Multiplication problem

Question

How can you answer this question. 

 

Juan puts 3 rows of 5 stickera in a book.  Then he puts 5 rows of 3 stickers on the next page.  How many stickers does Juan put in the book?

Answer 1

Let's do a picture:

let * be a sticker

 

Page 1:

 

* * * * *

* * * * *

* * * * *

 

Page 2:

 

* * *

* * *

* * *

* * *

* * *

 

On page one, each row has 5 stickers so we can just add the stickers up, 5 + 5 + 5 but wait, repeated addition is simply multiplication so we can rewrite that as 5x3

On page two, each row has 3 stickers so we can add those up 3 + 3 + 3 + 3 + 3 and yet once again, repeated addition is simply multiplication so it's 3x5

 

Now if we have 5x3 stickers on one page, and 3x5 stickers on another, we can add those up 5x3 + 3x5 to get the total.

If you want to remove all addition altogether you can also remember that 5x3 = 3x5(multiplication is associative)

so we have 5x3 + 5x3 which is 2x5x3(which is also 5x6 or 10x3)