Question

insert 6 rational numbers between -2/3 and 3/4

Answer 1

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-2/ 3× 4/4 = -8/12
3/4 ×3/3 = 9/ 12
hence 6 rational numbers between -2/3 and 3/4 are
-7/12, -6/12,-5/12, -4/12, -3/12, -2/12,-1/12
HOPE THIS WILL HELP YOU :)

Answer 2

The 6 rational numbers between $-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4}$ are $-\frac{7}{12} ,-\frac{6}{12} ,-\frac{5}{12} ,\frac{1}{12} ,\frac{2}{12} ,\frac{8}{12} .$

Given,

Two fractions:

$-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4} .$

To find,

6 rational numbers between the given fractions.

Solution,

A rational number can be defined as a number that can be expressed or written in the form of the ratio of two integers p and q, as $\frac{p}{q}$, provided that q ≠ 0.

Here, we have to find 6 rational numbers between

$-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4} .$

Now, to find the required numbers, first, we need to change them into like fractions.

We can see that the LCM of denominators, 3 and 4, is = 12.

So, the given fractions can be written as follows.

$-\frac{2}{3}=-\frac{2}{3} \times \frac{4}{4} =- \frac{8}{12}$

$\frac{3}{4} =\frac{3}{4} \times \frac{3}{3} =\frac{9}{12} .$

Now, all the fractions between $-\frac{8}{12}\hspace{3} and \hspace{3} \frac{9}{12}$ will be the rational numbers between $-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4} .$

⇒ the 6 rational numbers between $-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4}$

= $-\frac{7}{12} ,-\frac{6}{12} ,-\frac{5}{12} ,\frac{1}{12} ,\frac{2}{12} ,\frac{8}{12} .$

Therefore, the 6 rational numbers between $-\frac{2}{3} \hspace{3} and \hspace{3} \frac{3}{4}$ are $-\frac{7}{12} ,-\frac{6}{12} ,-\frac{5}{12} ,\frac{1}{12} ,\frac{2}{12} ,\frac{8}{12} .$

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