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Math Help - Fractions help needed grade 8 level

  1. #1
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    Fractions help needed grade 8 level

    Hi there, i need the grade 8 level fractions help. homework is below. Thank you!!

    twice a week i go swimming and swim the same number of lengths of the pool each time.
    as i swim, i count the lengths i've done so far, and make it into a fraction of the wohle number of lengths i know i'm going to swim.

    For example, if i swam 10 lengths each time, as i finished the 5th length i'd think that's 5/10.

    If i make that into a simpler fraction, I get 1/2. after 8 lengths it would be 8/10 or 4/5.

    But I don't swim 10 lengths. how many do i swim??

    here's the clue you need to work it out...

    After the first length, the only numbers of lengths that can't be changed to a simpler fraction are prime numbers.

    An example of such fraction would be 7/10.

    I swim the highest number of lengths for which this is possible.

    How many lengths do I swim each week??


    ----- i know that prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.. but i have problems working out word questions. please help me understand it. thank you!!
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  2. #2
    Member rtblue's Avatar
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    erm.. Well \frac{9}{10} can't be simplified.. so.. I dont really understand the question much. Elaborate more. But, from what you have given me, i have come to this conclusion. This is because if you swim 9 times, every swim session, do you swim 18 lengths each week?

    Also, I must point out that there is a flaw in your work. You have stated that prime numbers are the only numbers that cannot be simplified. This is incorrect, for example: \frac{9}{10} (9 is not a prime number, although it cannot be simplified when put over 10)

    Another prime number: 5. \frac{5}{10} can be simplified easily even though 5 is a prime number.
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  3. #3
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    Quote Originally Posted by rtblue View Post
    erm.. Well \frac{9}{10} can't be simplified.. so.. I dont really understand the question much. Elaborate more. But, from what you have given me, i have come to this conclusion. This is because if you swim 9 times, every swim session, do you swim 18 lengths each week?

    Also, I must point out that there is a flaw in your work. You have stated that prime numbers are the only numbers that cannot be simplified. This is incorrect, for example: \frac{9}{10} (9 is not a prime number, although it cannot be simplified when put over 10)

    Another prime number: 5. \frac{5}{10} can be simplified easily even though 5 is a prime number.

    omg thanks.. but the question was taken directly from the sheet that the teacher gave me... so ha! she's wrong.. lol..
    neways. i'm still thinking .. i've been thinking for 3 hours on this question. I don't understand either.

    I thought that the length = denominator.. (but the denominator can't be a 10 because it says that the person doesn't swim 10 length)

    it says "after the first length," which i assume that means that the numerator can't be 1, so it's greater than 1.... ??

    the only thing i get is that the final answer would be 2 times the length. since this person swims 2 times a week.

    it's due tomorrow.

    but thanks for your input so much. i'll still think with what you said.
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  4. #4
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    Let n be the number of lengths. n is either prime or it isn't.

    Suppose n is prime.
    The last lap gives the fraction n/n, which reduces, defying the hypothesis that fractions with prime numerator aren't allowed.

    So n cannot be prime.
    If n > 1, there is some prime p that divides n. Then the fraction p/n reduces.

    It can only be that n = 1.
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