forward and back fractions

a ppt is here

cancelling fractions

maybe slightly too many questions....
(not using a calculator, especially a scientific one, unless it's to check results)

the equivalent fractions below
involve all of the digits, 1 to 9

there are several more 1 to 9 versions for some of the fractions

reference: ben vitalis at fun with num3ers
many thanks to him

practice at multiplying and dividing

there is another one for a third

fraction cancelling

a ppt is here

sometimes, as in question (7) above, only part-cancelling a fraction helps to find the nth term rule
sometimes, for other fraction sequences, there is a stray fraction that cancels - not part of the general cancelling rule
some features of an overall generalisation are relatively easy to discern
and others aren't (for me anyway)
in questions (8) and (9) above, for example,  you need to persevere in writing out a list...

what is neat about the last two sheets is that the general form for the uncancelled sequence
is equivalent to the general form for the cancelled sequence

e.g. for the sheet with 3 questions:
question (1) has a generalisation 5n / (20n - 5) for the uncancelled fractions
and n / (4n - 1) for the cancelled fractions

whilst not a surprise, it's a neat consideration of how to cancel down algebraic fractions

cuisenaire rods and fractions

harder
if 3/5 is g
what is 1/5?
so what is 5/5?















a ppt is here