Faman39
  • Faman39
I have a question, how do you reduce large fraction fast? If you don't remember more multiplication.
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
welshfella
  • welshfella
find their prime factors
Faman39
  • Faman39
for example 456/678
welshfella
  • welshfella
456 = 2 * 2 * 2* 3 * 19 678 = 2 * 3 * 113 cancel out the duplicates in this case they are 2 and 3 so we have 2* 2* 19 / 113 = 76/113

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welshfella
  • welshfella
that took me a while - then I'm an old guy! lol
Faman39
  • Faman39
Do we usually need to reduce all large fraction with 2 or 3 ? yeah, I was thinking that how we can reduce large fraction like that faster if we don't remember longest or bigger multiplications
welshfella
  • welshfella
I don't think there's a faster way of doing this for large numbers All the division you do are pretty simple. You can use a calculator of course.
mathmate
  • mathmate
@Faman39 It depends on whether you can divide mentally by one-digit numbers.
Faman39
  • Faman39
Actually, I need to take tabe test within few month. They dont allow us to use calculator and they give really short time to solve those type of problem.
welshfella
  • welshfella
|dw:1443102044415:dw|
welshfella
  • welshfella
- thats how i do it by hand
mathmate
  • mathmate
Then practise dividing by single digit numbers. For the example, try 2 456/678=228/339 then try 3 228/339=76/113 and that's the end of it. Also, learn dvisibilities so you can spot easy factors, like 2,3,5,11. Example of a difficult one: 529/253 If you know divisibilities, you know 253=23*11 (note 2+3=5, therefore divisible by 23 and 11) Then try divide 529 by 23, or 529=23^2 so 529/253=23/11 Also, memorizing the squares of numbers from 1-20 (or even 30) helps you factorize the difficult ones (like 529).
Faman39
  • Faman39
Thank you so much for helping :)
welshfella
  • welshfella
Practicing as much as possible is I believe, the key here.
Faman39
  • Faman39
okay. Thanks so much @welshfella @mathmate
welshfella
  • welshfella
one tip If you have a large odd number , to find if its divisible by 3, add up all the digits until you get a single number - if you get 3,6 or 9 then its divisible by 3.
welshfella
  • welshfella
yw
mathmate
  • mathmate
you're welcome! ;)
Faman39
  • Faman39
@DanJS @ganeshie8, Do you guys have any ideas for my this post?
DanJS
  • DanJS
reducing fractions, i just use a calculator, but nah just keep taking common factors from top and bottom
DanJS
  • DanJS
i use a calculator to do addition, :-)
DanJS
  • DanJS
even numbers, keep taking out 2's till you cant anymore
ganeshie8
  • ganeshie8
try reducing \(\dfrac{1963}{2567}\)
ganeshie8
  • ganeshie8
actually i have just figured out a nice method do you know how to find the gcd of two numbers using euclid gcd algorithm ?
phi
  • phi
Here is info you should learn 1) divisibility rules https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320 (at least the easy ones up to 10) 2) prime numbers https://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_500_prime_numbers It is good to learn the primes up to 100. The more you remember of these, the easier to simplify big fractions
phi
  • phi
In general, people are not fast at reducing fractions, and with calculators and computer so common, there probably isn't any need to be.
ganeshie8
  • ganeshie8
Let \(d=\gcd(a,b)\). Then it is easy to find the integers satisfying \(a=a'd\) and \(b=b'd\). \[\dfrac{a}{b} = \dfrac{a'd}{b'd} = \dfrac{a'}{b'}\] It cannot reduce further since \(\gcd\) is the max factor that is common.
Faman39
  • Faman39
Thank you so much @phi @ganeshie8 @DanJS for coming here and helping me. I missed you all, wonderful openstudy moderators and friends.
ganeshie8
  • ganeshie8
np look up euclid gcd algorithm incase if you haven't before, pretty sure you will find it interesting :)
Faman39
  • Faman39
gcd, okay. Thing is, I can't use calculator on tabe test for solving large fraction like this. So I was confused and don't know what to do. And they give really short time to solve those problem
ganeshie8
  • ganeshie8
as the name says, it is an algorithm from "euclid" days: 300BC he had been able to invent that simple yet powerful algorithm probably because there were no calculators at that time
Faman39
  • Faman39
okay, I will try it. Thanks so much for amazing tricks! :)
Faman39
  • Faman39
Can you show me one more how do you solve large fraction with euclid? Cuz I am dumb enough :D
ganeshie8
  • ganeshie8
you'r not dumb do you have teamviewer ?
Faman39
  • Faman39
No
ganeshie8
  • ganeshie8
so do you see how gcd is related to our problem ?
Faman39
  • Faman39
yes.
ganeshie8
  • ganeshie8
explain quick so that i know that you know :)
DanJS
  • DanJS
is there a way to show a ridiculous ratio is in reduced form. one that would take time longer than the universe to calculate by hand or machine?
Faman39
  • Faman39
You set it up large fraction as cross multiply breaking in order reduce them easily
DanJS
  • DanJS
are there infinite primes?
ganeshie8
  • ganeshie8
lol yes and yes @DanJS
Faman39
  • Faman39
I know, Im wrong @ganeshie8
ganeshie8
  • ganeshie8
You're not wrong, I did not phrase the question properly. If you understand the question, you will answer it easily. Let me rephrase the question..
DanJS
  • DanJS
I think there is a numberphile video on that actually on the youtube
ganeshie8
  • ganeshie8
maybe lets see an example
ganeshie8
  • ganeshie8
\(\dfrac{15}{6}\) is that in reduced form ?
Faman39
  • Faman39
5/2
ganeshie8
  • ganeshie8
how did u get 5/2 ?
ganeshie8
  • ganeshie8
you have cancelled 3 whats special about 3 ?
ganeshie8
  • ganeshie8
gcd(15, 6) = ?
Faman39
  • Faman39
okay common factor is 3 for 15 and 6
ganeshie8
  • ganeshie8
3 is not just a common factor it is the GREATEST common factor i want you see that first
mathmate
  • mathmate
Try 437/851 to see the power of Euclid!
Faman39
  • Faman39
well, this is large one and I can't figure out what would be common factor of large number like this cuz I often forgot large multiplication
ganeshie8
  • ganeshie8
Exactly! that is the kind of problem which makes you love euclid dude.
ganeshie8
  • ganeshie8
so you do see that if you figure out the "greatest common factor" of 437 and 851 "somehow", then you can reduce the fraction easily
Faman39
  • Faman39
5?
ganeshie8
  • ganeshie8
what 5
Faman39
  • Faman39
common factor. I am guessing but not sure
ganeshie8
  • ganeshie8
Look at the numbers : 437 and 851 Is any one of them "appear" like divisible by 5 ?
ganeshie8
  • ganeshie8
both the numbers must be divisible by "common factor" that is the definition of "common factor"
Faman39
  • Faman39
I think, two?
Faman39
  • Faman39
that's also wrong
ganeshie8
  • ganeshie8
Are you saying 437 and 851 are divisible by 2 ?
ganeshie8
  • ganeshie8
doesn't matter if it is right/wrong... i appreciate that you're asking nice questions :)
Faman39
  • Faman39
okay. But I still don't get, how do I reduce large fraction quick if I can't figure out common factor or use euclid
Faman39
  • Faman39
okay. But I still don't get, how do I reduce large fraction quick if I can't figure out common factor or use euclid?
ganeshie8
  • ganeshie8
first you need to practice few simple things
Faman39
  • Faman39
okay
ganeshie8
  • ganeshie8
what do you know about even and odd ?
Faman39
  • Faman39
okay.
ganeshie8
  • ganeshie8
how do you say an integer is even or odd ?
ganeshie8
  • ganeshie8
Is 6 even/odd ?
Faman39
  • Faman39
even
ganeshie8
  • ganeshie8
why
Faman39
  • Faman39
I don't know why, but I know it's even
ganeshie8
  • ganeshie8
good, is 31 even ?
Faman39
  • Faman39
odd
ganeshie8
  • ganeshie8
how about 437 ?
Faman39
  • Faman39
odd?
ganeshie8
  • ganeshie8
Yes! here is the trick : An integer is even if it is divisible by 2.
ganeshie8
  • ganeshie8
6 is even because it is divisible by 2 : 6/2 = 3 leaves no remainder.
ganeshie8
  • ganeshie8
31 is not even because it is not divisible by 2 : 31/2 = 15, R=1 remainder is not 0, so not divisible by 2.
ganeshie8
  • ganeshie8
so when somebody asks you the definition of an "even" number, you can say this : A number is even if it is divisible by 2.
Faman39
  • Faman39
okay. Thanks so much for explaining me thoroughly :)
ganeshie8
  • ganeshie8
437 and 851 so do you see why "2" cannot be a common factor of above numbers ?
Faman39
  • Faman39
cuz they are odd number?
ganeshie8
  • ganeshie8
Yes, neither of them is divisible by 2; they are odd. So 2 is not a factor of any of them.
ganeshie8
  • ganeshie8
do you know how to tell if a number is divisible by 5 just by looking at the number ?
Faman39
  • Faman39
no
ganeshie8
  • ganeshie8
Is 10 divisible by 5 ?
Faman39
  • Faman39
yes
ganeshie8
  • ganeshie8
why
Faman39
  • Faman39
cuz 5x2 is 10, so yes
ganeshie8
  • ganeshie8
good, Is 13 divisible by 5 ?
Faman39
  • Faman39
no
ganeshie8
  • ganeshie8
why
Faman39
  • Faman39
13 is not divisible with any number
ganeshie8
  • ganeshie8
right, but why is it not divisible by 5
ganeshie8
  • ganeshie8
just divide and see
ganeshie8
  • ganeshie8
13/5 = 5*2, R=3 remainder is not 0, so we say that 13 is not divisible by 5
ganeshie8
  • ganeshie8
to say that a 13 is divisible by 5, the remainder when 13 is divided by 5 must be 0. but here the remainder is 3, which is not 0. so 13 is not divisible by 5.
Faman39
  • Faman39
got it now
ganeshie8
  • ganeshie8
lets do couple more quick examples
ganeshie8
  • ganeshie8
Is 18 divisible by 5 ?
Faman39
  • Faman39
no, cuz it will also leave remainder of 3
ganeshie8
  • ganeshie8
Good! Is 22 divisible by 5 ?
Faman39
  • Faman39
No, it will also give us remainder of 2 not 0.
ganeshie8
  • ganeshie8
Exactly! Now, can you write down first few positive integers that are divisible by 5 ?
Faman39
  • Faman39
11, 2
ganeshie8
  • ganeshie8
how
Faman39
  • Faman39
11x2 = 22 and 2x11 = 22 as well
ganeshie8
  • ganeshie8
Ahh ok. My question was different question. I was asking for the first few integers that are divisible by 5.
Faman39
  • Faman39
20, 10, 25, 30, 35, 40, 45
ganeshie8
  • ganeshie8
good, see anything special in them ?
Faman39
  • Faman39
they are increasing my 5
Faman39
  • Faman39
they are increasing by 5
ganeshie8
  • ganeshie8
thats true, more importantly, notice that the units digit in each of those numbers is either 0 or 5
ganeshie8
  • ganeshie8
so can we say this : if the units digit is 0 or 5, then the number is divisible by 5. ?
Faman39
  • Faman39
hmm, got it :) thanks
ganeshie8
  • ganeshie8
so, Is 3434345 divisible by 5 ?
Faman39
  • Faman39
well, I think so but not sure about it, cuz it has two 34 and one 45
ganeshie8
  • ganeshie8
It doesn't matter. The units digit is 5, so it is divisible by 5.
Faman39
  • Faman39
okay. so how do I divide with 5 this such long number?
ganeshie8
  • ganeshie8
we don't need to. if the units digit is 5 or 0, then the number is divisible by 5.
Faman39
  • Faman39
okay, I understood what you're saying. But if I need to reduce the largest like that digit, in that I often get blank, because I can't find common factor and how to reduce to them. Because I often forget bigger multiplication
ganeshie8
  • ganeshie8
one thing at a time
Faman39
  • Faman39
okay.
ganeshie8
  • ganeshie8
by now, you know how to tell if a number is divisible by 5, yes ?
Faman39
  • Faman39
yes
ganeshie8
  • ganeshie8
Is 898985 divisible by 5 ?
Faman39
  • Faman39
yes, it is divisible by 5
ganeshie8
  • ganeshie8
Yes, notice that, we don't need to divide the number and look at remainder to tell if a number is divisible by 5. That is really powerful.
Faman39
  • Faman39
ok
ganeshie8
  • ganeshie8
Is 894852 divisible by 5 ?
Faman39
  • Faman39
It is not divisible by 5
ganeshie8
  • ganeshie8
good, I see you got it!
ganeshie8
  • ganeshie8
Now throw them away, we don't really need all those divisibility rules because we're going to use euclid algorithm to find the gcd directly.
Faman39
  • Faman39
okay
ganeshie8
  • ganeshie8
Here it is https://www.youtube.com/watch?v=AJn843kplDw it is just 2 minutes long, but it explains very nicely... let me know if something doens't make sense..
Faman39
  • Faman39
okay, it makes sense in video but how do I apply it in fraction?
ganeshie8
  • ganeshie8
suppose we want to reduce \(\dfrac{12}{30}\) step1) find \(\gcd(12, 30)\)
Faman39
  • Faman39
so, we just need to divide denominator with numerator
Faman39
  • Faman39
is that correct?
ganeshie8
  • ganeshie8
yes, that video explains it better
Faman39
  • Faman39
I am sorry, I must be made you really tired. Extremely apologize you had to stuck here quite long for me. Thanks soooooo much for taking time for explaining everything thoroughly. You really helped me to understand everything very clearly.
Faman39
  • Faman39
You made everything so easy to understand
ganeshie8
  • ganeshie8
hey, no im not tired, i want you master euclid algorithm and use it to reduce fractions but just so you know... when i was first learning, it took me more than a week to understand euclid algorithm
Faman39
  • Faman39
But, really you did a lot to explain, which really helped. It mean a lot to me that you stayed with me quite long until I don't understand everything well. Thanks so much! I really appreciate what you did for me today. I was quite struggling with this kind of problem
Faman39
  • Faman39
So thank you sooooooooooooooooooooooooo much for help!
Faman39
  • Faman39
I can't believe you made everything so clear and easy for me, now I feel quite confident about doing the large fractions
ganeshie8
  • ganeshie8
np good to see that that you took time to find efficient methods in reducign fractions, that's exactly the kind of attitude is necessary to get good at math. keep it up :)
ganeshie8
  • ganeshie8
there is always more than one way to do a particular thing in math but often there is exactly one best way to do a thing.. if you spend time, you will find it...
Faman39
  • Faman39
Thanks for encouragement :) You're really genius math magician and amazing instructor :) I had really great time learning from you. Truly really enjoyed.

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