Question

Find out six rational numbers lying between -4/8 and 3/8.​

Answer 1

It is quite easy to ascertain six rational numbers between $\frac{-4}{8}$ and $\frac{3}{8}$, because they already share the same denominator, i.e. 8.

So, let us draw out the number line of and identify the position of these two numbers.

On referring to the diagram below, you will see that there exists six rational numbers already -

$\frac{-3}{8}, \frac{-2}{8} (or \frac{-1}{4}) , \frac{-1}{8}, 0, \frac{1}{8}, \frac{2}{8} (or \frac{1}{4})$

(P.S. - in case you are looking for one more rational number, other than 0, then you can take up the following steps);

($\frac{-1}{4}$ + $\frac{1}{8}$) ÷ 2 = $\frac{(-2)+1}{8}$ ÷ 2 = $\frac{-3}{8}$ × $\frac{1}{2}$ = $\frac{-3}{16}$

You can repeat the same procedure between two other successive rational numbers.

Hope this helps you. Also, do pardon any visual inaccuracy in the hastily-drawn number line.

Answer 2

RATIONAL NUMBERS

What are rational numbers?

→ Numbers which can be represented in the form of p/q where p and q are integers and q is not equal to 0 are known as rational numbers.

To find rational numbers between two rational numbers is an easy task.

If the range of the given rational numbers is small then multiply both the rational numbers with such a number so that there denominators remain same. By doing this, we are increasing the range of the rational numbers in order to find the required number of rational numbers.

As per the question,

The 6 rational numbers can be found in the given range only.

Let us have a look.

$\frac{-4}{8} \: and \: \frac{3}{8} \\ \\\frac{-3}{8},\:\frac{-2}{8}, \: \frac{-1}{8}, \: 0, \: \frac{1}{8}, \: \frac{2}{8}$

These are the 6 rational numbers between -4/8 and 3/8.

If more were asked, then

$\frac{-4}{8}*\frac{2}{2} = \frac{-8}{16} \\ \\and\\\\\frac{3}{8}* \frac{2}{2} = \frac{6}{16}$

The range has now changed and new one is -8/16 and 6/16. By multiplying like this you can find as many rational numbers you want.