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# Multiplying with area model: 16 x 27

Sal uses an area model to multiply 16x27. Created by Sal Khan.

## Want to join the conversation?

• Is it permissible to use this area concept by subtracting a 'negative' area?
For example, using our problem of 16 x 27, we could actually make an area of 20 x 27. We can then subtract an area of 4 x 27 to yield our answer.
We can easily calculate 20 x 27 = 540, and then subtract a similarly easy calculation of 4x27=108 → 540-108=432.
• Good point, I think you are absolutely right. We can even set up a diagram like Sal has done, using negative numbers in one or both sides of the multiplication.

Eg. Using (30 - 3) for 27, and (20 - 4) for 16 in the diagram below
We get 600 - 120 - 60 + 12 = 432

30      -3
.______________.
| | |
| | |
20 | +600 | -60 |
| | |
|________|_____|
| | |
-4 | -120 | +12 |
|________|_____|
• 30 -3
.____________.
| | |
| | |
20 | +600 | -60 |
| | |
|______|_____|
| | |
-4 | -120 | +12 |
|______|_____| this is my area model khan sir
• This is an interesting way of using area models to multiply. This is most useful for multiplying numbers that have high digits.
• Can you explain me how to do the area model negative numbers if it is possible?
Also what do you mean when you say subtracting a 'negative' area?
• I don't know what it means by subtracting a negative area, but the question basically says to multiply 16 by 27 which is 432. This probably doesn't help but I hope it does.
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• What would an aria model for 95 / 6 = ?

/ = divided by
• Yes that is true but even so some people could not understand that.