WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; this lesson is on the order of operations.
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For order of operations... operations we know are multiplying, dividing, adding, subtracting, things like that.
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Those are all called operations; we are going to look at the order.
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When we have several different operations we look at within a single problem,
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there is an order of which ones we have to do first.
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To help you remember the order of operations, there is this phrase right here.
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Please excuse my dear aunt sally.
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That is just an easy way for you to remember the order of operations.
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Try to say it out loud a few times; please excuse my dear aunt sally.
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That just means p for parentheses, e for exponent, m to multiply, d for divide, a for add, and s for subtract.
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No matter what, you are always going to solve within the parentheses first.
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If you have parentheses, then always solve that first.
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Then e for exponent; you are going to do the exponents next.
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For m and d, multiplying and dividing, they are actually the same.
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When it comes to multiplying and dividing, you are just going to multiply or divide across whichever ones come first.
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Multiplying and dividing are actually the same; adding and subtracting are also the same.
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For multiplying and dividing, there is no order.
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It is just whichever comes first when it comes to these two.
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For adding and subtracting, also the same.
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If there is something you have to subtract before you have to add, then you just go ahead and do that.
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They are the same; there is no order in here.
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But please excuse my dear aunt sally is just an easy way for you to remember the order of operations.
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Make sure you say it a few times and try to remember those.
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We just went over variables so I have some variables here to help us with the order of operations.
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A plus in parentheses B minus C plus D squared plus E times F.
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First thing we have to do is parentheses; this right here would be number one.
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That is the first thing you would have to do.
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When you have a number B minus a number C, that is the first thing you are going to solve out.
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The second thing you are going to solve out is exponent.
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This; this will be the second thing for you to solve out.
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Then you are going to just rewrite this problem with that part solved.
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The next would be to multiply; E times F.
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That is going to be the third step; you are going to multiply those two first.
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All you are going to have left are adding and subtracting.
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You are going to just do that last; you will get your answer that way.
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Let's do a few examples; let's look at this; 2 plus 3 times 5.
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My order of operations is P-E-M-D-A-S.
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That is PEMDAS--please excuse my dear aunt sally.
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I don't have parentheses; I don't have any exponents.
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But I do have a multiplication; you are going to do this first.
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Even though this comes first, you would have to multiply before you add.
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You are going to do 2 plus... 3 times 5 is 15.
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This is going to become 17.
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If you were to add first, if we don't follow the order of operations rule,
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let's say you just did 2 plus 3 and then you times 5.
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2 plus 3 is 5; times 5 is 25.
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See how that is a different answer; this is a wrong answer.
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You have to make sure you follow this rule so that you can get the correct answer, 17.
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Another example would be A plus in parentheses 4 minus 2.
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We know always, always solve within the parentheses first.
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This is going to be solved first.
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I am going to write this because I am not going to do anything to that.
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4 minus 2 is 2; 8 plus 2 now is 10.
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When you follow the order of operations, you are going to get the correct answer of 10.
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Another example, 9 minus 2 squared.
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We just discussed in the last couple lessons on exponents.
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2 squared is the same thing as 2 times 2; or 2 times 2 like that.
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Exponents come after parentheses; we are going to have to solve this before subtracting.
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2 times 2 is 4; I am going to write 9 minus the 4.
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9 minus 4 is 5; 9 minus 2 squared is 5.
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This next example, kind of long, I have a few operations I can perform to this.
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But remember we have to stick with the order.
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I am just going to write PEMDAS so I can see the order.
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Always, always parentheses first; I have a parentheses right here.
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I am going to write everything else out; solve the parentheses out.
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5 minus 2 is 3; that is 3 squared divided by 9.
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Here what is my next operation?--exponents.
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Since I have an exponent right here, I would have to solve this out before I do anything else.
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This is going to be 6 times... this remember is 3 times 3.
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3 squared is the same thing as 3 times 3.
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3 times 3 we know is 9; then divided by 9.
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I am just rewriting this out; then multiplication and division right here.
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When we have only these two, they are actually going to be the same.
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There is no order for multiplication and division.
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You are just going to solve out whichever comes first when it comes to multiplying and dividing.
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For this problem, it just happens to be multiplication.
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We are just going to solve this out; 6 times 9 is 54.
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54 divided by 9; I am just rewriting this; 54 divided by 9 is 6.
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My answer to this, 6 times 5 minus 2 squared divided by 9, as long as you follow the order of operations, your answer will be 6.
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That is it for this lesson on order of operations.
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Thank you for watching Educator.com.