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

### 3 Answers

- geezerLv 76 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.

- PuzzlingLv 76 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

Thank you very much.

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- DWReadLv 76 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

Thank you very much.

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Thank you very much.