Order of Operations

Introduction To Operations

Let's tackle a few basic order of operation questions together.

When evaluating a numerical expression, we're going to follow PEMDAS. Let's write that so we remember each step:

P is for parentheses

E is for exponents

M is for multiplication

D is for division

A is for addition and

S is for subtraction

Notice how I wrote multiplication and division, and addition and subtraction, next to each other. That's because those operations are done at the same step, whichever comes first from left to right. When we come across that, I'll explain more.

My first expression is 12 ÷ 2 × 3. For now we're going to be working with expressions that do not have parentheses or exponents, so we can go ahead and cross those off. This expression does have multiplication and division. Well, which do we do first? This is the left side and this is the right side. And in math, we generally move from left to right. Since our expression has both multiplication and division we are going to do the operation that comes first from left to right. This division right here comes first from left to right, so we are going to evaluate 12 ÷ 2 first. 12 ÷ 2 is six. So I'm going to write six under the purple line. Now I'm going to bring down the rest of the expression. What I'm circling in green is the rest of the expression. I'm going to bring down × 3. There is one step left to evaluating this expression. I'm going to evaluate 6 × 3. 6 × 3 is 18. I have no more multiplication or division, and I have no addition or subtraction. This expression evaluates to 18. I'm going to circle it. That's my final answer.

Our next expression is 8 + 2 - 7. I have no parentheses and no exponents. I also have no multiplication or division, so I'm left with the addition and subtraction step. Which operation comes first when moving from the left side of the operation to the right side? This addition comes first when moving from left to right, so I'm going to evaluate 8 + 2 first. 8 + 2 is 10 and now I bring down the rest of the expression. And to evaluate this last step 10 - 7 is three. I have no more addition or subtraction. This expression evaluates to 3. I'm going to circle my final answer.

Our next expression is 8 × 6 – 3. There are no parentheses, and no exponents. This expression does have multiplication. The first step of the this expression that I am going to evaluate and I’m going to evaluate is 8 × 6. 8 × 6 is 48. I bring down the rest of the expression. I have no more multiplication or division. The last step of this expression is 48 - 3. 48 – 3 = 45. This expression evaluates to 45.

Our last expression is 4 + 6 ÷ 3. No parentheses, no exponents. I do have division. Our first step is 6 ÷ 3. 6 ÷ 3 = 2. Now I bring down the rest of the expression. What's left is on the left side of what I just evaluated, but I am going to bring it down exactly as it is. 4 + 2. I have no more multiplication or division. 4 + 2 is my last step. 4 + 2 is 6. No more addition or subtraction. This expression evaluates to 6.