4.2.4 Moving Left to Right

There is one other point to note about using the PEMDAS code. Division is the opposite of multiplication; it “undoes” multiplication. If you multiply by three and then divide by three, you end up where you began. So, although multiplication comes before division in the PEMDAS code, they are really on the same priority level. The same is true of addition and subtraction: Because subtraction is the opposite of addition, addition and subtraction are on the same level. Therefore, we have an addendum to the PEMDAS code:

Let’s see how this works.

Suppose that you are trying to calculate five minus two plus four. There is a subtraction and an addition; these are at the same level, so work from left to right.

equation sequence five minus two plus four equals three plus four equals seven

Luckily the calculator knows about this aspect of the PEMDAS code and will automatically follow it.

Calculator symbol The calculator can be accessed in the left-hand side bar under Toolkit.

Activity symbol Activity: More on PEMDAS

Here are a couple more calculations to make sure that you have things straight. Try them without the calculator, and then use the calculator to check your answer.

(a) open one plus two close multiplication open one plus two minus three close

Hint symbol

Comment

Start by thinking through PEMDAS code. If you find more than one calculation at the same priority level, work through them from left to right.

Solution symbol

Answer

(a) open one plus two close multiplication open one plus two minus three close

Parentheses come first, but in the second set of parentheses, there is an addition followed by a subtraction. These are on the same level so when you do that calculation, work from left to right.

open one plus two close equals three and equation sequence open one plus two minus three close equals three minus three equals zero, so equation sequence open one plus two close multiplication open one plus two minus three close equals three multiplication zero equals zero

(b) open eight minus one plus three close multiplication two division five

Solution symbol

Answer

(b) open eight minus one plus three close multiplication two division five

Parentheses first: equation sequence open eight minus one plus three close equals seven plus three equals 10

Inside the parentheses, there is a subtraction operation followed by an addition operation. Because addition and subtraction have the same priority level, you will work from left to right, so equation sequence open eight minus one plus three close multiplication two division five equals open seven plus three close multiplication two division five equals 10 multiplication two division five

Now there is a multiplication and a division, so again, you’ll work from left to right:

equation sequence open eight minus one plus three close multiplication two division five equals 10 multiplication two division five equals 20 division five equals four

Make sure that you have added PEMDAS to your math notebook so that you can refer back to it easily if you need a reminder.

Now you have the hang of the basics try the activity on the next page. It’s a brainstretcher so don’t feel bad if you need to use the hints for help!

4.2.3 Further Practice with PEMDAS

4.2.5 PEMDAS Brainstretcher