Number properties

[shankarsg.89]

someone pls help me with this question
question : Ramon wants to cut a rectangle into identical square pieces. If the board is 18 inches by 30 inches . what is the least number of square pieces he can cut without wasting any of the board??

a.) 4 b.) 6 c) 9 d) 12 e) 15

[anupinkm5]

what is the answer? is it 15 squares?

[shankarsg.89]

yes answers is 15 ...but could you explain me in detail?

[tommywallach]

Hey Shankar,

So it's 18 by 30. Whatever dimensions we choose for the square, the side lengths need to divide evenly into both 18 and 30 (otherwise, there will be extra space at the end of some row/column).

So let's start with 3x3. 18 x 30 = 540 square units. Each square here is 9 square units. 540/9 = 60 squares.

But maybe we could make fewer. Let's go with 6x6. Each square here is 36 square units. 540/36 = 15.

6 is the biggest number that goes into both 18 and 30, so we're done!

-t

[danc]

Hey Tommy, I posted an explanation for this elsewhere but can't find it. Was I wrong in my analysis?

[bhupal014]

someone pls help me with this question
question : Ramon wants to cut a rectangle into identical square pieces. If the board is 18 inches by 30 inches . what is the least number of square pieces he can cut without wasting any of the board??

a.) 4 b.) 6 c) 9 d) 12 e) 15

answer is (a)
Let's see. cut from length side vertically leaving the length 18 such that 18:18
Secondly, cut the 12 by 18 horizontally leaving the side 12:12
Finally, cut rest of the piece vertically leaving the area 6:6
Therefore total of 4 squares and you are good to go. But remember, the squares are different in dimensions.
bhupal

[tommywallach]

Hey Dan,

Nope, you did great! It was an annoying forum issue. The poster in question actually posted his question twice, in two separate places (don't do that, forum-goers!). I responded to this one before I saw the one that you had responded to, and I had to delete one of them. If you feel like posting your awesome explanation here as well, you are welcome to, but don't feel an obligation. : )

-t