This week in math 10 I leaned how to use an area model. An area model is a big rectangle with a cross in the middle splitting it into four smaller boxes.

 

 Example 1:

For the equation 28 x 72 you would first start by simplifying 28 into two numbers that equal 28, which would leave us with 20 and 8. We would then place those numbers above our area model. Next we would simplify 72 into 70 and 2. We will place those two numbers on the left side of the area model. Now we need to fill our area model in. By looking at the model we can see that 20 and 70 need to be multiplied together for us to fill in the top left corner of our model, 20•70=1,400. Now to fill in the top right corner we will multiply 8 by 70, equalling 560. Now we’re going to solve for the bottom left corner which I will be 20•2=40. Now we will solve for the bottom right corner which is 8•2=16. Now we’ll add all the corners together, 1,400+560+40+16=2,016. With the help of the area model we now know that 28•72=2,016. 

 

Example 2:

This example is a bit more difficult but we will still begin with drawing a square with a cross in the middle, our area model. We would then take and separate it to make it more simple. To do this we would take and put it above the top left corner of our area model and +9/positive 9 above the upper right section of our model. Now that we’ve done that we will do the same with . We will place 7x outside the upper left side side of our model, -3/negative 3 will be placed outside the bottom left section of our area model. We will now multiply which equals and we will write it in the upper left box. Next we will multiply 9 by 7x which leaves us with 63x that will be placed in the upper right corner of our area model. is next and will be placed in the bottom left corner. This leaves us with , -27 is in the bottom right corner of the area model. Now we will write out our answers as an equation, .We now know that .