In this video, we're going to talk about order of operations. Perhaps you've heard of the expression PEMDAS. Please excuse my dear Aunt Sally. P stands for parentheses, E for exponents, M for multiplication, D for division, A addition, S subtraction. Now...
P, parentheses, has more priority than exponents. So you want to deal with the numbers inside of parentheses, and then the exponents. Multiplication and division has more priority than addition and subtraction. So you want to multiply or divide before you add or subtract. Addition and subtraction, they have about the same priority.
For example, let's say if we want to simplify this expression. 5 plus 8 minus 3. We can add the two numbers first. 5 plus 8 is 13, and then subtract. 13 minus 3 is 10. Now, notice if we subtract first and then add, the result is the same. 8 minus 3 is 5. 5 plus 5 is 10. So you get the same thing.
So for addition and subtraction, the order doesn't matter. Now what about multiplication and division? So let's say if we wish to divide 18 by 3, and then multiply by 4. So according to PEMDAS, does multiplication and division, do they have the same priority? Or is one greater than the other? Now, let's do this both ways.
Let's see if we're going to get a different answer or the same answer. Let's divide first. Let's go from left to right. 18 divided by 3 is 6. 6 times 4 is 24. Now, what's going to happen if we multiply?
3 times 4 is 12. 18 divided by 12 is 1.5. Which answer is the correct answer? If you're not sure, take a calculator and type in exactly what you see.
If you type in 18 divided by 3 times 4, in that order, it will give you 24. So this is the right answer. When you're dividing and multiplying, if you're dividing first and then multiplying second, go from left to right. In this case, it appears that division has more priority than multiplication. Now, what if it's the other way around?
What if multiplication comes first before division, like in this example? Does the order matter? Well, let's do it both ways.
12 times 6 is 72. And so, 72 divided by 2 is 36. Or, if we divide first, 6 divided by 2 is 3. 12 times 3 is 36. So it turns out that, if multiplication comes first, the order doesn't matter. You're going to get the same answer. But, if division comes before multiplication, you want to divide first. So, a general rule when you're dealing with multiplication and division, perform the operation from left to right. If you do that, it doesn't matter which one is going to come first.
You're going to get the answer correctly. Hey, let's try some examples. Try these two.
28 divided by 4 times 3, and 3 times 8 divided by 4. So, let's analyze it from left to right. 28 divided by 4 is 7, and 7 times 3 is 21. So this is the answer. If you do it the other way, you won't get the right answer. If you multiply 4 times 3, That's 12. 28 divided by 12 is not 21. Now in the second example, multiplication comes before division, so we can do it in any order. 3 times 8 is 24. 24 divided by 4 is 6. Now if we do it the other way, 8 divided by 4 is 2, and 3 times 2 is 6. So now we're going to go over a mixed review.
Examples contain addition, subtraction, multiplication, and division. So let's begin. 8 plus 9 times 6. What is the answer? Now, should we add or should we multiply first?
According to PEMDAS, multiplication and division has more priority than addition and subtraction. So you want to multiply before you add. But let's do it both ways. 9 times 6 is 54. 8 plus 54 is 62. So 62 is the right answer. Now, if you do it the other way, 8 plus 9 is 17. 17 times 6. 10 times 6 is 60. 7 times 6 is 42. 60 plus 42 is 102. These are not the same.
But to know the right answer... Type it exactly the way you see it in a scientific calculator. 8 plus 9 times 6 is 62. So multiplication has more priority than addition.
Now let's try to do the same thing. Let's try some more examples. What about 16 minus 14 divided by 2? Should we divide first or should we subtract?
Division has more priority than subtraction. So let's divide first. 14 divided by 2 is 7 and 16 minus 7 is 9. Now type it in the calculator and just confirm your answer.
16 minus 14 divided by 2 if you type it the exact same way you will get 9 so 9 is the right answer now for the sake of practice try this one 48 divided by 6 times 2 plus 7 So, multiplication and division has more priority than addition. So, we're going to save this 7 for last. Now, let's focus on this. We have division and multiplication.
If you're unsure about which way to go... Start from the left side and work your way towards the right side. 48 divided by 6 is 8. And then we have 8 times 2, which is 16. 16 plus 7 is 23. And so this is the answer. Now let's try one more example. What's 3 times 12 divided by 4 minus 9?
So we need to multiply and divide before we subtract. And when dealing with multiplication and division, let's start from the left side and work our way towards the right side. So let's multiply 3 by 12 instead of dividing it by 4. That is, dividing 12 by 4. Now because multiplication comes first, we can do it in any order.
3 times 12 is 36. 36 divided by 4 is 9. And 9 minus 9 is 0. So this is the final answer. Now let's talk about exponents. What is the difference between 3 squared, negative 3 squared, and also negative 3 squared? It sounds the same, but it's a little different. So let's start with 3 squared.
3 squared means that you're multiplying two 3's together. 3 times 3 is 9. Now, negative 3 squared means... that you're multiplying two negative 3's together and that's going to be positive 9. A negative times a negative is a positive number. Now what about the other negative 3 squared? What does that mean?
Now in this case, example the two applies to the negative and the three so we have two negatives and two threes in this example the two only applies to the three not the negative sign so we have one negative symbol and two threes multiply to each other negative three times positive three is negative nine so make sure you understand the difference between these two don't mix it up don't get it confused Now let's try some more examples. What's 3 plus 4 squared? Now according to PEMDAS, exponents have more priority than addition. So 4 squared, that's 4 times 4, that's 16. 3 plus 16 is 19. So that's the answer.
Try this one. And also this one too. Feel free to pause the video.
Now what's 2 to the 3rd power? This is 2 times 2 times 2, 3 times. 2 times 2 is 4. 4 times 2 is 8. 8 minus 7 is 1. now which one comes first division or exponents so according to PEMDAS Exponents has more priority than division. So we got to find out the value of 3 squared.
3 times 3 is 9. 36 divided by 9 is 4. Now for our final example, let's try this one. 2 to the 4th times 3 minus 8. So that's 2 times 2 times 2 times 2. 4 times. 2 times 2 is 4, so we have another 4. 4 times 4 is 16. 16 times 3 is 48. 48 minus 8 is 40. So now we're going to deal with examples that have parentheses and exponents.
So let's start with this one. What's 2 times 3 plus 5? So should we add or should we multiply?
When I mean add, should we work with what's inside the parentheses, or should we multiply first? It turns out for this example, the order doesn't matter. Ideally, you want to work out what's inside the parentheses first, but for this specific example...
you will get the same answer. 3 plus 5 is 8. 2 times 8 is 16. Now another way in which we could evaluate this expression is we could distribute the 2. 2 times 3 is 6. And 2 times 5 is 10. Now there's a plus sign between them. 6 plus 10 is 16. And as you can see, you will get the same answer. Now what about this example?
3 times 2 plus... 3 squared. Now you want to follow you want to work on what's inside the parentheses and then use the exponent before you multiply. It's easier if you do it that way. 2 plus 3 is 5. 5 squared which is 5 times 5 that's 25. 3 quarters is 75 cents so 3 times 25 is 75. Try this one.
What's 150 minus 2 times 2 plus 5 squared? So once again, we want to work on the inside of the parentheses and then use the exponents. And then we can multiply and then subtract. So let's follow this rule again.
So working with what's inside the parentheses, 2 plus 5 is 7. So we finished with P. Now let's move on to E. Let's work with the exponents.
7 squared, which is 7 times 7, that's 49. So now let's move on to multiplication. 2 times 49 is 98. Now let's move on to subtraction. 150 minus 98 is 42. So 42 is the final answer in this example. Actually, that is not 42. I take that back. That is 52. And you can confirm that with the calculator.
52 is the final answer. Here's the last example for this particular video. Should we divide first or should we work with what's inside the parentheses?
As a general rule, always evaluate the stuff inside the parentheses. 9 minus 5 is 4. 4 times 4, or 4 squared, is 16. 64 divided by 16 is 4. And so that's it. Now let's move on into some examples involving fractions. Try this one.
What's 3 times 4 squared minus 3 squared times 5 divided by 5 times 9? So let's start with the top. Let's work with the exponents before we multiply. 4 squared is 16, 3 squared is 9. And we can multiply 5 times 9, that's 45. Next, 3 times 16 is 48. 9 times 5 is 45. And now we can subtract what's on the top.
48 minus 45 is 3. And so this is what we have. And then finally, let's reduce the fraction. Let's divide both numbers by 3 because they're divisible by that. 3 divided by 3 is 1. 45 divided by 3 is 15. So this is the solution. Try this one.
3 plus 4 squared divided by 2 squared times 5. 4 squared is 16, 2 squared is 4. And then multiply. 4 times 5 is 20, 3 plus 16 is 19. So it's 19 over 20. Here's one more example. 5 times 8 times 6 squared divided by 12 times 10 times 4. So in this case, we're dealing with multiplication and maybe one exponent situation.
For this problem, let's break down the numbers into small numbers. 8 is 4 times 2, 12 is 6 times 2, 10 is 5 times 2, and 6 squared is 6 times 6. So we can cancel a 6, we can cancel a 4, we can cancel a 5. And we can cancel a 2. So we're left with 6 divided by 2, which is 3. And that's the answer.