http://mathforum.org/library/drmath/view/54341.html

As written, your expression ax/by should be evaluated left to right: a times x, divided by b, times y. The multiplication is not done before the division, but both are done in the order they appear.
Some texts make a rule, as in your second solution, that multiplication without a symbol ("implied multiplication") should be done before any other operations in an expression, including "explicit multiplication" using a symbol. Following this rule, you would multiply a by x, then multiply b and y, then divide one by the other. Some (probably most) texts don't mention such a rule - but some of those may use it without saying so, which is far worse.

I don't know of a general rule among mathematicians that implied multiplication should be done before explicit multiplication. As far as I'm concerned, all multiplications fit in the same place in the order of operations.



I notice a lot of people have misunderstood MDAS to strictly mean Multiply then Divide then Add then Subtract.

In reality, this should be read as (Multiply AND Divide) before (Add and Subtract).

This means that Multiplication and Division have the same level of importance, and evaluating an expression containing only multiplication and division operators is done left to right.


There are those who say that the expression 2(9+3) has an implied multiplication. Yes, that is correct. it is implied that 2 is multiplied by (9+3), and could thus be interpreted as 2*(9+3).

Some keep saying that in 2(9+3), we should recognize that the parenthesis expressions should be evaluated first. Correct! That is why 2(9+3) becomes 2(12).

Before 2(12), there is a 48÷ and some people say that since parenthesis operations should be done first, 2(12) should become 24. Well, 2(12) has the 2 beside the (12), yes, but the 2 is NOT INSIDE (12). 2(12) is simply 2*(12) or 2*12

Since the division operator came before the multiplication operator, it gets evaluated first. Again, I repeat, MDAS does not say that Multiplication has absolute precedence over Division. Mult and Div have the same level of precedence, to be evaluated from left to right.

48÷2(9+3) becomes

48÷2(12) becomes

48÷2*(12) becomes

48÷2*12

That last expression is then evaluated left to right because division came before multiplication. The result is 288.

And no, I did not flunk my math. I got 1.0 in many of them. And I took up stuff like Math 17, 53, 54, 55, 101, 114, and 150 among others.