Working with my 9 year old son on multiplying and dividing fractions.
Without any understanding but playing with a calculator he worked out that to multiply fractions you multiply across:
E.g. 2/7 x 3/5 = 6/35.
Then he started with dividing fractions and typed in
12/24 divide 2/4 ,
He decided you do this in the same way but divide top and bottom so (12 divide 2 ) / ( 24 divide 4) = 6/6 =1
This works and a bit of algebra and you can see why.
And it is consistent with the multiplication algorithm, however the standard way of dividing fractions is to invert the second one and multiply.
Does my son's approach which doesn't work as easily for all fractions offer anything in terms of understanding dividing fractions?
Without any understanding but playing with a calculator he worked out that to multiply fractions you multiply across:
E.g. 2/7 x 3/5 = 6/35.
Then he started with dividing fractions and typed in
12/24 divide 2/4 ,
He decided you do this in the same way but divide top and bottom so (12 divide 2 ) / ( 24 divide 4) = 6/6 =1
This works and a bit of algebra and you can see why.
And it is consistent with the multiplication algorithm, however the standard way of dividing fractions is to invert the second one and multiply.
Does my son's approach which doesn't work as easily for all fractions offer anything in terms of understanding dividing fractions?