Question

7. Find five rational numbers between 3/5 and 2/3. Answer is 11/80, 28/45, 19/30, 29/45, 59/90 Explain how?​

Answer 1

Answer:

Make, denominator of each given rational number equal to 15 ex the LCM

3/5 = (3 × 3)/(5 × 3) = 9/15 and

2/3 = (2 × 5)/(3 ×5) = 10/15

Since, five rational numbers are required, multiply the numerator and denominator of each rational number by 5 + 1 = 6

∴ 9/15 = 9 × 6/15 × 6 = 54/90 and

10/15 = 10 × 6/15 × 6 = 60/90

∴ Required rational numbers between 3/5 and 2/3 are = 55/90, 56/90, 57/90, 58/90, 59/90

= 11/18, 28/45, 19/35, 29/45 and 59/90

Answer 2

The required rational numbers are 91/150, 92/150, 93/150, 94/150, 95/150, 96/150, 98/150, 99/150and 97/150.

Given:

Rational numbers 3/5 and 2/3.

To find:

Find five rational numbers between 3/5 and 2/3      

Solution:

To find the rational numbers between 3/5 and 2/3    

Make the denominators as same by multiplying the same number by the numerator and denominator

=> $\frac{3}{5} \times \frac{3}{3} = \frac{9}{15}$    

=> $\frac{2}{3} \times \frac{5}{5} = \frac{10}{15}$      

Now multiply the above fractions by 10    

=> $\frac{9}{15}\times \frac{10}{10} = \frac{90}{150}$  

=> $\frac{10}{15}\times \frac{10}{10} = \frac{100}{150}$    

Now write any five rational numbers between 90/150 and 100/150

 

=> 91/150, 92/150, 93/150, 94/150, 95/150, 96/150, 98/150, 99/150and 97/150.        

Therefore,

The required rational numbers are 91/150, 92/150, 93/150, 94/150, 95/150, 96/150, 98/150, 99/150and 97/150.

Learn more at

https://brainly.in/question/17944783

#SPJ3