Introduction: Here is an interesting division problem. It is one that might amaze friends or family. See if you can figure out how it works.

Problem:

1. Start with the 6-digit number 273 273. Divide this number by 7, then divide the result by 11, and finally divide this result by 13. What is your final answer?
2. Now begin with the number 918 918. Divide it by 7, then divide the result by 11, and finally divide this result by 13. What is your final answer?
3. Without actually working out the division calculations, can you predict what final answer you would get if you divide 738 738 by 7, then that result by 11, and finally that result by 13? What is your prediction?
4. List another number you could start with that would result in a similar result to the pattern discovered in questions 1 to 3. Try it out.
5. Would it matter in which order you divide? For instance, would the result in the above questions be any different if you first divide by 11, then divide by 13, and then divide by 7? Explain why this would be the case.
6. Describe the 6-digit numbers on which the pattern works. Explain why the pattern works for these numbers but not for other 6-digit numbers.

Materials: pencil, paper, calculator

Extra Questions: Find two numbers so that if you divide the first number into 82 648 264 and then divide the second number into that result, you will get 8 264.

Numbers and operations, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
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