Question 945571: Rectangular cards, 2cm by 3cm, are cut from a rectangular sheet 24cm by 36cm. What is the greatest number of cards that can be cut from the sheet?
Sorry, I am not sure of the topic, so I chose Area and Surface Area.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE EXPECTED SHOW-YOUR-WORK WAY:
Steps 1 and 2:
Sharpen your pencil, or take out the calculator, and
in any order make the following two area calculations.
A) Calculate the surface area (in square centimeters) of one card.
B) Calculate the surface area (in square centimeters) of the rectangular sheet 24cm by 36cm.
Step 3:
Divide the surface area of the rectangular sheet by the surface area of one card.
 .
THE SMART AND FAST WAY TO DO IT FOR A TIMED TEST:
It is possible to visualize and quickly calculate the result in your head
(no calculator needed) as follows.
Since both length are divisible by both card dimensions, there are several ways to cut the cards without any waste.
If you are doing it at home, you may want make cut through one of the edges every 3-cm, parallel to the other edge, making strips.
Then, stacking the strips, you may cut 2-cm sections through the stack to make the cards. Or you may cut every 2-cm first.
If making cards is your business, you probably have a machine with criss-cross sharp edges that comes down over the 24cm by 36cm sheet and makes the cross-cuts all at the same time.
The end result may look like this
 ,or like this 
In either case, quick mental math gives you the answer.
For the first picture,
cutting the long, 36-cm edge at 3-cm intervals,
and cutting the short, 24-cm edge at 2-cm intervals,
you would be calculating
 .
For the second picture,
cutting the long, 36-cm edge at 2-cm intervals,
and he short, 24-cm edge at 3-cm intervals,
you would be calculating
 .
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