What are the 5 rational numbers between 1/-5 and 3/7? Thank you.?

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  • geezer
    Lv 7
    6 months ago

    Get them both over 35 (because 5 x 7 = 35)

    Now you have 5 rational numbers between -7/35 and 15/35

    Pick away .. there are SO MANY.

  • 6 months ago

    There are infinitely many rational numbers in that range, so we can't give you *the* 5 rational numbers.

    When you say 1/-5, I'm assuming you mean -1/5.

    Let's assume you want 5 arithmetic means (evenly spaced) between -1/5 and 3/7. First get a common denominator:

    -1/5 * 7/7 = -7/35

    3/7 * 5/5 = 15/36

    So from -7/35 to 15/35 is a distance of 22/35

    15/35 - (-7/35) = 22/35

    Then divide that into *6* equal spaces. That will give you *5* arithmetic means in between.

    (22/35) * (1/6)

    = 11/105

    So you want to keep adding 11/105. Let's get a common denominator of 105.

    -7/35 * 3/3 = -21/105

    15/35 * 3/3 = 45/105

    So the 5 arithmetic means would be:

    -21/105 + 11/105 = -10/105 (or -2/21)

    -10/105 + 11/105 = 1/105

    1/105 + 11/105 = 12/105 (or 4/35)

    12/105 + 11/105 = 23/105

    23/105 + 11/105 = 34/105

    Answer:

    -2/21, 1/105, 4/35, 23/105, 34/105

    Attachment image
  • DWRead
    Lv 7
    6 months ago

    "The" five rational numbers? There are infinitely many rationals between -7/35 and 15/35.

    For example,

    -6/35, -1/7, -4/35, -3/35, -2/35, -1/35, 0, 1/35, 2/35, 3/35, 4/35, 1/7, 2/7

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