Question

Find 5 rational numbers between 3/5 and 7/10​

Answer 1

Given,

The numbers 3/5 and 7/10.

To Find,

5 rational numbers between 3/5 and 7/10

Solution,

A large number of rational numbers lying between two rational numbers can be found by converting the denominators of both the given rational numbers into the same denominator, i.e., we take the LCM of the denominators of the given rational numbers.

• Hence, to solve this question, we first take the LCM the denominators of 3/5 and 7/10:

                        LCM of 5 and 10 is 10

• Then, we divide the LCM by the denominators and multiply both the numerator and denominator with the number we get after dividing the LCM by the denominator.

       In the case of 3/5: the LCM 10 is divided by the denominator 5.

                              10 ÷ 5 = 2

             Then, we multiply 3/5 by 2

                        (3 × 2) / (5 × 2) = 6/10      

      In the case of 7/10: the LCM 10 is divided by the denominator 10

                        10 ÷ 10 = 1

       Then, we multiply 7/10 by 1

                        (7 × 1) / (10 × 1) = 7/10              

•  If the new equivalent rational numbers do not have enough numbers between their numerators, multiple the numerators, and denominators by 10.

                    (6 × 10) / (10 × 10) = 60/100

                     ( 7 × 10) / (10 × 10) = 70/100

Hence, 5 rational numbers lying between 3/5 and 7/10 are 61/100,   62/100, 63/100, 64/100, and 65/100.