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Question:

A teacher has a rectangular piece of paper which is 52 cm long and 38 cm wide. She cuts the paper into squares, each measuring 5 cm by 5 cm. What is the largest number of whole squares she cuts?

A
70

Explaination

The key to solving this problem is realizing that you are looking for the number of whole, 5x5 cm squares that can be cut from this paper. There will be paper left over, since the dimensions of the paper are not exactly divisible by 5 cm.

There will be only 7 rows of squares possible along the 38-cm side, because $2742_w96_h13.png$. This is rounded to 7 because the .6 would only provide a 3 cm side and we need 5 cm sides. The 3 cm would be a leftover scrap, not useful for cutting another square.

(Note: The normal rounding process is different for problems like this. Normally, you would round 7.6 to 8. However, since the decimal value here is unusable, you just discard it when rounding and round down instead.)

Similarly, there will be only 10 columns of squares possible along the 52-cm side, because $3400_w105_h14.png$ or 10. (The extra 2 cm is also not enough for a square side.) $3172_w90_h14.png$ whole, 5 x5 cm squares

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