Five divided by two times a number is 1/4 - What is the number? Basic Algebra!
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- เผยแพร่เมื่อ 29 เม.ย. 2024
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The number could be 10 and it could also be 0.1.
It is critical to use precise language when writing word problems like this.
For example:
5 divided by the product of 2 and a number is ¼. What is the number?
or
If you divide 5 by 2 then multiply the result by a number, you get ¼. What is the number?
It can be quite cumbersome to express a mathematical problem in natural languages like English. That's why mathematical notation exists.
These problems are so fun. Thank you ❤
Got it with no paper, in my jead before you revealed it. I am only 76. Not senile yet.
Order if operations says you should divide first, since it comes first (5/2)*n. Division and multiplication happen at the same time reading left to right. The answer is 0.1. To be more clear, you could say "5 divided by the result of 2 times a number" or "5 divided a number doubled" - then it would be clear that you want to multiply first.
I, too, believe that's how it reads, but not in practical interpretation. He would have written it as "five halves times a number equals one quarter".
@@louf7178 -- No, it's not about being "practical." It is about understanding English and the Order of Operations. If It was the other way, then it needed to phrased similar to " 5 divided by the *quantity of 2 times a number* is 1/4. What is the number?"
@@robertveith6383 I agree that's how it should be technically worded. But I'm not going go bother trying to explain the rest to you; you won't even try.
Order of operations is a tool for interpreting mathematical expressions written using infix notation. It has got absolutely nothing to do with interrupting English language sentences.
Order of operations is irrelevant here.
@gavindeane3670 But when the English is ambiguous, you have to resort to some standard. If we simply interpreted the words as written into mathematical notation, we would have "5÷2*n=1/4". Why is it more logical to take phrase "2 times a number" and deal with that first, instead of taking "5 divided by 2" and deal with that first? If the English was not ambiguous, you wouldn't have so many people disagreeing about it.
Thank you
People who are saying the problem was written incorrectly apparently did not read it right. With word problems, the solver needs to set up the equation correctly. I found the question to be written quite clearly. And so did most of the other commenters, by the way.
John gets an A+++ and a big fat smiley face.
10 is the answer(using the cross - multiplication method.
Good morning Debbie. 5 divided by 2 times a number is 5/2 ×n =1/4
The problem is carelessly written. It looks like the author probably meant 5/(2x)=¼ not (5/2)x=¼, but the wording is ambiguous and a teacher should know better. It is trivially easy to rewrite the question properly.
I can't believe I did this in my head and got 10. Not too shabby for an old goat of 85.
I got it real fast, too, once I pictured it as five _over_ a number. "Five over what equals one fourth." Easy. Then don't forget to divide by 2.
Hey, great that you're trying to re-learn this stuff at 85. I'm 74 and really enjoying learning (or re-learning) from this channel.
Thank god for the skip forward button, though!
@@Astrobrant2 😀😀😀😀😀
You two are making me feel like a youngster -- I'm not quite 70 .... Isn't it great that we get to test our memories and maybe learn a little something by watching John's math videos?!
Ata boy
@@debbieholoquist2059 Ah, to be 70 again. LOL. 😁😁😁😁😁
Love your videos
Thank You 4 doing this.
What would you say is the ratio of nice people to haters? Just a rough estimate. I really want to know
I know you don't sweat it because the haters get you paid too.
Thanks again 👍❤
John, I suggest you rethink this one. The problem can just as well be read as (5/2)× n = 1/4. The PEDMAS way. So I think you must accept the PEDMAS solution n= 1/10
got it 10 5/(2x) = 1/4 cross multiply and solve. easy thanks for the fun.
That is incorrect.
I want my certificate. ;)
Just kidding!
Thanks for an easy one.
But I wanted a certificate of excellence!😅😊
10
Mvss. 5÷2 ×10=25. 5 divided by 2 times a number. That's my interpretation. Any comments
Call the number x
Five divided by two times a number would be 5/2x
and 5/2x = 1/4
2x = 20 x = 10
Your second line is actually correct. 5/2x does *not* mean 5/(2x) because of the Order of Operations. Because of the Order of Operations, the problem is (5/2)x = 1/4. --->
x = (2/5)(1/4) = 1/10
@@robertveith6383 There's no order of operations reason why 5/2x can't mean 5/(2x). Problem is, it can also mean (5/2)x. There's no universal standard for how to parse implied multiplication after inline division. In the real world we write division as a fraction, so this problem doesn't arise.
If you are writing inline, just use parentheses to make the meaning clear, as (5/2)x or 5/(2x).
As written and following order of operations, the answer of 10 is not correct. In order for the answer to be 10, there would need to be parentheses around 2 times x. Remember PEMDAS???
PEMDAS and order of operations is for interpreting mathematical expressions written using infix notation.
That's irrelevant here. We are not being asked to interpret a mathematical expressions. We're being asked to interpret an English language sentence.
Unfortunately the sentence is not clear. It could reasonably be interpreted as 5/(2x)=¼ and also as (5/2)x=¼.
The question needs to be rewritten so it's unambiguous.
Just a minor thing, but you've been doing this so long, you should probably start pronouncing "algebraic" correctly. It's not al-ge-bar-ic. It's al-ge-bray-ic.
That said, I like almost all of your videos.
Algebarric isn’t a word. You probably meant algebraic. Shocking that an alleged math teacher can’t pronounce that word.
5÷2×n = 1/4.
5/2. n. = 1/4
n = 1/4 ×2/5. =5/2.
Anything wrong with my interpretation. Like your comment
Nothing wrong with interpreting it as (5/2)×n = ¼.
But something went wrong after that with your calculation because that interpretation gives n=0.1, not n=5/2.
It is 2/20 = 1/10 You used PEDMAS order of operations and your solution is valid. Let's wait for John to do a follow up and acknowledge this.
5/2x =2.5/x, and that equals .25. Dividing 2.5 by ten, shifting the decimal place to the left, is a giveaway.
Very confusing John
Because it could be written to be 5/2 (N) =1/4
True, what matters here is the rules of English grammar which allows sufficient ambiguity. I say there are two answers, 10 and 1/10.
Wrong. It's not "could be written ..." It must be written equivalently to that.
@@buddyroeginocchio9105 -- No, there are not two answers. By English and the Order of Operations, it is equal to (5/2)x = 1/4, for some number x. The only answer is 1/10.
@@robertveith6383 Five divided by 2 times a number...
vs: Five divided by 2 times a number...
better: Five, divided by 2 times a number...
Without commas or other qualifiers there exists an ambiguity in presenting the problem. The responsibility is on the presenter of the problem to be clear. The responsibility of the critic is to understand the issue.
1/4 = 5/2x
cross-multiply...
2x = 20
x = 10
5/2 x N = 1/4 solution let us multiply both side by 2 then this is the result 5N = 1/2 answer is N = 1/10
Yes, or multiply each side by 2/5.
i watch lots of math, but i dont understand it
1/4 times 4 is 1. 1 times 5 is 5. so 1/4 times 20 is 20/4 or 5. 20/2=10. So if you devide 5 by „two times 10“ you get 1/4. So the number is 10.
Wrong. You do not understand the order of operations given in the problem.
Since english ain't my native language, why is this not read as 2/5xN=1/4
5/2*x=1/4 that is
See my comment above.
@@stefanfrank6875 -- It *is* read that way, for a number x, by English and the Orders of Operations. People who are saying differently do not understand.
@@robertveith6383by English it's ambiguous.
Order of operations is irrelevant. Order of operations is not a tool for interpreting English. It's a tool for interpreting mathematical expressions (specifically, mathematical expressions written using infix notation).
It can be read as (5/2)x=¼ and also 5/(2x)=¼.
It's a carelessly worded sentence. The question needs to be rewritten to remove the ambiguity.
Oh dear. This question is ambiguous. Math questions should not be ambiguous. Is it 5÷ (2 x N) or (5÷2) x N?
Oh, dear, it is *not* ambiguous. By the English and the Order of Operations, it only means
(5/2)x = 1/4, for some number x.
Exactly. It could easily be rewritten unambiguously. This is not a mistake a teacher should be making.
Result, the number = 0.10
Yes.
Ten
Wrong. It is 1/10.
5 is a quarter of 20
so 20= 2 x 10
the number is 10
Wrong. See the reply to philipkudma above.
The # is 10
No, it is not. The number is 1/10.
More of an English test than math....Understand????
20
opps typo 10
Wrong. The answer is 1/10.
1/10
Yes.
I also believed the sentence is wrong. My answer is 1/10.
No, the sentence is not wrong, but the answer *is* 1/10.
Yes, the sentence is carelessly written. It can be interpreted as 5/(2x)=¼ and also (5/2)x=¼.
Answer is 10
No, the answer is 1 /10.
It's 20
Wrong.
If you read it as (5/(2N)) = 1/4, then N = 10. If you read it as (5/2)N = 1/4, then N = 1/10. Not everyone reads these things the same way you do. I would hate to be one of your students who read it the second way, had it marked wrong, then got admonished by you for reading it incorrectly when it can be read either way with equal validity because of the ambiguous way it is worded.
Wrong! It is not written ambiguously. From the English and the Order of Operations, it must be taken as (5/2)x = 1/4, for some number x. To be taken the other way, it must be written equivalently as "5 divided by the *quantity of* 2 times a number is 1/4. What is the number?"
@@robertveith6383 Agreed, but, if you have to suggest alternate wording to make it clearer as to what the presenter wanted, you are admitting that it was written ambiguously, which is precisely my point. The presenter isn't very good at conveying his intent when he formulates word problems; this much is obvious from many other problems he has posted.
@@robertveith6383To be unequivocally interpreted your way the sentence needs to be rewritten as well.
Where have you got this notion that order of operations has got anything to do with interpreting English?
Number is 10
Wrong. The number is 1/10.
Like always, too much explanation for something really easy.
5/2x = 1/4 --> 2x = 5*4 --> 2x = 20 --> x = 10
Solved it in 10 à 15 seconds.
You solved it *wrong* in 10 to 15 seconds. 5/2x does *not* mean 5/(2x), and the problem does not mean 5 divided by the quantity of 2 times a number equals 1/4, either.
@@robertveith6383 I have the right answer. So my explanation is not wrong. And of course I meant 5/(2x)
I did it in less than 30 seconds. Why you spend so much time on these sort of easy math?
5/2x = 1/4
= 2x = 20
= x = 10
Wrong. You do not understand that 5/2x means (5/2)x. You don't understand the meaning of the sentence in English. The answer is 1/10.
10
10
No, it is 1/10.
No, it is 1 /10.
10
No, it is 1/10.
10
No, it is 1/10.
10
No, the answer is 1/10.
10
No, it is 1/10.
No, it is 1/10.
5 divided by (.1x2) =25, not 5.