Find three rational number Iying between 3 5 and 7 8 How many rational numbers can be determined between these two numbers?

Given, Consider 3 5 < 7 8 Then x = 3 5 , y = 7 8 and n = 3 d = y - x n + 1 = 7 8 - 3 5 3 + 1 = 35 - 24 40 4 = 11 160 . Rational numbers in-between x and y are: x + d , x + 2 d and x + 3 d So we get, the rational numbers are = 3 5 + 11 160 , 3 5 + 2 × 11 160 and 3 5 + 3 × 11 160 = 96 + 11 160 , 3 5 + 11 80 and 3 5 + 33 160 On further calculation we get, the rational numbers are = 107 160 , 48 + 11 80 and 96 + 33 160 = 107 160 , 59 80 and 129 160 Infinitely many rational numbers can be determined in-between the given numbers.

Find four rational numbers between 3 7 and 5 7 .

Given, we have to find two rational numbers between 3 7 and 5 7 . Let us consider 3 7 = 3 × 3 7 × 3 = 9 21 And 5 7 = 5 × 3 7 × 3 = 15 21 As we know 9 21 < 10 21 < 11 21 < 12 21 < 13 21 < 14 21 < 15 21 Thus, the four rational numbers which lie in-between 3 7 = 9 21 and 5 7 = 15 21 are 10 21 , 11 21 , 12 21 and 13 21 .

Find five rational numbers between 3 5 and 2 3 .

Given, 3 5 and 2 3 Now, 3 × 3 5 × 3 = 9 15 and 2 × 5 3 × 5 = 10 15 So, 9 15 < 10 15 Thus, 3 5 < 2 3 As d = y - x n + 1 Let x = 3 5 , y = 2 3 and n = 5 . So, d = y - x n + 1 = 2 3 - 3 5 5 + 1 = 10 - 9 15 6 = 1 90 Rational numbers in-between x and y are x + d , x + 2 d , x + 3 d , x + 4 d and x + 5 d . Therefore, 3 5 + 1 90 , 3 5 + 2 1 90 , 3 5 + 3 1 90 , 3 5 + 4 1 90 and 3 5 + 5 1 90 = 54 + 1 90 , 3 5 + 1 45 , 3 5 + 1 30 , 3 5 + 2 45 and 3 5 + 1 18 = 55 90 , 27 + 1 45 , 18 + 1 30 , 27 + 2 45 and 54 + 5 90 = 11 18 , 28 45 , 19 30 , 29 45 and 59 90 Hence, five rational numbers between 3 5 and 2 3 are 11 18 , 28 45 , 19 30 , 29 45 and 59 90 .

E M B I B E

Secondary School Mathematics FOR CLASS 9>Number Systems>Chapter 1 - Number Systems>EXERCISE 1A

R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: EXERCISE 1A

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: EXERCISE 1A

Attempt the free practice questions from Exercise 1: EXERCISE 1A with hints and solutions to strengthen your understanding. Secondary School Mathematics FOR CLASS 9 solutions are prepared by Experienced Embibe Experts.