3.3.12 Multiplication and Division Puzzle

Multiplication and division require practice; the best way to learn is to invest time. Depending on how you learn, you might spend that time playing games, practising on paper, and/or watching videos.

Here’s a multiplication and division puzzle you can baffle your friends and family with.

Give someone your calculator and tell them “Think of any three-digit number and enter it on the calculator—for example, 562. Now enter the same three figures again to give you a six-digit number—for example, 562,562.”

Now, you pretend to think hard and finally say, “Divide that six-digit number by … er … 13.”

Pretend to think hard again, and then say, “Now, divide the number you’ve got by … um … 11.”

Finally, say, “Right—I’ve got it! Divide your new number by seven, and you’ve got back to the number you started with.” Hopefully they’ll be impressed by your new math skills!

You can tell them how it works if you want. As you now know, dividing by 13, then 11, and then seven is the reverse of multiplying by 13, then 11 then seven.

13 multiplication seven multiplication 11 equals 1001 (try it on your calculator). Multiplying any three-digit number by 1001 will give you the same three figures repeated: try that now. It’s like multiplying any single digit by 11 will give you the figure repeated: six multiplication 11 equals 66, for example, and eight multiplication 11 equals 88.

So dividing a six-digit number, made up of a repeated pair of three-digit numbers, by 13, 11, and then seven will result in returning to the number your friend started with. Have fun!

Well done, you have reached end of another unit! Before you move on try this game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] , which helps us practice our multiplication skills.

 Now it is time to do the self-check questions and end of unit quiz. Good luck!

3.3.11 Calculator Exploration—A Practical Problem

3.4 Self-Check