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

Writing the given numbers with the same denominator 6 (LCM of 3 and 2 ) we get, - 1 3 = - 1 × 2 3 × 2 = - 2 6 and - 1 2 = - 1 × 3 2 × 3 = - 3 6 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 2 + 1 i.e. by 3 , we get - 6 18 , - 9 18 , which are equivalent to the given number. As - 6 > - 7 > - 8 > - 9 Arrangement in ascending order: - 6 18 > - 7 18 > - 8 18 > - 9 18 , - 1 3 > - 7 18 > - 4 9 > - 1 2 Hence, the two rational numbers between - 1 3 and - 1 2 are - 7 18 , - 4 9 and in ascending order - 1 3 , - 7 18 , - 4 9 , - 1 2 .

Find three rational numbers between 5 7 and 6 7 .

We need to find three rational numbers between 5 7 and 6 7 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 3 + 1 i.e. by 4 , we get 20 28 , 24 28 , which are equivalent to the given number. As 20 < 21 < 22 < 23 < 24 , 20 28 < 21 28 < 22 28 < 23 28 < 24 28 , 5 7 < 3 4 < 11 14 < 23 28 < 6 7 Hence, the three rational numbers between 5 7 and 6 7 are 3 4 , 11 14 , 23 28 .

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

Writing the given numbers with the same denominator 15 (LCM of 3 and 5 ) we get, 1 3 = 1 × 5 3 × 5 = 5 15 and 4 5 = 4 × 3 5 × 3 = 12 15 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 3 + 1 i.e. by 4 , we get 20 60 , 48 60 , which are equivalent to the given number. As 20 < 48 We can take any number between 20 60 and 48 60 Arrangement in descending order: 48 60 > 43 60 > 35 60 > 24 60 > 20 60 , 4 5 > 43 60 > 7 12 > 2 5 > 1 3 Hence, the three rational numbers between 1 3 and 4 5 are 2 5 , 7 12 , 43 60 and in descending order 4 5 , 43 60 , 7 12 , 2 5 , 1 3 .

Find five rational numbers between 3 5 and 4 5 .

We need to find five rational numbers between 3 5 and 4 5 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 5 + 1 i.e. by 6 , we get 18 30 , 24 30 , which are equivalent to the given number. As 18 < 19 < 20 < 21 < 22 < 23 < 24 , 18 30 < 19 30 < 20 30 < 21 30 < 22 30 < 23 30 < 24 30 , 3 5 < 19 30 < 2 3 < 7 10 < 11 15 < 23 30 < 4 5 Hence, the five rational numbers between 3 5 and 4 5 are 19 30 , 2 3 , 7 10 , 11 15 , 23 30 .

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

Writing the given numbers with the same denominator 35 (LCM of 5 and 7 ) we get, - 2 5 = - 2 × 7 5 × 7 = - 14 35 and 1 7 = 1 × 5 7 × 5 = 5 35 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 10 + 1 i.e. by 11 , we get - 154 385 , 55 385 , which are equivalent to the given number. As - 154 < 55 We can take any ten numbers between - 154 385 and 55 385 . - 154 385 < - 145 385 < - 130 385 < - 124 385 < - 11 385 < 0 < 10 385 < 25 385 < 34 385 < 37 385 < 44 385 < 55 385 , - 2 5 < - 29 77 < - 26 77 < - 124 385 < - 11 385 < 0 < 2 77 < 5 77 < 34 385 < 37 385 < 44 385 < 1 7 Hence, the ten rational numbers between - 2 5 and - 1 2 are - 29 77 , - 26 77 , - 124 385 , - 11 385 , 0 , 2 77 , 5 77 , 34 385 , 37 385 , 44 385 .

Find six rational numbers between 1 2 and 2 3 .

Writing the given numbers with the same denominator 6 (LCM of 2 and 3 ) we get, 1 2 = 1 × 3 2 × 3 = 3 6 and 2 3 = 2 × 2 3 × 2 = 4 6 . Since, we want to find two rational numbers between the given numbers, multiplying the numerator and denominator of each of the given numbers by 6 + 1 i.e. by 7 , we get 21 42 , 28 42 , which are equivalent to the given number. As 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28 , 21 42 < 22 42 < 23 42 < 24 42 < 25 42 < 26 42 < 27 42 < 28 42 , 1 2 < 11 21 < 23 42 < 12 21 < 25 42 < 13 21 < 27 42 < 2 3 Hence, the six rational numbers between 1 2 and 2 3 are 11 21 , 23 42 , 12 21 , 25 42 , 13 21 , 27 42 .

E M B I B E

CBSE Syllabus Standard Mathematics for Class IX>Chapter 1 - Number System>Exercise 1.1

M L Aggarwal Solutions for Chapter: Number System, Exercise 1: Exercise 1.1

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Number System, Exercise 1: Exercise 1.1

Attempt the practice questions on Chapter 1: Number System, Exercise 1: Exercise 1.1 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class IX solutions are prepared by Experienced Embibe Experts.