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28 September, 03:59

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 77 / ... 333

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Answers (2)
  1. 28 September, 04:19
    0
    3333 and 4333

    Step-by-step explanation:

    To know this, and to convert the fraction 77 / ... 333 into a reducible fraction, we need first to analyze the numerator.

    77 has two multiples. These are 7 and 11. This means that this number can only be divided by 7 or 11. You can prove this, bye multiplying 7*11 = 77.

    So, the denominator should be a multiple of 7 and 11.

    In order to know this, we should divide by 7 and 11 and see if the result is multiple of 7 or 11.

    1. 1333/7 = 190.4; 1333/11 = 121.2 They are Not multiples

    2. 2333/7 = 333.3; 2333/11 = 212.1 They are Not multiples

    3. 3333/7 = 476.1; 3333/11 = 303 Multiple of 11

    4. 4333/7 = 619; 4333/11 = 393.9 Multiple of 7

    5. 5333/7 = 761.9; 5333/11 = 484.8 They are Not multiples

    6. 6333/7 = 904.7; 6333/11 = 575.7 They are Not multiples

    7. 7333/7 = 1047.6; 7333/11 = 666.6 They are Not multiples

    8. 8333/7 = 1190.4; 8333/11 = 757.5 They are Not multiples

    9. 9333/7 = 1333.3; 9333/11 = 848.5 They are Not multiples

    Therefore we can conclude that only 3333 and 4333 are the possible cases to turn 77 / ... 333 into a fraction reducible.
  2. 28 September, 04:47
    0
    Answer: The only two numbers that allow us to make the fraction reducible are 4333 and 3333. (So the digit can be 4 or 3)

    Step-by-step explanation:

    77 can be written using prime numbers as:

    7*11 = 77

    So the only way in which we can make the fraction reducible is if the number ... 333 is a multiple of 7 or 11. (so we can write it as 7*something or 11*something)

    333 is not a multiple of 7 nor 11.

    1333 is not a multiple of 7 nor 11

    2333 is not a multiple of 7 nor 11

    3333 is a multiple of 11, (11*303 = 3333) then this number can make the fraction reducible.

    then 77/3333 = 7/303

    4333 is a multiple of 7, (7*619 = 4333) then this number can make the fraction reducible

    then 77/4333 = 11/619

    5333 is not a multiple of 7 nor 11

    6333 is not a multiple of 7 nor 11

    7333 = is not a multiple of 7 nor 11

    8333 = is not a multiple of 7 nor 11

    9333 = is not a multiple of 7 nor 11

    The only two numbers that allow us to make the fraction reducible are 4333 and 3333.
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