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Hi
I want to know how we can easily compare a big fraction number ?
Like,
Which is greater:127/255 Vs 162/320or 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
Hi Imran,
The method taught in school can be found here – http://www.quickanddirtytips.com/education/math/how-to-compare-fractions
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.
Hi Imran,
If you haven’t already done so, and if you liked this course, please leave a review.
Thank you for the support Imran 🙂
I 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) 1/10Apply 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 🙂
Hi 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.
When 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.
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