Question

. Find three rational numbers between2/3
and
3/4​

Answer 1

Gívєn :

• Two rational numbers – $\sf\frac{2}{3}$and $\sf\frac{3}{4}$

Tσ fínd :

• Rational numbers between them.

Sσlutíσn :

• Given numbers are 2/3 and 3/4
• Rational number: Rational is a number that can be written in terms of “numerator” upon the “denominator”, but denominator should not be equal to zero. The numerator and denominator are the integers.  
• Rational number is in the form of  p/q, here q≠0
• Where p is the “numerator” and q is the “denominator”
• The formula to find the rational number between two numbers is $\frac {(a+b)}{2}2(a+b)$
• $\begin{lgathered}\begin{array} { l } { \text { Here } a = \frac { 2 } { 3 } } \\\\ { \mathrm { b } = \frac { 3 } { 4 } } \\\\ { = \frac { \left( \frac { 2 } { 3 } + \frac { 3 } { 4 } \right) } { 2 } } \end{array}\end{lgathered}$ Here a=32b=43=2(32+43)
• $\begin{lgathered}\begin{array} { l } { = \frac { \left( \frac { 8 + 9 } { 12 } \right) } { 2 } } \\\\ { = \frac { 17 } { 24 } } \end{array}\end{lgathered}=2(128+9)=2417$
• Therefore, the rational number between 2/3 and 3/4 is 17/24

Answer 2

2/3 and 3/4

LCM of 3&4 is 12

2/3×4/4=8/12

3/4×3/3=9/12

Required rational numbers=3

3+1=4

8/12×4/4=32/48

9/12×4/4=36/48

Three rational numbers between 2/3 and 3/4 are 33/48, 34/48, 35/48

i.e. 11/16, 17/24, 35/48