How to perform the following division?

Question

How to perform the following division?

74628/25/12?

which division is to be performed first?First or second and why?

Answer 1

Order of operations dictates that you go from left to right and that you treat $\times$ and $/$ as equally important. So $74628/25/12 = (74628/25)/(12)$.

I find it helps to replace each $``/ n"$ with $``\times \dfrac 1n"$.

So $74628/25/12 = 74628 \times \dfrac{1}{25} \times \dfrac{1}{12}$

As amWhy has pointed out, I don't mean for you to do things like

$74628/25/12 = 74628/(25/12) = 74628 \times \dfrac{1}{25/12}$.

That is wrong. You must proceed from left to right as shown in my example.

Answer 2

In the absence of grouping symbols, one normally performs multiplication and division in order from left to right. So this would mean $(74628/25)/12$.

If $74628/(25/12)$ were intended, the grouping symbols would be necessary.

Answer 3

Division is not commutative so the order does matter. Math is read from left to right, so written like that, the correct order would be (74628/25)/12.