Hello all!

I am a new member of this forum, and am eager to partake in many wonderful math discussions and offer as much help as I can!

My first post, however, is a bit of an embarrassing confession (especially considering I enjoy math so much that I teach it at the high school level)! I have an order of operations misunderstanding, it would seem, and am looking for some clarification.

The problem as given is:

3st^2 / st + 6

where s = 4 and t =8.

My understanding of the problem, then, is:

3*4*8^2 / 4 * 8 + 6

Order of operations state that parentheses ought to go first, then exponents, then multiplication or division, then addition or subtraction.

My order of solving the problem:

3*4*64 / 4 * 8 + 6 (exponents first)

12 * 64 / 4 * 8 + 6 (left to right multiplication or division)

768 / 4 * 8 + 6

192 * 8 + 6

1536 + 6 (addition)

1542

Wolfram alpha did corroborate my answer: 3*4*8^2/4*8+6 - Wolfram|Alpha (although I'm not sure I used the proper division symbol)

However, this is not the answer that the book gives! The book gives an answer of 30. I can reproduce this answer IF I choose to multiply all my numbers first, then divide, then finish by adding.

Who is right? Is my understanding of Order of Operations flawed? Do I really need to complete all of my multiplication, then jump to division? I thought I merely went left to right on order of operations when I arrived at related operations (ie multiplication and division, or addition and subtraction).

Please help!

Thanks!