Home › Community › Questions & Answers › Mental Math Q & A › Fraction Comparing
 This topic has 12 replies, 3 voices, and was last updated 2 years, 5 months ago by ImranOfpad.

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October 10, 2017 at 10:28 am #5115
Hi
I want to know how we can easily compare a big fraction number ?
Like,
Which is greater:
127/255 Vs 162/320
or even more big.I know this content not include in your lecture. But still i believe that, you care your student much. That’s why you always response everyone question. For that reason i post this question. If you give me some valuable source. It will helpful for me.
Thank you
Best Regards,
Imran
October 10, 2017 at 10:31 am #5117Hi Imran,
The method taught in school can be found here – http://www.quickanddirtytips.com/education/math/howtocomparefractions
To find approximately which fraction is higher, there are 3 steps.
Step 1 – Find the amount you must multiply to the numerator to bring it close to the denominator.
In the example 127/255 Vs 162/320 we can see the amount is approximately 2 for both fractions.
If the numbers were different both fractions, then you can directly go to step 3 and say that the smaller number is greater fraction. But here in this example we have to do additional step of step 2 because we multiplied both fractions with the same number 2 to bring it close to the denominator.
Step 2 – Find whether you must add or subtract something to bring the answer of the multiplication exactly close to the denominator
127 * 2 = 254. This number 254 is lesser than the denominator 255 by 1.
So to get exactly 255 you must multiply more than 2. You don’t have to find out exactly how much this value should be, but for this explanation I will say the exact number is 2 + x. (Where x is some decimal number greater than 0 but less than 1)
Similarly 162 * 2 = 324. This number is greater than the denominator 320 by 4.
To get exactly 320, you must multiply less than 2. So it is 2 – y. (Where y is a decimal number greater than 0 but less than 1)
Step 3 – The greater fraction will have the smaller number.
In this case (2 – y) is the smaller number and so 162/320 is the greater fraction.
If the numbers you multiplied the numerator with was different in Step 1, (eg 2 for fraction A and 3 for fraction B) , then you can skip Step 2 and immediately find the answer.
This is one way I would guesstimate which number is greater quickly.
Hope this explanation helped.
October 10, 2017 at 10:32 am #5119Thank you so much for your explanation. I already know, you will give perfect solution. Because you are a fantastic and helpful person.
October 10, 2017 at 10:33 am #5121Hi Imran,
If you haven’t already done so, and if you liked this course, please leave a review.
October 10, 2017 at 10:34 am #5123So Comparing fraction Using Benchmark 1/2 is really helpful. Like based on your explanation ,
123/250 Vs 171/340
123*2 = 246and 171*2 = 342 So here, 246 less than half of 250 and 342 is bigger than half of 340.
So 171/340 will be greater.
I just summarize your explanation.Again, Thank you so much for your time.
October 10, 2017 at 10:38 am #5125I will leave a review. But i need sometime because i want to write a best review for this course.
October 10, 2017 at 10:39 am #5127Thank you for the support Imran 🙂
October 10, 2017 at 10:40 am #5129I found another way, So it could be better if I share with you. So,If the question is
Of the following, which is greater than 1/2?
(a) 2/5 (b) 4/7 (c) 4/9 (d) 1/10
Apply cross method
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So answer is (b) 4/7 is greater.
Today i feel interested with math, only for your course. I know, you are so knowledgeable. But i wish to share with you. That’s why 🙂
October 10, 2017 at 10:43 am #5131Hi Imran,
This is called cross multiplication. It is a great method for small numbers. But in your first example it was really large numbers that need to be multiplied i.e. 3 digit numbers. In such scenarios the first method is a better way to guestimate.
October 10, 2017 at 10:44 am #5133Exactly, this cross multiplication just for small number. But your first method is better. Because 3 digit number applying this method time consuming. i am just share with you nothing else.
October 10, 2017 at 10:44 am #5135I have a question. Is it possible to apply your first method for this example? –
Which is smaller: 21/20 vs 1013/1012
If possible , Could you please explained?I am extremely sorry because i know i ask you lot of question. Even i haven’t reviewed yet.
October 10, 2017 at 10:46 am #5137When the numerator is greater than the denominator you don’t have to apply any trick. You can just see the numbers and come up with your answer immediately. Its just a matter of how you write the numbers.
21/20 can be written as (20 + 1)/20 which can be written as 20/20 + 1/20 which can be written as 1 + 1/20
Similarly you can write 1013/1012 as 1 + 1/1012
Equating the two fractions
1 + 1/20 = 1 + 1/1012
1/20 = 1/1012
Cross multiplying we get 1012 > 20
So in summary when the numerator is greater than the denominator, all you have to do is subtract (numerator – denominator) for both fractions and cross multiply.
(21 – 20)/20 = (1013 – 1012)/1012
1/20 = 1/1012
Cross multiplying we get 1012 > 20
This of course cannot be done when the numerator is smaller than the denominator.
October 10, 2017 at 10:47 am #5139But if you calculate
1013/1012 = 1.000
and21/20 = 1.05
so the answer will be this1013/1012
. I mean smaller . 
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