NCERT Class 7 Mathematics

RATIONAL NUMBERS 181

Thus, we find that number of integers between two integers are limited (finite).
Will the same happen in the case of rational numbers also?

Reshma took two rational numbers–3–1and
53

.

She converted them to rational numbers with same denominators.

So

• 3–9 –1–5and
  515 315

We have

• 9–8–7–6–5
  15 15 15 15 15
  <<<< or–3–8–7–6–1
  5151515 3
  <<<<

She could find rational numbers

• 8–7–6,,
  15 15 15 between

(^31) and
53
.
Are the numbers
876
,,
15 15 15 the only rational numbers between
31
and
53?
We have

• 3–18 –8–16and
  530 1530

And

• 18 – 17 –16
  30 30 30
  <<. i.e.,
  
  
  • 3–17–8
    53015
    <<
  
  
  
  

Hence

• 3 –17 –8 –7 –6 –1
  5301515153

<<<<<

So, we could find one more rational number between–3–1and
53

.

By using this method, you can insert as many rational numbers as you want between
two rational numbers.

For example,

• 3 –3 30 –90and–1 –1 50 –50
  5 5 30 150 3 3 50 150

××

××

We get 39 rational numbers

(^89) , ..., 51
150 150
⎛⎞⎜⎟
⎝⎠ between

• 90 – 50
  and
  150 150 i.e., between


• 3–1and

53. You will find that the list is unending.

Can you list five rational numbers between

• 5–8and
  37?
  We can find unlimited number of rational numbers between any two
  rational numbers.

TRYTHESE

Find five rational numbers

between

(^53) and
78.