Maha's NEW method for dividing decimals

Don was helping Maha with problems she was having trouble with on the SSAT test. The problem they looked at was: '16 is 25% of what number?' Don's first reaction was to write this as 16 = 25%* ? One method Don had was 16'1/4 = 16*4/1= 64. Maha knew that she should divide 16 by .25; she wrote  . They talked about the 'normal' way to do this: Move the decimal point 2 places to the right in each number, so  would change to . Don made sure that Maha understood why this would give the same answer. He showed her that ' = 30/40 because when you multiply the top and bottom of a fraction by a number, say 10, to get , and  . Now what happens if you multiply a number by 1? It doesn't change anything. So  = =  =  =  ; and  by multiplying top and bottom by 100. That's why they taught us to 'move the decimal 2 places to the right' (multiply top and bottom by 100) - and make a whole number 25 outside the box.

The above was a little background to Maha's method: 

She took  and changed it to  , which is NOT the same problem any more. But with a little discussion, she agreed that when she got her answer she would have to multiply it by 100, because she divided 16 by 100 to get .16 .  Maha tried the division on the right below first, .1 ' .2 ; she added a couple of 0's to get .100 and she put the decimal point in the answer above the decimal point below it. She said 20 into 100 will go 5 times. So her answer was .5  . Don checked this with strips (.2 of the 10x10 square will go into .1, ' or .5 times). They checked it also by multiplying .5 * .20 = .100 = .1 .

Maha then did their original division, above left,  .16000 ' .25 = .64 (because 25 will go into 160 6 times, then 25 will go into 100 4 times), then she multiplied .64 by 100 to get the correct answer of 64.

What Maha did was very exciting, because she made up this new way to divide decimals, that neither of them had seen before!!

Fine job, Maha!!