This is a little math trick that we can use when dividing by fractions.
What we’re doing is converted the division by a fraction to a multiplication by the reciprocal of the fraction.
That’s a lot of math words but you can really just think of the reciprocal as a fraction being flipped on its head - So the reciprocal of 1/3 = 3/1
For reference, the defining trait of the reciprocal is that any number multiplied by its reciprocal always 1.
If we look at it in the context of how I’ve used it here, we’re saying that 3 ÷ (1/3) = 3 * (3/1).
I’d encourage you to run both of these statements through a calculator to confirm that they both equal 9 (and maybe try some other examples as well, like 4 ÷ 3/5 = 4 * 5/3).
As for BODMAS, I prefer to think of it as BO(DM)(AS), since the order of multiplication/division and addition/subtraction are always solved left to right. You also have many tricks that allow you to treat division like multiplication and subtraction like addition, so they’re not really separate things.
To explain how your calculation differed from mine, I solved it as 9 - (3 ÷ (1/3)) + 1 whereas you solved it as ((9 - 3) ÷ (1/3)) + 1.
So, you’ve done a subtraction first, then a division, then an addition.
My best advice for tackling calculations like this is to try and add in some extra parentheses to help make things as clear as possible.
Thankfully, most mathematicians will do this for you when initially writing the equation, since they want you to actually be able to solve it without adding unnecessary ambiguity to the solution (math is hard enough as it is without making it worse!)
