Insert two rational numbers between 1 3 and 1 4 , and arrange in ascending order.

Given, To write the rational numbers between 1 3 and 1 4 and arrange them in descending order. We know, If a , b are any two rational numbers, then a + b 2 is a rational number and it lies between them. i.e., If a < b , then a < a + b 2 < b . Therefore, we get the rational numbers between 1 4 , 1 3 : 1 4 + 1 3 2 = 7 12 2 = 7 24 7 24 + 1 4 2 = 13 24 2 = 13 48 Thus, we get the numbers as 1 3 , 1 4 , 2 24 , 13 48 . Hence, arranging them in ascending order, we get: 1 4 < 13 48 < 7 24 < 1 3 .

Insert two rational numbers between - 1 3 and - 1 2 , and arrange in ascending order.

Given, To write the rational numbers between - 1 3 and - 1 2 and arrange them in descending order. We know, If a , b are any two rational numbers, then a + b 2 is a rational number and it lies between them. i.e., If a < b , then a < a + b 2 < b . Therefore, we get the rational numbers between - 1 3 , - 1 2 : - 1 3 + - 1 2 2 = - 5 6 2 = - 5 12 - 5 12 + - 1 3 2 = - 3 4 2 = - 3 8 Thus, we get the numbers as - 1 3 , - 1 2 , - 5 12 , - 3 8 . Hence, arranging them in ascending order, we get: - 1 2 < - 5 12 < - 3 8 < - 1 3 .

Insert three rational numbers between 1 3 and 4 5 , and arrange in descending order.

Given, To write the rational numbers between 1 3 and 4 5 and arrange them in descending order. Writing given numbers with same denominator (LCM of the denominators 3 and 5 ). We get: 1 3 = 1 × 5 3 × 5 = 5 15 and 4 5 = 4 × 3 5 × 3 = 12 15 As we know, 12 > 11 > 10 > . . . > 6 > 5 . ⇒ 12 15 > 11 15 > 10 15 > . . . > 6 15 > 5 15 Let us take any three rational number between 12 15 and 5 15 . ⇒ 9 15 > 8 15 > 7 15 Therefore, Descending order of the numbers is: 4 5 > 9 15 > 8 15 > 7 15 > 1 3

Find five rational numbers between 3 5 and 4 5 .

Given, Find five rational numbers between 3 5 and 4 5 . Since we have to write 5 rational numbers, multiply the numerator and denominator of each of the given numbers by 5 + 1 = 6 . We get: 3 5 = 3 × 6 5 × 6 = 18 30 and 4 5 = 4 × 6 5 × 6 = 24 30 As we know, 24 > 23 > 22 > 21 > 20 > 19 > 18 . ⇒ 24 30 > 23 30 > 22 30 > 21 30 > 20 30 > 19 30 > 18 30 Therefore, the rational numbers between 3 5 and 4 5 are: 19 30 , 20 30 , 21 30 , 22 30 , 23 30 .

Find ten rational numbers between - 2 5 and 1 7 .

Given, To write the rational numbers between - 2 5 and 1 7 . Writing given numbers with same denominator (LCM of the denominators 5 and 7 ). We get: - 2 5 = - 2 × 7 5 × 7 = - 14 35 and 1 7 = 1 × 5 7 × 5 = 5 35 Since we have to write 10 rational numbers, multiply the numerator and denominator of each of the given numbers by 10 + 1 = 11 . We get: - 14 × 11 35 × 11 = - 154 385 and 5 × 11 35 × 11 = 55 385 As we know, - 154 < - 153 < - 152 < . . . < 53 < 54 < 55 . ⇒ - 154 385 < - 153 385 < - 152 385 < . . . < 53 385 < 54 385 < 55 385 Therefore, ten rational numbers between - 2 5 and 1 7 are: - 3 385 , - 2 385 , - 1 385 , 1 385 , 2 385 , 3 385 , 4 385 , 5 385 , 6 385 , 7 385 .

Find six rational numbers between 1 2 and 2 3 .

Given, To write the rational numbers between 1 2 and 2 3 . Writing given numbers with same denominator (LCM of the denominators 2 and 3 ). We get: 1 2 = 1 × 3 2 × 3 = 3 6 and 2 3 = 2 × 2 3 × 2 = 4 6 Since we have to write 6 rational numbers, multiply the numerator and denominator of each of the given numbers by 6 + 1 = 7 . We get: 3 × 7 6 × 7 = 21 42 and 4 × 7 6 × 7 = 28 42 As we know, 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28 . ⇒ 21 42 < 22 42 < 23 42 < 24 42 < 25 42 < 26 42 < 27 42 < 28 42 Therefore, six rational numbers between 1 2 and 2 3 are: 22 42 , 23 42 , 24 42 , 25 42 , 26 42 , 27 42 .

E M B I B E

Understanding ICSE Mathematics Class 9>Pure Arithmetic>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.1

M L Aggarwal Solutions for Exercise 1: EXERCISE 1.1

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 1: EXERCISE 1.1

Attempt the free practice questions from Exercise 1: EXERCISE 1.1 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 9 solutions are prepared by Experienced Embibe Experts.