Question

Write five rational number between 1/2 and 5/7

Answer 1

Answer:

1/2 × 7/7 = 7/14

5/7 × 2/2 = 10/14

7/14 × 5/5 = 35/70

10/14 × 5/5 = 50/70

Therefore 5 rational numbers between 1/2 and 5/7 are 36/70, 37/70, 38/70, 39/70 and 40/70.

Answer 2

To find any no. of rational nos. between any two nos., we find the mean between the two nos.

For Rational No. 1, $\frac{\frac{1}{2}+\frac{5}{7}}{2}= \frac{\frac{7+10}{14}}{2}=\frac{17}{28}$

For Rational No. 2,$\frac{\frac{1}{2}+\frac{17}{28}}{2}=\frac{\frac{28+34}{56}}{2}=\frac{31}{56}$

For Rational No. 3, $\frac{\frac{5}{7}+\frac{17}{28}}{2}=\frac{\frac{20+17}{28}}{2}=\frac{37}{56}$

For Rational No. 4, $\frac{\frac{31}{56}+\frac{37}{56}}{2}= \frac{\frac{31+37}{56}}{2}=\frac{34}{56}=\frac{17}{28}$

As Rational No 4 = Rational No 1, so we have to reject this

Again for Rational No. 4, $\frac{\frac{1}{2}+\frac{31}{56}}{2}=\frac{\frac{28+31}{56}}{2}= \frac{59}{128}$

For Rational No. 5, $\frac{\frac{5}{7}+\frac{31}{56}}{2}=\frac{\frac{40+31}{56}}{2}=\frac{71}{128}$

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