9*(-8)*7÷(-5) = ? Reddit order of operations with negative numbers r/homeworkhelp

How to evaluate 9*(-8)*7÷(-5)? We will have to follow the order of operations and work with negative numbers. This problem is from Reddit r/homeworkhelp. See the original post below
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#math #algebra #mathbasics

[@bprpmathbasics]

According to Google calculator, 1/0 = ? (A) undefined (B) 0 (C) 1 (D) Infinity Answer here: kzbin.info/www/bejne/pqLFgXaErZmUbrM

[@cdkw8254]

good is bad at math confirmed

[@arnoygayen1984]

Infinity

[@electriclegend6390]

Undefined

[@RdX.369]

A. and D. if Limits?

[@juan_ta]

The specific public to this video, don't they know about factorization?: It's the fastest path to the sought answer! (No ambiguity in the first example; no need to go from left to right --as long as you keep the common understanding that the dividend goes to the left of ÷ and the divisor to the right).

[@JubeiKibagamiFez]

7:41 I always say PEMDAS=PEDMSA, but honestly, I love your pyramid the most. It's the best explanation for order of operations.

[@bprpmathbasics]

Thanks!

[@mhzellers]

The original question though was “is there any way this doesn’t end in in decimals?” It should be obvious without doing all the multiplication and division that there would be a remainder or fractional part of the answer since the numbers being multiplied and then divided by 5 don’t have a factor of 5.

[@tommyb6611]

Also it's funny they believe the paranthesis would change something.

[@user-kh6mr5up4j]

since we already use ÷ symbol we also should add 100 4/5 (without + symbol) as an answer to make it more cursed.

[@solidpixel]

I agree the pyramid is more clear. That's why I never bothered remembering PEMDAS when we covered it in school.

[@ethohalfslab]

Have you ever done a video on implied multiplication's order in PEMDAS? Like, for instance, a lot of people would agree that 2÷4x is the same as 2÷(4x). But when you have 2÷4(3), there is debate over whether this means 2÷(4*3) or (2÷4)*3.

[@ThePeer1987]

I wouldn't agree that 2÷4x is the same as 2÷(4x). I would agree it is the same as (2)÷(4)(x) though

[@kirkanos771]

Because it's PE(MD)(AS) and not PEMDAS. People forget.

[@Sonicgott]

Sometimes I think math is really an English grammar test.

[@XxskoolxX]

My calc 3 prof told me every thing up to calc 3 is really just learning grammar for doing math.

[@guessundheit6494]

Which is why science and business majors have better English skills than arts majors. Exactness matters when dealing with laws or precision.

[@JubeiKibagamiFez]

I did already watch this, but the other division x\y came uo in the newest video, so when converting x\y to long division, does the x go in the box or the y?

[@guessundheit6494]

8:10 - Too many people don't understand that division ~IS~ multiplication, and has equal order of precedence. It should be taught that way, that division is multiplying by a fraction. 12 / 3 x 4 = 12 x (1/3) x 4 = 48 x (1/3) = 48 / 3 = 16

[@malto_only]

I have made an arithmetic operation that i want to share with you. It's called append operator, As name suggests it is used to append a number into the right end of another number. I have designed a symbol but it doesn't has its unicode so I will denote it as (+P) Eg: 17 (+P) 0 = 170 168 (+P) 78 = 16978 It has some properties, 1. (Add what number to get smallest next digit number) like 17(+P)0 = 170 so the addative digit is 170 - 17 = 153

[@lerarosalene]

You've just invented JavaScript /hj

[@nikolausmoll9201]

I do not agree that "100R4" is a solution, because the information about the ramainder is pretty useless, if I do not know the divisor... sure, the divisor is part of the calculation, but it is "lost" in the solution.

[@LaMirah]

Neither 9, nor 8, nor 7 have 5 as a factor, and all operations are multiplications and division, so it's impossible to get an integer result, even if you were to rearrange the terms.

[@Amil006]

here, I have a question. Why is the area of a rectangle is its base times hight? What is the logic of this?

[@Leopoldshark]

Because rectangles are rows of 1x1 squares organized into columns

[@XxskoolxX]

I understand where you are coming from, but I would also emphasize that writing problems like that can also be very messy. I've seen a lot of high level courses have mistakes be made in lectures ( in particular my solid state materials class) devolve in to chaos because it wasn't clear what was supposed to be divided. Parenthesis should be used to dictate intention. I.E : 12 / (3x4) or (12/3) x 4.

[@steffanreichenbach3124]

if we look at 2x3x4x5x6x7 and 3:3:4:4:5:5 we can clearly see, that in the first row it doesn´t matter how you multiplicate its always the same, in the later it is different according your order. BUT why is it so at the division ?? is there a known underlying reason for this ???

[@sbyrstall]

For example, 2*3÷4*5. You aren't able to communicate because the ÷ is attached to the 4. Division can be rewritten by multiply by the reciprocal. This the expression becomes 2*3*(1/4)*5. Now you can communicate all you want.

[@steffanreichenbach3124]

thanks for answering. But it´s not my point.... i know he rules and how you can note it differently, look just additing, substracting and multiplication doesn´t demand an order, why just diivision need it ??? @@sbyrstall

[@lagomoof]

@@steffanreichenbach3124 a×b = b×a but a÷b ≠ b÷a in general (and watching out for divisions by zero). That's why division appears to do strange things. The fancy way of saying this is: division is _non-commutative._ Subtraction has the same problem. You might also be thinking about the property, where a×(b×c) = (a×b)×c but a÷(b÷c) ≠ (a÷b)÷c. This is division being _non-associative._ Subtraction also has this problem. That's why doing things left to right is important. If everyone agrees that's the way, then we can all get the same answers.

[@Raihan_Badat]

I have a small question When we address number smaller than zero let’s say -2 Sometimes we say “negative two” and sometimes we say “minus two” What is the difference between these two?

[@diegocfq]

If you're referring to the integer number correspondent to two units before 0 in the integers sequence, it's more appropriate to say 'negative two'. If you're referring to a operation where you subtract 2 from something else, it's more approapriate to say 'minus two'. I usually use negative two when it's by itself (as a result or whole value, for example) and use minus two when it's part of an equation where there are other numbers or literals interacting with it.

[@Raihan_Badat]

@@diegocfq thanks

[@tubepkn]

The symbol ÷ should be banned from mathematics; if you use fractions then all these PEMDAS issues go away.

[@Proferk]

It is actually, it's mainly used in arithmetic. When you get to algebra pretty much always you'll represent it as a ratio of two numbers.

[@pi_xi]

There are many cases where ÷ can make an equation more readable, but you can always also use a×(1/b) instead of a÷b

[@Alians0108]

a/b ​@@pi_xi

[@jacobD643]

I'm guessing you're referring to his example at the end, we just need to understand the ÷ only apply to the next number, because you can move it around, ex. 12 ÷ 3 * 4 = 12 * 4 ÷ 3. the same way 12 - 3 + 4 = 12 +4 - 3, the - is attached to 3, not to 3 + 4, the same way the ÷ is attached to the 3, not the 4. the controversial take on pemdas is it doesn't mention juxtaposition, famous ex. 6 ÷ 2(2 + 1) if you only know pemdas, you'll see this as: 6 ÷ 2 * (2 + 1) and doing 6/2 first, but juxtaposition should be in higher priority than multiplication and division and the ex. should read as: 6 ÷ ( 2 * (2+1) ) so the division is done last.

[@pi_xi]

@@jacobD643 The invisible multiplication operator has no higher order of operation than the visible one, so you still evaluate this from left to right.

[@tau93]

in my opinion 100 R 4 is not a valid answer because a remainder is only contextualized by its divisor, and this question was not asked as a mere division problem

[@bengt-goranpersson5125]

Would 100 + 4/5 be an acceptable answer?

[@hunggaming5118]

It equals to 100.8, however schools would consider that an unsimplified answer and you will lose full marks, so it’s best to write in decimal, or fractions

[@jok9342]

Would have been fine at my school

[@bengt-goranpersson5125]

@@hunggaming5118 Sounds fair enough, thanks for clarifying.

[@Grizzly01-vr4pn]

@@jok9342 School of Hard Knocks?

[@iCarus_A]

@@hunggaming5118... and then you get docked points for oversimplifying and using an imprecise decimal instead of fractions in later classes. Remind me why people hate math

[@andycole5957]

While this is the best answer; I prefer mine: The question is there "any way" the answer doesn't have decimal/fraction. My preferred answer is yes, if you changed all the operators to additions. Or a little more sarcastic, yet technically true is: Yes, if you don't mind a wrong answer.

[@michaelbarnes12314]

hey, can you explain why the limit x -> 0 sin(x)/x = 1 ?

[@maddenbanh8033]

Sin(x)/x becomes closer to 1 as x approaches 0, sin(0.1)/0.1=0.99833 therefore the limit would be 1

[@iCarus_A]

also, lim x -> 0 sin(x) = x lastly, you can use le hospital and derive both sides, giving you cos(x)/1, which approaches 1 as x approach 0.

[@Proferk]

I like how he uses the algebra "dot" instead of the cross (x) for showing multiplication, but then refuses to show division as a fraction. Instead he uses the arithmetic division operator.

[@firstname4337]

"the arithmetic division operator" -- literally looks like a fraction

[@Proferk]

@@firstname4337 I meant this symbol: "÷"

[@WerewolfLord]

​@@Proferkwhich literally looks like a fraction; the expression to the left being the upper dot, and the expression on the right being the lower dot.

[@azer67]

@@Proferk Using fractions actually add some complexity to the order of operations. When you have one fraction, you always do all the calculation needed on the numerator separately from the denominator, so it doesn't act like the "÷" symbol. Exemple : Numerator is 5+8, denominator is 7. You start with the addition (5+8) then you do the division. If it were written in a line, you have to write parenthesis. Generally people don't make this mistake with fractions, it's only when using the arithmetic division operator that many people make the mistake.

[@JubeiKibagamiFez]

Now, in the comments of another of these videos, someone brought up "implicit multiplication." I'm unfamiliar with this term still, but the commenter explained it as multiplication always being done before division. Again, I'm wholly unfamiliar with this term. If anyone can give more insight, please do.

[@Silvar55x]

*In algebra* implicit multiplication (also called "multiplication by juxtaposition") means that you can omit the multiplication symbol everywhere except between numbers: "3x" means "3 · x" "ab" means "a · b" "3(x + 2)" means "2 · (x + 2)" "(x - 1)(x + 1)" means "(x - 1) · (x + 1)" but "7 · 12" requires the multiplication symbol. If implicit multiplication appears together with regular multiplication and/or division, there is no clear order of operations between them; while implicit multiplication "appears" more closely bound to its neighbor, it isn't necessarily so. Essentially there are two or more "correct" answers, but the question is incorrect. This mostly appears in "90% of people can't solve this" type clickbait that is deliberately designed to be ambiguous. Also, implicit multiplication is algebra. It should not appear in arithmetic, so the fact it does in those "problems" clearly indicates that they're just fabricated controversy and engagement generators. In algebra there is no confusion since division bars are used instead of division symbol. When in doubt, add parentheses.

[@JubeiKibagamiFez]

@@Silvar55x Okay, now that makes actual sense. So much confusion on other platforms.

[@iCarus_A]

@@JubeiKibagamiFezimplicit multiplication is usually evaluated before division, ie, "5/2x". This does not evaluate to 2.5x (in fact this is already a simplified fraction), where as "5/2*x" does. This is just a ploy to make maths more confusing.

[@RatulBiswas_is_op]

Could anyone please explain me , why do we use this pyramid ? . What is the reason of calculating divison first than substraction . (What is the logic behind this ? ) Pls explain

[@elcugo]

If you do the operations in different order, you can get completely different results. So people agreed to follow this convention many years ago to avoid confusion.

[@RatulBiswas_is_op]

@@elcugo Thanks , elcugo ❤

[@juaneldesconocido2186]

Can you solve this? isolate y in y^3+3y-2x=0 I don't understand Wolfram Alpha

[@Trafulgoth]

y^3 + 3y = 2x Or are they asking to solve for y?

[@juaneldesconocido2186]

@@Trafulgoth Oh I already solve it. Yes is solving for y x+-sqrt(x^2-3)

[@riy0h]

Is this channel sponsored by Expo? That's a lot of markers!

[@pi_xi]

bprp literally stands for: black pen red pen

[@bprpmathbasics]

Unfortunately they are not sponsoring. We can only hope if they ever will.

[@jasongodding6655]

Since they only asked about whether there was a remainder, the answer is pretty obviously "there must be", because the denominator contains a prime number (5) that none of the terms in the numerator have. Meanwhile, there really isn't any way to misinterpret order of operations here that would affect the answer.

[@firstname4337]

what are you talking about ??? OBVIOUSLY there is a remainder

[@0LoneTech]

Eh, paraphrasing error. The question was "Is there any way this _doesn't_ end in an answer with remainders", and it was translated into "whether there was a remainder". So it's "no, there's no way the answer is integer".

[@jasongodding6655]

Yeah, sorry, what 0LoneTech said.

[@mspeir]

I understand the order of operations. What I do not understand is how we arrived at that order. Why not addition before multiplication? Why not multiplication before division? Why not right to left as opposed to left to right? You'll say, "Because the answer would be incorrect!" However, I'd counter that the answer is incorrect because of the order of operations. Hence, we're back at the beginning. So, how do we break out of this circular logic?

[@Silvar55x]

It's just convention. Every mathematician needs to use the same order of operations so they can exchange information and understand each other. A different convention could have been chosen originally, but the one in use was deemed to make the most sense: Most powerful operations are done first inside-out, and equally powerful operations are done left-to-right as a sort of a tie-breaker. A single formal correct order of operations also minimizes the need of parentheses.

[@mspeir]

@@Silvar55x But that begs the question: Did we make the correct choice? If not, math(s) is wrong. That has striking implications!

[@mp7311]

@@mspeir That's a misunderstanding of math. Math is an invention, and we based our rules around the universal rules of convention. It cannot be "wrong" in that sense.

[@mspeir]

@@mp7311 That's a good answer.

[@LionsShareYT]

There’s more to it than just convention. Addition and subtraction are “lower-order” operations than multiplication and division; that is, multiplication and division are defined in terms of addition/subtraction. Similarly, exponentiation is defined in terms of multiplication/division. Parentheses exist for those cases where we want to force the lower-order operations to take precedence. Ultimately, yes, we could have picked a different order, but saying it’s just convention makes it sound arbitrary when in reality it’s very logical.

[@professorsogol5824]

The original question was "Is there any way this doesn't end in an answer with decimals? Since division by 5 is involved and no multiplication by 5 or a multiple of 5, the answer is "no" without any further consideration. No need to look at the order of operations.

[@JubeiKibagamiFez]

I just read a comment bringing up left to right as an issue. It made me think about this equation I remember in school.... "30=A+5×B, Solve for A and B." How does someone do left to right in this circumstance?

[@darranrowe174]

This is interpreted as 30 = A + (5 × B). Left to right means left to right only in terms of ×÷ or +-.

[@JubeiKibagamiFez]

@@darranrowe174 Ah, okay.

[@adarshsrinivasan517]

that question doesnt make sense (you cant find a and b) but anyway it is basically what the first reply said

[@JubeiKibagamiFez]

@@adarshsrinivasan517 You can solve for A and B by trial and error.

[@adarshsrinivasan517]

@@JubeiKibagamiFez there are infinite possible answers

[@Theoreticaly]

I appreciate using the pyramid instead of the initialism, as I've definitely seen people think that e.g. multiplication has higher precedence than division. I do however take some issue with repeating the "left to right" idea as if it is a rule, which it just isn't. In the video, both the case problem and the example problem at the end are ambiguous expressions which we then try to make unambiguous by imposing our own law on top of basic mathematics notation... rather than just writing the expressions clearly in the first place. I can respect "left to right" as a convenient addition to the order of operations, but I would much rather write my expressions to correctly adhere to the accepted standard notation rather than expect my readers to have been taught incorrectly in the exactly correct way. Or maybe I'm just being stubborn, and this is how change happens - it is, after all, useful, and I suppose there's no ruling council of mathematics notation anyway :)

[@mantasr]

But if there is a very long expression how do you write it "properly" and not have someone start solving it in the middle? Infinite parentheses on top of parentheses? Left to right just makes sense.

[@WerewolfLord]

I end up with 1/50 × 7!

[@narfwhals7843]

Left to right or multiplication before division are both conventions that are used in different contexts. Is left to right more common in school?

[@phiefer3]

This difference is usually more a matter of semantics rather than an actual difference. As even in contexts that specify multiplication first, usually also restrict division to the form of fractions which makes the priority irrelevant. It's literally only in reddit questions and memes that it ever makes a difference, because in actual mathematics things are not written in a way where it matters.

[@UberAffe1]

Why would anyone use multiplication before division? That would mean you cannot swap a "*.5" and a "/2". left to right 10*.5*5 = 10/2*5, Mult first 10*.5*5 != 10/2*5 If you use Mult first then in order for that equality to work, you also have to wrap everything to the left in parenthesis. You should be using parenthesis to disambiguate expressions anyways, but Mult first breaks without them.

[@darranrowe174]

The big thing to remember is that it can all be written as multiplication anyway. Really, the early emphasis on left to right or division before multiplication is to stop cases where you have, as an example, 4 ÷ 2 × 3 and you attempt the 2 × 3 first. Division can be seen as a transforming operator, and in this case, the value of the 2 in ÷ 2 isn't 2, it is 1/2. As an aside, if you handle even this correctly, you can evaluate this right to left and still get the correct answer. 4 ÷ 2 × 3 = 4 × 1/2 × 3 = 4 × 3/2 = 12/2 = 6. This takes advantage of division being equivalent to multiplication by the reciprocal, (÷ n = × 1/n), and you can always replace an operation with the inverse if you properly handle it.

[@darranrowe174]

@@UberAffe1 Umm, I have no idea what you are trying to get at. But an interesting fact about division is that it can always be written in terms of multiplication. 10/2*5 as an example, 10 ÷ 2 × 5 = 10 × 1/2 × 5. Since 1/2 = 0.5, then you can swap.

[@sangram4627]

a + b + c = 6 a² + b²+ c² = 14 a³ + b³ + c³ = 36 ab + bc + ac = 11 abc =6 Values of a , b and c are ? Help me, solve this

[@nakano15]

Uh, came something stupid to my mind, and I think might be the answer: a = 1 b = 2 c = 3

[@sasukesuite1]

5 is not a factor of 7, 8, or 9 so the answer has decimals

[@thecheapaudioengineer]

100R4=

[@upriver7292]

isnt multiplication by juxtaposition considered a higher priority than regular multiplication?

[@pi_xi]

No, it is still evaluated from left to right. The multiplication dot is just invisible.

[@battle00333]

@@pi_xi Generally Juxtaposition is handled together with the Parenthesis and is a higher order than Explicit Division and Explicit multiplication. In the case of 2 / 3(5), you resolve the 3(5) first. to get 15. Then you do 2 / 15. Whereas if you had 2 / 3 * 5, you would do 10 / 3.

[@pi_xi]

@@battle00333 That is not correct. Just think about an invisible multiplication dot.

[@battle00333]

If Implicit and Explicit Multiplication are the same, Then look at this. We accept that a/a = 1, where Any term divided by itself is 1, Correct? But if they are the same, then what happens to ab/ab? ab/ab = a * b/a * b = b * b = b^2 But "ab" is a single term. so does ab/ab = 1, or does ab/ab = b^2? What about a(b)/a(b)?

[@pi_xi]

@@battle00333 ab/ab is ambigious, because it is not clear whether you mean (ab)/(ab), a(b/a)b or (ab/a)b. That is why you should avoid to use the division slash in such contexts. I would usually intepret ab/ab as (ab/a)b. The division sign ÷ is much more understandable in arithmetic problems. a(b)/a(b) is the same as ab/ab, because the braces are evaluated first and then you end with exactly the same term.

[@afre3398]

In any educational setting should you ever use the ÷ symbol at all. I think it introduce a lot of confusion. That would not be the case if this was written out with a proper fraction line. I know you can't write fraction lines easy in all situations like here in the comment section

[@pi_xi]

There is the fraction slash symbol in unicode and it even renders digits nicely 1312⁄69, however, ÷ is more readable in certain contexts.

[@firstname4337]

you are WRONG -- the ÷ symbol is literally the symbol of a fraction -- 6/2(2+1) -- a "proper" fraction does NOT get rid of the confusion

[@afre3398]

@@firstname4337 Have you ever open a math/physics/engineering formula collection book?? Tell me how many ÷ symbol you find in it. Hint it is zero and it is for reason. The ÷ symbol is useful on a calculator, and if you are doing napkin math. Besides that not so much

[@anewman513]

Why is the use of that symbol confusing? It is not even remotely confusing for me.

[@avaraportti1873]

Seeing that awful 12/4*3 just gives an annoying feeling of someone intentionally trying to create confusion.

[@phiefer3]

That's generally what it is. Think about how often and where you actually see the division symbol (obelus) used in mathematics beyond gradeschool. The answer is probably never, because we very quickly switch to using fractions to clearly distinguish between what is being multiplied and what is being divided. So many people get caught up arguing over whether or not multiplication has higher or equal priority to division that they don't even realize that the problem that they're looking at would never actually be written that way if it wasn't designed to start arguments.

[@richardhole8429]

Those who create math problems for monetization need lots of comments to get lots of money. Writing confusion increases their income stream. (This teacher is a rare exception)

[@andreaahplay6152]

Nope.

[@unholycrusader69]

Man

[@vtgrphy3907]

Instead of 504/5, I would write 100 4/5.

[@floopyy_]

Main issue with this is that it ends up looking as 100*(4/5)

[@Silvar55x]

​@@floopyy_"100 4/5" is clearly a mixed fraction. You can't omit multiplication symbol between two numbers.

[@floopyy_]

@@Silvar55x I was writing something about ½x being interpreted as a multiplication but the fraction is in the opposite side of where it was in the original comment, so I guess you have a point. I think it'd still cause some confusion though, since I don't think that way of writing fractions is very common

[@nicholasscott3287]

Or you can just immediately look at the prime factorisation of the expression and immediately say "no", because youre dividing by a 5 and there are no fives in the prime factorisations of the numbers in the numerator.

[@ihatemyselfxd7252]

Very early

[@technicallightingfriend4247]

In 🇮🇳 india I am learn BODMAS B=Brackets O= Order D=Division M=Multiplication A=Addition S=Subtraction

[@firstname4337]

100 4/5 == no decimals