
3 (8+12)
3 (20)
=60

That means the sum of the two numbers 24+36=60!

Sheet 1 What is Distributive Property

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