Introduction:

A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, a rational number can be written in the form a/b, where a and b are integers and b is not equal to zero. In this case, we are given two rational numbers -2/3 and -1/5, and we need to find a rational number that does not lie between them.

Explanation:

To find a rational number that does not lie between -2/3 and -1/5, we can consider the number line and analyze the given fractions in relation to it.

-2/3:
-2/3 can be represented on the number line as a point that lies closer to the left side of zero. It is approximately -0.67 when rounded to two decimal places.

-1/5:
-1/5 can be represented on the number line as a point that lies closer to the left side of zero, but it is farther from zero compared to -2/3. It is approximately -0.2 when rounded to one decimal place.

Number between -2/3 and -1/5:
Now, let's consider the numbers that lie between -2/3 and -1/5 on the number line. Since -2/3 is a smaller value than -1/5, any number that lies between them will be greater than -2/3 but smaller than -1/5.

We can start by finding the average of -2/3 and -1/5:
(-2/3 + -1/5) / 2 = (-10/15 + -3/15) / 2 = -13/30

The number -13/30 lies between -2/3 and -1/5 on the number line. It is approximately -0.43 when rounded to two decimal places.

A rational number not between -2/3 and -1/5:
To find a rational number that does not lie between -2/3 and -1/5, we can consider any number that is either smaller than -2/3 or greater than -1/5 on the number line.

-1:
For example, the rational number -1 is smaller than -2/3 and lies to the left of it on the number line.

Conclusion:
To summarize, the rational number -1 is an example of a number that does not lie between the rational numbers -2/3 and -1/5. It is important to note that there are infinitely many rational numbers that do not lie between these two fractions, and -1 is just one of them.

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