Fraction Comparing

Home Community Questions & Answers Mental Math Q & A Fraction Comparing

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  • #5115
    ImranOfpad
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    • Topics: 3
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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 162/320 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

    #5117
    Ofpad
    Participant
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    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.

    #5119
    ImranOfpad
    Participant
    • Topics: 3
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    Thank you so much for your explanation. I already know, you will give perfect solution. Because you are a fantastic and helpful person.

    #5121
    Ofpad
    Participant
    • Topics: 0
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    Hi Imran,

    If you haven’t already done so, and if you liked this course, please leave a review.

    #5123
    ImranOfpad
    Participant
    • Topics: 3
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    So Comparing fraction Using Benchmark 1/2 is really helpful. Like based on your explanation , 123/250 Vs 171/340  123*2 = 246

    and 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.

    #5125
    ImranOfpad
    Participant
    • Topics: 3
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    I will leave a review. But i need sometime because i want to write a best review for this course.

    #5127
    Ofpad
    Participant
    • Topics: 0
    • Replies: 158

    Thank you for the support Imran 🙂

    #5129
    ImranOfpad
    Participant
    • Topics: 3
    • Replies: 10

    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) 1/10

    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 🙂

    #5131
    Ofpad
    Participant
    • Topics: 0
    • Replies: 158

    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.

    #5133
    ImranOfpad
    Participant
    • Topics: 3
    • Replies: 10

    Exactly, 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.

    #5135
    ImranOfpad
    Participant
    • Topics: 3
    • Replies: 10

    I 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.

    #5137
    Ofpad
    Participant
    • Topics: 0
    • Replies: 158

    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.

    #5139
    ImranOfpad
    Participant
    • Topics: 3
    • Replies: 10

    But if you calculate 1013/1012 = 1.000  and 21/20 = 1.05  so the answer will be this 1013/1012 . I mean smaller .

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