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Faman39
 one year ago
I have a question, how do you reduce large fraction fast? If you don't remember more multiplication.
Faman39
 one year ago
I have a question, how do you reduce large fraction fast? If you don't remember more multiplication.

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.6find their prime factors

welshfella
 one year ago
Best ResponseYou've already chosen the best response.6456 = 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

welshfella
 one year ago
Best ResponseYou've already chosen the best response.6that took me a while  then I'm an old guy! lol

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1Do 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
 one year ago
Best ResponseYou've already chosen the best response.6I 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
 one year ago
Best ResponseYou've already chosen the best response.3@Faman39 It depends on whether you can divide mentally by onedigit numbers.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1Actually, 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
 one year ago
Best ResponseYou've already chosen the best response.6dw:1443102044415:dw

welshfella
 one year ago
Best ResponseYou've already chosen the best response.6 thats how i do it by hand

mathmate
 one year ago
Best ResponseYou've already chosen the best response.3Then 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 120 (or even 30) helps you factorize the difficult ones (like 529).

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1Thank you so much for helping :)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.6Practicing as much as possible is I believe, the key here.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1okay. Thanks so much @welshfella @mathmate

welshfella
 one year ago
Best ResponseYou've already chosen the best response.6one 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.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1@DanJS @ganeshie8, Do you guys have any ideas for my this post?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0reducing fractions, i just use a calculator, but nah just keep taking common factors from top and bottom

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0i use a calculator to do addition, :)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0even numbers, keep taking out 2's till you cant anymore

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1try reducing \(\dfrac{1963}{2567}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1actually i have just figured out a nice method do you know how to find the gcd of two numbers using euclid gcd algorithm ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0Here 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
 one year ago
Best ResponseYou've already chosen the best response.0In general, people are not fast at reducing fractions, and with calculators and computer so common, there probably isn't any need to be.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Let \(d=\gcd(a,b)\). 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
 one year ago
Best ResponseYou've already chosen the best response.1Thank you so much @phi @ganeshie8 @DanJS for coming here and helping me. I missed you all, wonderful openstudy moderators and friends.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1np look up euclid gcd algorithm incase if you haven't before, pretty sure you will find it interesting :)

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1gcd, 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
 one year ago
Best ResponseYou've already chosen the best response.1as 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
 one year ago
Best ResponseYou've already chosen the best response.1okay, I will try it. Thanks so much for amazing tricks! :)

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1Can you show me one more how do you solve large fraction with euclid? Cuz I am dumb enough :D

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you'r not dumb do you have teamviewer ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so do you see how gcd is related to our problem ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1explain quick so that i know that you know :)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0is 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
 one year ago
Best ResponseYou've already chosen the best response.1You set it up large fraction as cross multiply breaking in order reduce them easily

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0are there infinite primes?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1lol yes and yes @DanJS

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1I know, Im wrong @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1You'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
 one year ago
Best ResponseYou've already chosen the best response.0I think there is a numberphile video on that actually on the youtube

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1maybe lets see an example

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{15}{6}\) is that in reduced form ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you have cancelled 3 whats special about 3 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1okay common factor is 3 for 15 and 6

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.13 is not just a common factor it is the GREATEST common factor i want you see that first

mathmate
 one year ago
Best ResponseYou've already chosen the best response.3Try 437/851 to see the power of Euclid!

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1well, 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
 one year ago
Best ResponseYou've already chosen the best response.1Exactly! that is the kind of problem which makes you love euclid dude.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1common factor. I am guessing but not sure

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Look at the numbers : 437 and 851 Is any one of them "appear" like divisible by 5 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1both the numbers must be divisible by "common factor" that is the definition of "common factor"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Are you saying 437 and 851 are divisible by 2 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1doesn't matter if it is right/wrong... i appreciate that you're asking nice questions :)

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1okay. 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
 one year ago
Best ResponseYou've already chosen the best response.1okay. 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
 one year ago
Best ResponseYou've already chosen the best response.1first you need to practice few simple things

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1what do you know about even and odd ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1how do you say an integer is even or odd ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1I don't know why, but I know it's even

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes! here is the trick : An integer is even if it is divisible by 2.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.16 is even because it is divisible by 2 : 6/2 = 3 leaves no remainder.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.131 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
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1okay. Thanks so much for explaining me thoroughly :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1437 and 851 so do you see why "2" cannot be a common factor of above numbers ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1cuz they are odd number?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, neither of them is divisible by 2; they are odd. So 2 is not a factor of any of them.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to tell if a number is divisible by 5 just by looking at the number ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Is 10 divisible by 5 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1good, Is 13 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.113 is not divisible with any number

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1right, but why is it not divisible by 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.113/5 = 5*2, R=3 remainder is not 0, so we say that 13 is not divisible by 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1to 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.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1lets do couple more quick examples

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Is 18 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1no, cuz it will also leave remainder of 3

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Good! Is 22 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1No, it will also give us remainder of 2 not 0.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Exactly! Now, can you write down first few positive integers that are divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.111x2 = 22 and 2x11 = 22 as well

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Ahh ok. My question was different question. I was asking for the first few integers that are divisible by 5.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.120, 10, 25, 30, 35, 40, 45

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1good, see anything special in them ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1they are increasing my 5

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1they are increasing by 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1thats true, more importantly, notice that the units digit in each of those numbers is either 0 or 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so can we say this : if the units digit is 0 or 5, then the number is divisible by 5. ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so, Is 3434345 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1well, I think so but not sure about it, cuz it has two 34 and one 45

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1It doesn't matter. The units digit is 5, so it is divisible by 5.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1okay. so how do I divide with 5 this such long number?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1we don't need to. if the units digit is 5 or 0, then the number is divisible by 5.

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1okay, 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
 one year ago
Best ResponseYou've already chosen the best response.1by now, you know how to tell if a number is divisible by 5, yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Is 898985 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1yes, it is divisible by 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, 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.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Is 894852 divisible by 5 ?

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1It is not divisible by 5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1good, I see you got it!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Now 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.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Here 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
 one year ago
Best ResponseYou've already chosen the best response.1okay, it makes sense in video but how do I apply it in fraction?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1suppose we want to reduce \(\dfrac{12}{30}\) step1) find \(\gcd(12, 30)\)

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1so, we just need to divide denominator with numerator

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yes, that video explains it better

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1I 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
 one year ago
Best ResponseYou've already chosen the best response.1You made everything so easy to understand

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1hey, 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
 one year ago
Best ResponseYou've already chosen the best response.1But, 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
 one year ago
Best ResponseYou've already chosen the best response.1So thank you sooooooooooooooooooooooooo much for help!

Faman39
 one year ago
Best ResponseYou've already chosen the best response.1I can't believe you made everything so clear and easy for me, now I feel quite confident about doing the large fractions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1np 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
 one year ago
Best ResponseYou've already chosen the best response.1there 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
 one year ago
Best ResponseYou've already chosen the best response.1Thanks 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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