Order of Operations

Homework Statement

okay. So here is the problem:

x= 48÷2(9+3)

The Attempt at a Solution

So, what I am thinking, is how should the order of operation should be followed. There are different answers when tried using a different order of solving. So, could you please help me?

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SammyS
Staff Emeritus
Homework Helper
Gold Member
The method on the right more closely follows the rules for order of operations. It does begin by changing the division to the equivalent multiplication. After that it does the operations in an order consistent with the rules for order of operations.

The method on the left uses some properties of equations to rewrite the equation as an equivalent equation in a number of its steps. It also makes use of the associative law and does some rather fancy division of fractions. (It's fancy if you're asking this basic a question.) All the steps are the result of legal algebraic operations, so you get the correct result for x.

eumyang
Homework Helper
The order of operations should be followed, period. I'm confused that you said that you get different answers, but the two attempts you attached give you the same answer.

If you did a search, you would have found this thread, which has the exact same question:

Last edited by a moderator:
The order of operations should be followed, period. I'm confused that you said that you get different answers, but the two attempts you attached give you the same answer.

If you did a search, you would have found this thread, which has the exact same question:

Yeah. I have found that thread. But, with so many words and posts, I'm very much confused on which to follow.

Last edited by a moderator:
Mark44
Mentor
To summarize that very long thread, expressions such as 48÷2(9+3) should be avoided because of their ambiguity; namely, is 48 being divided by just 2, or is it being divided by [2 * 12]?

To make matters worse, two different calculator models from the same company yield two different answers for the same expression.

To avoid this problem use parentheses to indicate clearly what you're dividing by. If you mean
$$\frac{48}{2 \cdot 12}$$

write it as 48/(2 * 12)

Here the parenthese make it clear that the multiplication should occur before the division occurs.