Find three rational numbers between - 2 3 and 1 4 .

The given rational numbers are - 2 3 and 1 4 . Make denominator same, by finding LCM of the denominators. LCM of 3 and 4 is 12 . We write - 2 3 = - 2 3 × 4 4 = - 8 12 1 4 = 1 4 × 3 3 = 3 12 So that denominators of numbers are some. Now, we can find rational numbers between - 8 12 and 3 12 . There are 9 rational number we can write directly between - 8 and 3 , - 7 , - 6 , - 5 , - 4 , - 3 , - 2 , - 1 , 1 , 2 Hence, Taking any three we can obtain required rational numbers, - 7 12 , - 6 12 , - 5 12 .

Find five rational numbers between - 3 2 and 5 3 .

Given, - 3 2 and 5 3 . Make denominator same, by finding LCM of the denominators. - 3 2 = - 3 2 × 3 3 = - 9 6 ( Multiply numerator and denominator of - 3 2 by 3 ) 5 3 = 5 3 × 2 2 = 10 6 ( Multiply numerator and denominator of 5 3 by 2 ) Now, we can find the rational number between - 9 6 and 10 6 , Hence, 5 rational numbers are, - 8 6 , - 7 6 , 4 6 , 5 6 , 7 6

Find ten rational numbers between 3 5 and 3 4 .

Given, numbers are 3 5 and 3 4 . LCM of 5 and 4 = 20 . So, 3 5 = 3 5 × 4 4 = 12 20 and 3 4 = 3 4 × 5 5 = 15 20 Now again, we change the rational numbers to their equivalent rational numbers, 12 20 = 12 20 × 8 8 = 96 160 and 15 20 = 15 20 × 8 8 = 120 160 Hence, ten rational numbers between 3 5 and 3 4 are 97 160 , 98 160 , 99 160 , 100 160 , 101 160 , 102 160 , 103 160 , 104 160 , 105 160 , 106 160 . There can be numerous rational numbers between 3 5 and 3 4 .

Find three rational numbers between - 2 3 and - 1 3 .

Given, - 2 3 and - 1 3 We change the rational numbers to their equivalent rational numbers, - 2 3 × 4 4 = - 8 12 - 1 3 × 4 4 = - 4 12 So, the rational numbers between - 8 12 and - 4 12 are - 4 12 < - 5 12 < - 6 12 < - 7 12 < - 8 12 Hence, there are three rational numbers, - 5 12 , - 6 12 , - 7 12 .

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START UP MATHEMATICS>Chapter 1 - Rational Numbers>EXERCISE 1.9

Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 9: EXERCISE 1.9

Author:Monicaa Abhijit

Monicaa Abhijit Mathematics Solutions for Exercise - Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 9: EXERCISE 1.9

Attempt the practice questions on Chapter 1: Rational Numbers, Exercise 9: EXERCISE 1.9 with hints and solutions to strengthen your understanding. START UP MATHEMATICS solutions are prepared by Experienced Embibe Experts.