Question

insert 100 rational number between -5/8 and 1/2​

Answer 1

Answer:

Any 100 numbers between the values -3/13 and 9/13 is the answers. The numbers be - \frac { 299 } { 1300 } , - \frac { 298 } { 1300 } , - \frac { 297 } { 1300 } , - \frac { 296 } { 1300 } , \ldots−

1300

299

,−

1300

298

,−

1300

297

,−

1300

296

,…

Solution:

Given the values are

\begin{gathered}- \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 }\\\end{gathered}

−

13

3

and

13

9

To insert “100 rational numbers between” - \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 }−

13

3

and

13

9

Let us multiply and divide the terms by 100,

\begin{gathered}\begin{aligned} - \frac { 3 } { 13 } & = - \frac { 3 \times 100 } { 13 \times 100 } \\\\ = & - \frac { 300 } { 1300 } \\\\ \frac { 9 } { 13 } & = \frac { 9 \times 100 } { 13 \times 100 } \\\\ & = \frac { 900 } { 1300 } \end{aligned}\end{gathered}

−

13

3

=

13

9

=−

13×100

3×100

−

1300

300

=

13×100

9×100

=

1300

900

∴ “100 rational numbers between” - \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 } = 100 \text { numbers between } - \frac { 300 } { 1300 } \text { and } \frac { 900 } { 1300 }−

13

3

and

13

9

=100 numbers between −

1300

300

and

1300

900

Any 100 rational numbers between - \frac { 300 } { 1300 } \text { and } \frac { 900 } { 1300 } \text { is } - \frac { 299 } { 1300 } , - \frac { 298 } { 1300 } , - \frac { 297 } { 1300 } , - \frac { 296 } { 1300 } , \ldots−

1300

300

and

1300

900

is −

1300

299

,−

1300

298

,−

1300

297

,−

1300

296

,…