Fraction Comparison Tricks 🔥 | Speed Math Class 1 | SSC, Railway & Banking Exams| SSC MONK

Added: 2026-05-05

[00:00:00]Hello everyone. Welcome to SSC Monk.

[00:00:01]This is our first class of speed math calculation series and in this series I will teach you fraction comparison. The motto of this series is very clear.

[00:00:09]After completing this whole series, whichever examination you sit in India, I am guaranteeing you 100% that you will not face any sort of calculation issue after this series. Plus, after completion of this series, your speed will be 2x of your current speed. So, let's start, guys. So, everyday I will be giving you one class. As you know, today we'll be covering fraction comparison and will teach you fraction comparison in five best methods which you can use in your examination and solve questions within 5 to 10 seconds.

[00:00:40]Okay? Now, after every class, I will give you one practice PDF which will consist of 50 questions and that PDF can be downloaded from SSC Monk Telegram channel. So, once you complete the class, join the Telegram channel and start practicing the questions because whatever you are learning, if you are not implementing those things, you won't get the benefit out of this whole tricks, okay? So, let's start. Now, why am I telling you or teaching you all this fraction comparison thing? Because you are seeing these sort of questions directly coming in your SSC and railway examination. So, this calculation series will not only teach you the tricks and tips, also it will prepare you for your examination. Now, the basic part of a fraction is whenever we say it is 4/8 or 2/4 or anything that sort. This means if I divide a single thing, if I divide one part into eight parts and from that eight parts I'm taking four parts, it will be known as 4/8. And this four is known as numerator, eight is known as denominator. Clear? Same for 2/4. I have one pizza, cut it into four parts and from that four part I took two parts.

[00:01:48]So, what is the fraction? 2/4. Same way, I have a one pizza, I cut it into six parts and from that I took three parts, so it is 3/6. Now, whatever we are seeing, we are seeing here the numerator is less than the denominator. That means the upper part is less than the denominator. That means it is known as proper fraction. And the details of fraction I will teach you in the foundation series also, so don't worry. For now, understand this. Now, there are seven types of fractions.

[00:02:17]Starting with proper fraction, improper fraction, numerator is less than denominator. In improper fraction, numerator, the upper part is greater than the lower part, that is known as denominator. In [clears throat] mixed fraction, we get a whole number plus a proper fraction. So, mixed fraction is always written as whole number plus proper fraction. And we can convert the improper fraction into mixed fraction.

[00:02:44]Now, unit fraction means where numerator is one. Like fraction means where denominator is same.

[00:02:51]Unit and like fraction you need to understand. In unlike fraction, it has no comparison or no similarity between each and every fraction and it is similar to proper fraction. And equivalent fraction means what? The actual value of all these fractions are similar. What do I mean by actual fraction? Now, see. When I write 6/8, 6/8 can be simplified into a smaller version. How can I simplify? If I divide 6 by 2, I will get 3. If I divide 6 by 8 by 2, I'll get 4. So, 6/8 value is equal to 3/4 which is known as the simplified version or also I can say 3/4 is the equivalent fraction of 6/8. And this applicable for anything. Like if I write 3/4, in 3/4 if I multiply 101 here and in the denominator I multiply 101, how much I will get? 303 in the numerator, 404 in the denominator. So, 303/404 is what? The simplified version of 3/4 or equivalent fraction of 3/4. So, these sort of fraction you will encounter and how to deal with these fractions while comparing or solving the questions, I'll teach you now. So, there are five methodology that in which we will be comparing the fractions and finding whichever is the higher, whichever is the lowest fraction or arrange it in the ascending and descending order. So, in same numerator case, same numerator means what? In same numerator, whatever in the upper part, this is equal. That means 5/6, 5/7, 5/8. Now, see.

[00:04:32]In same numerator case, smaller the denominator, greater the fraction. This means what? Now, see. We have 5/6, 5/7, 5/8. That means out of six part I'm getting five part, out of seven part I'm getting five part, out of eight parts I'm getting five part. So, by default, this is greater than this and this is greater than 5/8 and 5/7 is greater than 5/8. So, whenever the numerators are equal, whichever the denominator is smaller, that fraction will be greater.

[00:05:04]Fine? In case of denominator, it is the opposite. Let's say it is written as 1/7, 3/7, 4/7, 6/7. Now, in here, denominators are equal. Now, in case of same denominator, in case of same denominator, larger or greater the numerator, greater the function.

[00:05:31]Greater the fraction. Clear? So, you need to understand it. Here, highest numerator is six, then four, then three, then one. So, 6/7 is greater than 4/7 greater than 3/7 greater than 1/7. Now, why did I tell you? In certain cases, you can either equalize the numerator or equalize the denominator and solve it.

[00:05:53]Also, how to do that I will tell you.

[00:05:56]Then, there will be LCM, cross multiplication and difference method. I will teach you in next slides. Let's continue.

[00:06:03]Now, many students get confused in ascending and descending order.

[00:06:08]Ascending means what? Smallest to largest. Remember this.

[00:06:12]Descending means what? Largest to smallest. Ascending means A to Z.

[00:06:19]Descending means D to A. Clear?

[00:06:22]From D, you are getting down. Okay? Now, 2/7, 3/7. This is our first fraction. In this fraction, we are seeing what? Seven is same. When denominator is same, whichever a fraction has the greatest value in the numerator, that will be the greatest fraction. So, in the first question we saw same denominator, higher or greater the numerator, greater the fraction. Next. Now, this is what? In this case, numerator is equal or this is also unit fraction. Now, when numerators are equal, whichever denominator is smaller, that will be the greater fraction. So, 1/2 is greater than 1/3.

[00:07:05]So, two cases are done. Now, 3/4, 6/8, 9/12. See.

[00:07:12]6/8, if I simplify it, if I divide it by two, it will be 2 * 3 = 6, 2 * 4 = 8.

[00:07:19]That means 6/8 is exactly 3/4. So, 3/4 is equal to 6/8. Now, same for 9/2. If I divide it by three, 3 * 3 = 9, 3 * 4 = 12. That means what? 3/4 is equal to 6/8 is equal to 9/12. Clear? Equivalent fractions are always equal. Okay? Now, 4/5 and 3/7. Now, here what will happen?

[00:07:46]Here we will be solving these things in two methodology. One is known as LCM method, another is known as cross multiplication method. Okay? Now, what will happen in terms of LCM method?

[00:07:59]So, in the LCM method, we will equal the denominator.

[00:08:05]How to equalize the denominator? So, step one is take LCM of five and seven, the denominator. So, LCM of five and seven will be what? See, these are two co-primes, so LCM will be 5 * 7, that is equal to 35. Now, in step one, when this is 35, in step two, what we'll do? We'll divide LCM divided by the denominator.

[00:08:32]Whatever the result we get, we will multiply with that numerator. Now, what is the LCM? 35. When I divide 35 by five, how much I will get? Sir, 35 by five is equal to seven. So, I'll multiply seven in the denominator, seven in the numerator. So, what is the value now? 28/35. Now, see.

[00:08:52]4/5 is equal to 28/35.

[00:08:55]Okay? Why am I doing this? By equalizing both the denominator, I can easily use the formula of same denominator and find the largest fraction. Okay? Now, in step three, the same will happen over here. 35 divided by seven, that means five should be multiply over here. So, 3 * 5 = 15, 7 * 5 = 35. Now, in step three, we got the equivalent value of 4/5 is 28/35, equivalent value of 3/7 is equal to 15/35. Now, numerator are different, denominator are equal. So, when the denominators are equal, greater the numerator, greater the fraction. So, 28 by 35 is greater than 15 by 35. When 28 is greater than 35, that means what?

[00:09:44]4/5 is greater than 3/7.

[00:09:48]This is known as LCM method. In LCM method, first we did what? We took the LCM of the denominator because we want to equalize it.

[00:09:57]Then, what we did? Then we divide the LCM by the denominator and whatever we got we multiply in both in the numerator and denominator and from that we found the equivalent fraction and we compared the equivalent fraction. Now, someone will feel confident or comfortable in this method, so they can proceed with it. Now, in cross multiplication what happened?

[00:10:17]Cross multiplication is specifically for smaller fractions like this. When the numbers will be higher or greater, it will be difficult for you to use cross multiplication or LCM method to solve the question. So, for that I will also tell you one more method that is known as difference method. But for now, understand cross multiplication. Now, when two fractions are there, 4/5 and 3/7. In the step one, you will cross multiply the denominator with the numerator numerator with the denominator. So, step one, 4 into 7, 3 into 5. Step two, see, I'm writing the steps to help you understand or remember the whole thing.

[00:10:54]But you need to understand one thing that these things will be done in your head, okay? Step two, the value of 28 here, value 15 here. Sir, 28 is greater than 15. The step two, we got it. So, in step three, we know that 4/5 is greater than 3/7. Now, someone will say, "Sir, it is easier than or quicker than LCM method." Absolutely. Someone will say, "Sir, if numbers are difficult, I may not find this, you know, comfortable." No problem. My job is to tell you all the types of tricks that can help you increase your speed 2x. So, you need to practice more, feel whichever you are comfortable with and use it as usual, okay? Now, 3/7, 5/13. So, what I will do? 13 * 3, 39. 7 * 5, 35. Which is greater? Sir, 39 is greater. If 39 is greater, I'll write 3/7 is greater than 5/13.

[00:11:51]Clear?

[00:11:52]Next. 9/4, 18/5. Now, see. Here, numerator is greater than denominator.

[00:12:00]So, this means what? This is improper fraction.

[00:12:04]Now, in improper fraction, you should not directly start with cross multiplication or LCM method. In improper fraction, first you will convert it into what? Mixed fraction.

[00:12:19]Convert it to mixed fraction. Then only you will start with the solution. Now, see.

[00:12:26]4 2's a 8, 1/4. 9/4 can be written as 2/4, 2 1/4. 18/5 can be written as 5 3's a 15, 3 remaining, 3/5. Now, see.

[00:12:40]A number starts with 2 + 1/4. Another number starts with 3 + 3/5. Now, when we saw that 2 is less than 3/5, that means this fraction is greater than this fraction.

[00:12:56]Clear? So, first thing we'll see in step two that whole number is equal or lesser or greater than the other number.

[00:13:12]Then only we can see. Now, if this whole fraction was similar, what we should do?

[00:13:17]I will tell you in the next question.

[00:13:19]Now, see. Here it is what? 7/3 and 13/5.

[00:13:23]Sir, numerator greater than denominator, so improper fraction I will convert into mixed fraction. 3 2's a 6, 1/3.

[00:13:32]3 2's a 6 + 1, 7/3. Now, 13/5 can be written as 5 2's a 10, 3/5. Now, see.

[00:13:39]Sir, here both these value are equal.

[00:13:42]So, what I do? So, I have to check the fractional value. Whichever fraction is greater, that value will be greater.

[00:13:48]Sir, here 1/3. Sir, here 3/5. I can take LCM method or cross multiplication over here. If I cross multiply, 5 * 5, 3 * 9.

[00:13:58]That means what? 9 is greater than 5.

[00:14:01]That means what? 2 3/5 is greater than 2 1/3. That means what? 13/5 is greater than 7/3.

[00:14:11]Clear? So, this is how we can do it.

[00:14:13]Now, see. 99% of all these things will done in your head, okay? So, you do not have to panic. You just to practice it multiple times, okay? Now, 2/9, 5/7, 3/8. All are proper fraction.

[00:14:29]Now, we'll compare it. Either I can take LCM of all these three and find the answer or I'll do the cross multiplication. So, in cross multiplication, first I will check between 2/9 and 5/7. 7 * 14, 9 * 45.

[00:14:43]That means 5/7 is greater than 2/9. Then, second part, comparison between 5/7 and 3/8. 8 * 40, 7 * 21. That means 40 is greater than 21. That means 5/7 is greater than 3/8. Now, third part, comparison between 2/9 and 3/8. 8 * 16, 9 * 27. That means 2/9 is less than 3/8. This means what?

[00:15:12]Sir, this means 5/7 is greater than 3/8 and 3/8 is greater than 2/9. This is known as what? This is known as first the larger number, then the smaller number, then the smallest number. This is known as descending order.

[00:15:27]Now, if it asked to write this whole thing in ascending order, in ascending order, it will be 2/9, 3/8, and 5/7. Clear? So, this is how you should be approaching fraction comparison in your examination. Now, next. Sir, here 7/9, 11/5, and 3/8. Now, see.

[00:15:49]Sir, 11/5 here denominator is less than numerator. That means it is an improper fraction. That means this value is greater than one. So, this will be the highest among all because all the proper fraction are less than one. So, this is the greatest. Now, I just need to compare between 7/9 and 3/8. Sir, 7/9, 3/8. 8 * 56, 9 * 27. That means 56 is greater than 27. That means 7/9 is greater than 3/8. So, I will write 11/5, then 7/9, then 3/8. Or I can write 3/8, 7/9, 11/5.

[00:16:35]Clear? I hope you do not have any doubt over here, okay? You will cross multiply and find the answer. Now, see.

[00:16:41]Multiplying 13 into 13, 19 into 5, 20 into 5, 13 into 8. All these are easy, right? But if the fractional values are if the fractional values are greater over here, you can't cross multiply. So, here you will learn difference method.

[00:17:00]What you will learn?

[00:17:02]Difference method.

[00:17:04]So, what does this this What does this difference method tells us?

[00:17:08]We need to check the difference between denominator and Sir, difference between 13 and 19 is 6, 5 and 13 is 8, 8 and 20 is 12.

[00:17:19]So, 6, 8, 12, I got the difference. Now, I will take what? I'll take the LCM of all this. LCM means 2 3's a 6, 2 4's a 8, 2 6's a 12. Then again, 3 1's a 3, 4, 3 2's a 6. Then again, 2 1, 2 2 4, 2 1. Now, I'll multiply everything. 2 3 4, 2 3 6, 2 12, 2 24.

[00:17:45]So, LCM is 24. So, this is step one. In step two, what you will do? Sir, here what is the numerator? 13.

[00:17:53]You will multiply 13 into the LCM we find out. Here, what is the LCM? Sir, LCM is 24.

[00:18:02]Divided by the difference, 6. Here, 5 * 24 / 8. Here, 8 * 24 / 12. Now, 13 into 24 / 6, 4.

[00:18:18]5 * 24 / 8, 3. 8 * 24 / 12, 2. Sir, 13 * 52. 5 * 15.

[00:18:27]15. 8 * 16. So, which is greater? Sir, 52 greater than 16, greater than 15.

[00:18:35]That means 13/19 is greater than 8/20, greater than 5/13. Clear? Now, see.

[00:18:45]When we are solving this for the first time, we are feeling that this is a bit tough.

[00:18:52]What we are feeling? This is bit tough.

[00:18:54]But if you practice it multiple times in huge fractions like this, it will be a ramban for you, okay? So, let's practice few questions more. Now, 12/15, 14/18, 15/21. Now, if you go for LCM method or any other method, it will be take a lot of time. Or a cross multiplication also take time. So, here difference method will be the panacea.

[00:19:17]Now, 12 15 difference, 3. 14 18 difference, 4. 15 21 difference, 6. So, 3 4 6, LCM.

[00:19:25]Sir, 2 3, 2 2's a 4, 2 3 6. 3 1, 2 1.

[00:19:30]Clear? So, what is the LCM? 2 2 4 into 3, 12. Sir, if 12 is the LCM, it will be written as Sir, here 12 numerator multiplied by 12 / 3. Sir, 14 multiplied by 12 / 4. Sir, 15 multiplied by 12 / 6.

[00:19:49]So, it can be written as 12 into 12 / by is equal to 4. That is equal to 48. This can be written as 14 into 12 divided by 4 is equal to 3. 14 * 3 = 42. This will be 15 multiplied by 12 * 6 = 2. That is equal to 30. So, among all these, which is greater? Sir, 48. Then 42. Then 30.

[00:20:11]Yes or no?

[00:20:13]So, 48 means I can write 12 by 15 is greater than 14 by 18 greater than 15 by 21.

[00:20:21]Got it? This is known as what?

[00:20:24]Descending order. If I have to write this whole thing in ascending order, what I will write? Sir, 15 by 21, then 14 by 18, then 12 by 15. Sorted.

[00:20:38]Next.

[00:20:39]25 by 28, 53 by 59, 41 by 45, 93 by 105.

[00:20:45]Now, see. Here, you can't use cross multiplication or LCM method. So, difference method will be working.

[00:20:52]Difference are three.

[00:20:54]Difference are six.

[00:20:55]Difference are four.

[00:20:57]Difference are 12. Clear? Now, what we'll do? Three, four, six, 12 LCM. 3 * 1 = 3. Four as it is. 3 * 2 = 6. 3 * 4 = 12. Now, two, one, two, one, two. Then again, two, one, one, one, one. So, what is the LCM?

[00:21:16]3 * 2 * 6 * 2 = 12. So, I will write 25 multiplied by 12 divided by 3. 53 multiplied by 12 divided by 6.

[00:21:26]41 multiplied by 12 divided by 4. 93 multiplied by 12 divided by 12.

[00:21:32]So, this can be written as 25 into 12 divided by 3 is equal to 4. That is equal to 100. So, this can be written as 53 multiplied by 12 divided by 6 is equal to 2. That is equal to 106. So, this can be written as 41 into 12 divided by 4 is equal to 3. That is equal to 123.

[00:21:51]So, this can be written as 93 into 1.

[00:21:53]That is equal to 93. Clear? So, which is the greatest? 123. So, 123 greatest.

[00:22:01]Then 106. Then 100. Then 93. Yes or no?

[00:22:07]Yes. That means 123 means 41 by 45 is the greatest fraction. Then 106 means 53 by 59 is the greatest fraction. Then 100 means 25 by 28. Then 93 by 105.

[00:22:24]This is known as descending order. In ascending order, it will be the opposite. 93 by 105. Then 25 by 28. Then 53 by 59. Then 41 by 45. Now, you can use anything, any calculator, or you convert this fraction into decimal.

[00:22:44]You can check everything. But, this will be the quickest possible method for every sort of questions. Okay? 14 by 15, 37 by 10 38, 28 by 29, 70 78 by 79. Now, sir, here all the difference are equal.

[00:23:00]What I need to do? So, when the difference between when difference between denominator and numerator are equal in all the fractions, then highest numerator is the greatest fraction.

[00:23:25]Clear? So, 78 is greater than all the numbers. So, 78 by 79 is the greatest fraction. Then 37 by 38. Then 28 by 29.

[00:23:38]Then 14 by 15. You got the idea? Yes or no? Yes. Now, I am giving you as a homework. You tell me the answer in the comment both in ascending and in descending order, what will be the value. Clear? Now, after this class, go and download the class practice question from SSC Mock Telegram channel. And do like this video, share with all your friends, and put some lovely comments in the comment section of this video, so that I will be motivated and bring such amazing classes for all of you. So, see you in the next class. So, tomorrow, what will be covering? Tomorrow, we will be covering the next class in the speed math comparison series in speed math calculation series, that is division tricks with an amazing shortcut. Okay? So, see you tomorrow.