Eg. 8 over 3 divided by 1 over 3 = 8 over 3 times 3 over 1
In: 13
Division is the opposite of multiplication.
So dividing by a dividing thing is a double-division, so the opposite of the opposite of multiplication; which is just multiplication.
Because division and multiplication are the same kind of thing(ish), we can always do them in any order. So:
> 8/3 divided by 1/3
can be split up into:
> 8 divide by 3, divide by 1, divide by “divide by 3”
but that “divide by divide by 3” is a double division, so a multiplication:
> 8 divide by 3, divide by 1, multiply by 3
We can now re-order that:
> 8 divide by 3, multiply by 3, divide by 1
and then join these bits up together again to get:
> 8/3 multiply by 3/1
It is a deceptively complicated process but it only relies on division being the opposite of multiplication, and that you can re-order (and regroup) division and multiplication.
And understanding that fractions are the same as division.
[This also means that phrasing and brackets are important. 8/1/3 could be “8 divide by 1, divide by 3”, or it could be “8 divide by (1 divided by 3)” (so 8 multiplied by 3). ]
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