Log in Corey Gray 12 years agoPosted 12 years ago. Direct link to Corey Gray's post “I have always thought tha...” I have always thought that within the same level of priority that the specific order (left to right, right to left, jumping around, etc.) wasn't important. At Sal solves left to right: 40 / 2 - 5 x 6 = 20 - 30 = -10 But if I don't do it in the same order I get the same answer: 10 x 2 - 5 x 6 = 20 - 30 = -10 Thoughts? • (178 votes) Peter Collingridge 12 years agoPosted 12 years ago. Direct link to Peter Collingridge's post “This confused me when Sal...” This confused me when Sal first said it too, but it can make a difference. For example, if the question were rearranged to: 10 / 2 x 4 - 5 x 6 Then you can't do 2 x 4 first i.e: 10 / (2 x 4) - 5 x 6 Otherwise you would get: 10 / 8 - 5 x 6 1.25 - 30 -28.75 Similarly, in the example at 1 + 2 - 3 + 4 - 1 = (1 + 2) - (3 + 4) - 1 = 3 - 7 - 1 = -5 (178 votes) Angela.Galileo 12 years agoPosted 12 years ago. Direct link to Angela.Galileo's post “The practice questions ex...” The practice questions expect you to accept that a fraction bar is the equivalent of putting parentheses around the whole numerator and the whole denominator. Did Sal cover this in either of the order of ops vids? I can't find it but maybe I missed it. If not, would be a good addition to the vids. • (82 votes) Valentine 10 years agoPosted 10 years ago. Direct link to Valentine's post “I'm not sure that he cove...” I'm not sure that he covered this in the video, but when you have multiple operations over a fraction bar, with more operations or a single number underneath, the implication is that you are dividing the entire operation by the number underneath the fraction bar (fractions are essentially saying "the numerator divided by the denominator"). You cannot divide the operation until you have solved it, of course, so it is implied in the layout of the equation itself that you need to solve the numerator and/or denominator before dividing. (22 votes) Harshika M 7 years agoPosted 7 years ago. Direct link to Harshika M's post “I have been taught BODMAS...” I have been taught BODMAS which is • (25 votes) Luis 7 years agoPosted 7 years ago. Direct link to Luis's post “The way I have been taugh...” The way I have been taught is with PEMDAS; parenthesis, exponent, multiplication, division, addition, and subtraction. When it comes to multiplication and division, you do whichever comes first in a left to right order, same goes for addition and subtraction. (27 votes) jaredona1 12 years agoPosted 12 years ago. Direct link to jaredona1's post “i'm a bit confused... :? ...” i'm a bit confused... :? • (18 votes) ԃαɱσƚα.ɱαɾƈσԃʂ #JesusIsKing 3 years agoPosted 3 years ago. Direct link to ԃαɱσƚα.ɱαɾƈσԃʂ #JesusIsKing's post “PEMDAS = BIDMAS = BODMAS...” PEMDAS = BIDMAS = BODMAS PEMDAS parentheses; exponents; mult/div; add/sub BIDMAS brackets (parentheses); indices (exponents); div/mult (mult/div); add/sub BEDMAS brackets (parentheses); exponents; div/mult (mult/div); add/sub They're all the same way of order of operations. It's just that people use other words to tell the same thing. (8 votes) Sophia 3 years agoPosted 3 years ago. Direct link to Sophia's post “Uhm hi uhh I wanna know, ...” Uhm hi uhh I wanna know, uhh what is the meaning of "Exponents" It is a hard word to remember and spell. Can't they just eliminate it? • (7 votes) Skylar 3 years agoPosted 3 years ago. Direct link to Skylar's post “Hi Lexi! I am not Sal, bu...” Hi Lexi! I am not Sal, but I can still help you understand exponents if you want to. (10 votes) thinkname 10 months agoPosted 10 months ago. Direct link to thinkname's post “This is BEDMAS:-B = Brac...” This is BEDMAS:- • (11 votes) 27reillyr 4 years agoPosted 4 years ago. Direct link to 27reillyr's post “PEMDAS is what it would b...” PEMDAS is what it would be for short • (11 votes) Zachary 10 years agoPosted 10 years ago. Direct link to Zachary's post “Could you do order of ope...” Could you do order of operations with fractions? • (8 votes) Somansh 4 years agoPosted 4 years ago. Direct link to Somansh's post “You can and should do it ...” You can and should do it with everything from integers to decimals to fractions. (4 votes) SM 4 years agoPosted 4 years ago. Direct link to SM's post “is there an easier way to...” is there an easier way to do it. • (6 votes) RapidCoder 4 years agoPosted 4 years ago. Direct link to RapidCoder's post “No this is only way. Othe...” No this is only way. Other methods are modified. (10 votes) ͢∘⊽∘ 3 years agoPosted 3 years ago. Direct link to ͢∘⊽∘'s post “Please help me with math....” Please help me with math. Anything! I got a 67, and I need help. Specifically: Scientific Notation! And square roots. And pi. • (5 votes) Philip 3 years agoPosted 3 years ago. Direct link to Philip's post “*Square roots*: Square r...” Square roots: (9 votes)Want to join the conversation?
5:40
7:50
Bracket
Of
Division
Multiplication
Addition
Subtraction .
This is mostly the same as brackets and parentheses are the same and exponents is a different thing but then am I supposed to do multiplication first or division ??
I have been taught that I have to divide first but here they have explained something else . What do I have to do ?
All help appreciated😊
I live in england and my teacher told us to do:
Brackets (parentheses)
Indices (exponents)
Division
Multiplication
Addition
Subtraction
...so i dont do add and sub in the same group and if they are together go from left to right coz i would do the addition then the subtraction... is it different over in the US???? plz i am going mad thinking about it, which one is right????????
Thanks, Sal
- Lexi! <3
Exponents are numbers like this: 10⁵
The big number is the base while the smaller number floating is the number of times you multiply a base by itself. For example, in the exponent "10⁵", the expanded sentence is 10*10*10*10*10, which is 100,000. A trick only in exponents when 10 is the base is the number of 0's in the value is the small number. Like in the example, 10⁵, 5 is the small number or the exponent. So there will be 5 0's in the answer, 100,000. in exponents when 2 is the base, you just double the number the amount of times the small number, or the exponent is. For example, if the problem is 2⁵, I double 2, 4 times to get 32 (The first time doesn't count because 2¹ is just 2). also if 1 is the base, no matter what the small number is, the answer is always 1. and if the small number is 1, then the answer or value is always the base.
Hope this helps!
B = Brackets = Rank 1
E = Exponents = Rank 2
D = Division = Rank 3
M = Multiplication = Rank 3
A = Addition = Rank 4
S = Subtraction = Rank 4
BEDMAS - That's how I remember it
Always go left to right when doing the same rank.
There is also GEMS:-
G = Groupings = Rank 1
E = Exponents = Rank 2
M = Multiply/Divide = Rank 3
S = Subtract/Add = Rank 4
This is basically the same thing as Bedmas!!
Please upvote;)
Square roots are basically the “inverse operation of 2nd powers”. Remember that when something is raised to the second power, it is that value of the base multiplied by itself once. For example, 7^2 equals 7x7, which equals 49. In other words, whatever x-value raised to the 2nd power, if you apply the square root to it the result will return to the original x-value. The square root of 49 will equal 7. The square root of 4 will equal 2. When you have the square root function, it basically means it is wanting you to go back to the value which, when multiplied by itself, will reach the value inside the square root.
The expression “√x=y” is telling you, x = y^2, and√64=8, because you are being asked, “What value squared equals 64?” The answer is 8, because 8^2=64. For a constant, n, or when rewritten into the expression x = y^2, it is “What value do you need to plug into the y (your answer) so you get the amount displayed inside the square root?”
•Square roots for most values, except those which already are perfect squares, will result in an irrational value.
•If you haven't already, practice and learn multiplication and division, as well as prime factorization. Next, memorize the squares of all the single-digit numbers (I would recommend that you do so such that you eventually am able to instantly recall the square of any single-digit in less than a second). They will greatly help in memorizing which values are perfect squares. You can also try memorizing the squares of a few 2-digit numbers. Then, practice simplifying square roots through prime factorization. Even if your calculator is not designed for engineering and can only give decimal approximations, as long as there is the square root function you should be fine. Do practices of one value subtracted by a simplified version and see if the difference is 0 or something very close to it (E.g. √8 minus 2√2, √125 minus 5√5, etc.).
•After you are proficient (or even a "master") at recognizing perfect squares and their square roots, first memorizing some decimal approximations of simple values, such as √2, and use those values to help make estimates of non-perfect-squares.
•Here are some values squared (the arrow is pointing towards the result after the original value is applied the second power; if you want, I can add more values and their squares into this list. Just post a comment to let me know).
•1=>1
•2=>4
•3=>9
•4=>16
•5=>25
•6=>36
•7=>49
•8=>64
•9=>81
•10=>100
•11=>121
•12=>144
•13=>169
•14=>196
•15=>225
•16=>256
•17=>289
•18=>324
•19=>361
•20=>400
•21=>441
•22=>484
•23=>529
•24=>576
•25=>625
•26=>676
•27=>729
•28=>784
•29=>841
•30=>900
•31=>961
•32=>1024
•33=>1089
•34=>1056
•35=>1225
•36=>1296
•37=>1369
•38=>1444
•39=>1521
•40=>1600
Therefore, things are working the other way around: If you have say √1024, then your answer will be 32 because 32, when squared, gives you 1024. By memorizing a number of perfect squares, you can check if the value within the square root is a perfect square, and if it is not find the two perfect squares nearest to it, one greater and one less. For example, if you have √1500 [a decimal approximation is 38.7298, you may be able to quickly see that since 1500 is between 1444 and 1521, then the square root of 1500 is between 38 and 39.
(This is the same way cube roots and other radicals/roots work, except that cube roots use 3rd powers, etc.)
Simplifying square roots by factoring: Start by factoring perfect squares out of the value displayed within the square root symbol. For example, if you have √50, you can factor it into √(25x2). Whatever values are perfect squares may be moved out of the square root sign while turning that perfect square into the square root (since the value is “no longer being affected by the square root”. √(25x2) equals 5 x √(2), approximately 7.07. However, remember that the square root values outside are multiplied together (and not added). Finally, whatever factors which are not perfect squares are left within the square root sign. If there is more than one factor, then those get multiplied within the square root. For example, if there is √1800, you can do it in these steps (the xs are multiplication signs, not variables):
•Factor a 100 (or two 10s) out of the 1800, so you have √(100 x 18)
•Factor a 9 (or two 3s) out of the 18, so you have √(100 x 3 x 3 x 2)
•Applying the square root to 100 means you have 10, and applying the square root to 9 means you have 3. (Remember that for square roots, whatever “pair of two equal numbers” means a perfect square.)
•10 x 3 = 30; since there is only a single 2, not a pair, you end up with 30 x √(2).
Video transcript
In this video we're goingto talk a little bit about order of operations. And I want you to pay closeattention because really everything else that you'regoing to do in mathematics is going to be based on youhaving a solid grounding in order of operations. So what do we even mean whenwe say order of operations? So let me give you an example. The whole point is so that wehave one way to interpret a mathematical statement. So let's say I have themathematical statement 7 plus 3 times 5. Now if we didn't all agree onorder of operations, there would be two ways ofinterpreting this statement. You could just read it left toright, so you could say well, let me just take 7 plus 3, youcould say 7 plus 3 and then multiply that times 5. And 7 plus 3 is 10, and thenyou multiply that by 5. 10 times 5, itwould get you 50. So that's one way you wouldinterpret it if we didn't agree on an order of operations. Maybe it's a natural way. You just go left to right. Another way you could interpretit you say, I like to do multiplication beforeI do addition. So you might interpret it as --I'll try to color code it -- 7 plus -- and you dothe 3 times 5 first. 7 plus 3 times 5, which wouldbe 7 plus 3 times 5 is 15, and 7 plus 15 is 22. So notice, we interpretedthis statement in two different ways. This was just straight leftto right doing addition then the multiplication. This way we did themultiplication first then the addition, we got two differentanswers, and that's just not cool in mathematics. If this was part of some effortto send something to the moon because two people interpretedit a different way or another one computer interpreted oneway and another computer interpreted it another way, thesatellite might go to mars. So this is just completelyunacceptable, and that's why we have to have an agreedupon order of operations. An agreed upon way tointerpret this statement. So the agreed upon order ofoperations is to do parentheses first -- let me write it overhere -- then do exponents. If you don't know whatexponents are don't worry about it right now. In this video we're not goingto have any exponents in our examples, so you don'treally have to worry about them for this video. Then you do multiplication --I'll just right mult, short for multiplication -- then you domultiplication and division next, they kind of have thesame level of priority. And then finally you doaddition and subtraction. So what does this order ofoperations -- let me label it -- this right here,that is the agreed upon order of operations. If we follow these order ofoperations we should always get to the same answerfor a given statement. So what does this tell us? What is the best way tointerpret this up here? Well we have no parentheses --parentheses look like that. Those little curlythings around numbers. We don't have anyparentheses here. I'll do some examples thatdo have parentheses. We don't have anyexponents here. But we do have somemultiplication and division or we actually just havesome multiplication. So we'll order of operations,do the multiplication and division first. So it says do themultiplication first. That's a multiplication. So it says do thisoperation first. It gets priority overaddition or subtraction. So if we do this first weget the 3 times 5, which is 15, and then we add the 7. The addition or subtraction --I'll do it here, addition, we just have addition. Just like that. So we do the multiplicationfirst, get 15, then add the 7, 22. So based upon the agreed orderof operations, this right here is the correct answer. The correct way tointerpret this statement. Let's do another example. I think it'll make things alittle bit more clear, and I'll do the example in pink. So let's say I have 7 plus 3 --I'll put some parentheses there -- times 4 divided by2 minus 5 times 6. So there's all sorts of crazythings here, but if you just follow the order of operationsyou'll simplify it in a very clean way and hopefully we'llall get the same answer. So let's just follow theorder of operations. The first thing we have todo is look for parentheses. Are there parentheses here? Yes, there are. There's parenthesesaround the 7 plus 3. So it says let's do that first. So 7 plus 3 is 10. So this we can simplify,just looking at this order operations, to10 times all of that. Let me copy and pastethat so I don't have to keep re-writing it. So that simplifies to10 times all of that. We did our parentheses first. Then what do we do? There are no more parenthesesin this expression. Then we should do exponents. I don't see any exponents here,and if you're curious what exponents look like, anexponent would look like 7 squared. You'd see these little smallnumbers up in the top right. We don't have any exponentshere so we don't have to worry about it. Then it says to domultiplication and division next. So where do we seemultiplication? We have a multiplication,a division, a multiplication again. Now, when you have multipleoperations at the same level, when our order of operations,multiplication and division are the same level, thenyou do left to right. So in this situation you'regoing to multiply by 4 and then divide by 2. You won't multiplyby 4 divided by 2. Then we'll do the 5 times6 before we do the subtraction right here. So let's figureout what this is. So we'll do thismultiplication first. We could simultaneously do thismultiplication because it's not going to change things. But I'll do thingsone step at a time. So the next step we're goingto do is this 10 times 4. 10 times 4 is 40. 10 times 4 is 40, then youhave 40 divided by 2 and it simplifies to that right there. Remember, multiplication anddivision, they're at the exact same level so we're goingto do it left to right. You could also express this asmultiplying by 1/2 and then it wouldn't matter the order. But for simplicity,multiplication and division go left to right. So then you have 40 dividedby 2 minus 5 times 6. So, division, you justhave one division here, you want to do that. You have this division and youhave this multiplication, they're not together so youcan actually kind of do them simultaneously. And to make it clear that youdo this before you do the subtraction becausemultiplication and division take priority over addition andsubtraction, we could put parentheses around them to saylook, we're going to do that and that first before I do thatsubtraction, because multiplication anddivision have priority. So 40 divided by 2 is 20. We're going to have that minussign, minus 5 times 6 is 30. 20 minus 30 is equalto negative 10. And that is the correctinterpretation of that. So I want to make somethingvery, very, very clear. If you have things at the samelevel, so if you have 1 plus 2 minus 3 plus 4 minus 1. So addition and subtraction areall the same level in order of operations, you shouldgo left to right. So you should interpret this as1 plus 2 is 3, so this is the same thing as 3 minus3 plus 4 minus 1. Then you do 3 minus 3is 0 plus 4 minus 1. Or this is the same thingas 4 minus 1, which is the same thing as 3. You just go left to right. Same thing if you havemultiplication and division, they're at the same level. So if you have 4 times 2divided by 3 times 2, you do 4 times 2 is 8divided by 3 times 2. And you say 8 divided by 3 is,well, we got a fraction there. It would be 8/3. So this would be 8/3 times 2. And then 8/3 times tois equal to 16 over 3. That's how you interpret it. You don't do thismultiplication first or divide the 2 by that and all of that. Now the one time where you canbe loosey-goosey with order of operations, if you have alladdition or all multiplication. So if you have 1 plus 5 plus 7plus 3 plus 2, it does not matter what order you do it in. You can do the 2 plus 3, youcan go from the right to the left, you can go from theleft to the right, you could start some place in between. If it's only all addition. And the same thing is true ifyou have all multiplication. It's 1 times 5 times7 times 3 times 2. It does not matter whatorder you're doing it. But it's only with allmultiplication or all addition. If there was some divisionin here, if there's some subtraction in here, you'rebest off just going left to right.
