I dont know what Im doing wrong - mutiples of 10 (special cardboard for work)

[Garth]

Hello,

I posted a couple of months back about special cardboard I need to order at work.
Each piece is 187 x 97 (mm) and a need 10 per item I make in the factory - they get glued together.
So Excel tells me:
187 x 97 = 18139
Multiplied by 10 is 1870 x 970 = 1813900

But if for example I need 20 sheets and I say 20 x 18139 it comes to 362780. How can that be?
Shouldn't it come to 3627800?
And 10 x 18139 comes to 181390 but then why does it come to 1813900 when the 187 and 97 are multiplied by 10 first?

I really dont get it.
Thank you,
Garth

 

[Deleted member 4993]

Hello,

I posted a couple of months back about special cardboard I need to order at work.
Each piece is 187 x 97 (mm) and a need 10 per item I make in the factory - they get glued together.
So Excel tells me:
187 x 97 = 18139
Multiplied by 10 is 1870 x 970 = 1813900

But if for example I need 20 sheets and I say 20 x 18139 it comes to 362780. How can that be?
Shouldn't it come to 3627800?
And 10 x 18139 comes to 181390 but then why does it come to 1813900 when the 187 and 97 are multiplied by 10 first?

I really dont get it.
Thank you,
Garth

That is correct.

3627800 = 200 x 18139

 

[Dr.Peterson]

Hello,

I posted a couple of months back about special cardboard I need to order at work.
Each piece is 187 x 97 (mm) and a need 10 per item I make in the factory - they get glued together.
So Excel tells me:
187 x 97 = 18139
Multiplied by 10 is 1870 x 970 = 1813900

But if for example I need 20 sheets and I say 20 x 18139 it comes to 362780. How can that be?
Shouldn't it come to 3627800?
And 10 x 18139 comes to 181390 but then why does it come to 1813900 when the 187 and 97 are multiplied by 10 first?

I really dont get it.
Thank you,
Garth

This part is wrong. You are apparently trying to distribute where it is inappropriate. I see a lot of students doing this.

The distributive property applies to multiplying a sum: a * (b + c) = a*b + a*c.

What you have here is a product, 10 * (187 * 97), not 10 * (187 + 97), so you don't multiply each number by 10. Here, the property that applies is the associative property, a * (b * c) = (a * b) * c. You could do (10 * 187) * 97. But you don't need to; just multiply 18139 by 10!

What you did, multiplying both factors by 10, is like multiplying both the length and the width of a rectangle by 10. You end up not with 10 times the area, but 100 times, because there will be 10 rows of 10 rectangles! To multiply an area by 10, you would just multiply one of the sides by 10, as in (10 * 187) * 97 above.

 

[Garth]

This part is wrong. You are apparently trying to distribute where it is inappropriate. I see a lot of students doing this.

The distributive property applies to multiplying a sum: a * (b + c) = a*b + a*c.

What you have here is a product, 10 * (187 * 97), not 10 * (187 + 97), so you don't multiply each number by 10. Here, the property that applies is the associative property, a * (b * c) = (a * b) * c. You could do (10 * 187) * 97. But you don't need to; just multiply 18139 by 10!

What you did, multiplying both factors by 10, is like multiplying both the length and the width of a rectangle by 10. You end up not with 10 times the area, but 100 times, because there will be 10 rows of 10 rectangles! To multiply an area by 10, you would just multiply one of the sides by 10, as in (10 * 187) * 97 above.

Thank you so much Dr. Peterson, that makes a lot of sense.
I didnt even know such rules about maths exist.
You have helped me a lot.