Why do we need order of operations?

In this cartoon, the girl put the grocery items in the bag in the wrong order.  How could something as simple as loading groceries have a "right" order?  Well, if more delicate items like bread or eggs go in the bag first, and then a heavy item like milk or a watermelon goes in next, what would happen?  Mom certainly wouldn't be happy.  Although the cartoon above is a silly representation, do you see why it depicts the importance of the order of operations?

You all know that putting items in a grocery bag requires an order.  Did you know, though, that number operations require an order, too?  In math, we call this the Order of Operations.  In order to get the right answer on a complex math problem, we must do the individual operations in the right order:

• Parentheses
• Exponents
• Multiplication &
• Division
• Addition &
• Subtraction

For example, let's look at the problem  5 + 4 x 2.  What happens if we do the operations from left to right as they appear, without using the order of operations?  We would first do 5 + 4 and get 9.  Then we would do 9 x 2 and get 18.  Is this the correct answer?  No!  We need to use PEMDAS to determine the correct order of operations.  We should first do the multiplication:  4 x 2 = 8.  Then, we should add 5 + 8 = 13.  Do you see the difference?

In your math journal, come up with a complex math problem like my example.  Using more than two operations in your problem, show how using the incorrect order of operations gives you the wrong answer.  Be sure to do the problem correctly, and circle your answer.