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Write the number 12345679 on the board (note the missing 8).

Ask the student to name any digit from 1 to 9. Suppose it is three.

Tell the class that if they multiply 12345679 by 27, they will get a big surprise.

Children love surprises. You can see the astonishment on their faces when they get
the answer 333333333.

Repeat the stunt with a different digit, say 8.Now the multiplier is 72 and the product is 888888888.

How do you know what multiplier to give?

Dividing 111111111 by 9 yields 12345679,

so multiplying that number by 9 gives 111111111.

If 111111111 is multiplied by any digit A, the product will be AAAAAAAAA.

So, the multiplier is 9A, where A is the chosen digit.

Since 9 x 12345679 = 111111111,

Then A x (9 x 12345679) = AAAAAAAAA or

(9A) x 12345679 = AAAAAAAAA