Represent 3 7 on the number line.

The given rational number is 3 7 . To represents the given rational number on the number line, we have the following steps: 1 . Draw a line l . 2 . Mark a point O , to represent zero. 3 . On the right of O , mark 1 , 2 , . . . as 1 unit each. 4 . As 3 7 lies between 0 and 1 , we divide the distance between 0 and 1 into 7 equal parts. Then, OA represents 3 7 of a unit. Hence, point A represents 3 7 on the number line as shown below

Represent - 2 5 on the number line.

The given rational number is - 2 5 . To represents the given rational number on the number line, we have the following steps: 1 . Draw a line l . 2 . Mark a point O , to represent zero. 3 . On the left of O , mark - 1 , - 2 , . . . as 1 unit each. 4 . As - 2 5 lies between 0 and - 1 , we divide the distance between 0 and - 1 into 5 equal parts. Then, OA represents - 2 5 of a unit. Hence, point A represents - 2 5 on the number line. as shown below

Represent 2 2 3 on the number line.

The given mixed fraction is 2 2 3 . To represents the given rational number on the number line, we have the following steps: 1 . Draw a line l . 2 . Mark a point O , to represent zero. 3 . On the right of O , mark 1 , 2 , 3 , . . . on each 3 cm = 1 unit . 4 . As 2 2 3 = 2 + 2 3 lies between 2 and 3 . We divide the third unit into 3 equal parts. Then, OA represents 2 2 3 of a unit. Thus, A represents 2 2 3 on the number line.

Find twenty rational numbers between - 3 4 and 7 6 .

Given rational numbers are - 3 4 and 7 6 . To find any twenty rational numbers lying between - 3 4 and 7 6 . We have to make their denominators equal by taking LCM of both the denominators of the two given rational numbers. Now, LCM of 4 , 6 = 12 . Now, - 3 4 = - 3 4 × 3 3 = - 9 12 and 7 6 = 7 6 × 2 2 = 14 12 . ∴ Rational numbers lying between - 3 4 and 7 6 are - 8 12 , - 7 12 , - 6 12 , - 5 12 , . . . 11 12 , 12 12 , 13 12 . Hence, any twenty rational numbers out of these may be taken i.e. - 8 12 , - 7 12 , - 6 12 , - 5 12 , - 4 12 , - 3 12 , - 2 12 , - 1 12 , 0 , 1 12 , 2 12 , 3 12 , 4 12 , 5 12 , 6 12 7 12 , 8 12 , 9 12 , 10 12 , 11 12

Find thirty rational numbers between 1 3 and 3 5 .

Given rational numbers are 1 3 and 3 5 . To find any thirty rational numbers lying between 1 3 and 3 5 . We have to make their denominators equal by taking LCM of both the denominators of the two given rational numbers. ⇒ LCM of 3 , 5 = 15 . Now, 1 3 = 1 3 × 5 5 = 5 15 and 3 5 = 3 5 × 3 3 = 9 15 . Since, both the obtained rational numbers are not enough to provide thirty rational numbers, we have to multiply and divide both by 10 . We have: 1 3 = 5 15 = 5 15 × 10 10 = 50 150 and 3 5 = 9 15 = 9 15 × 10 10 = 90 150 ∴ Rational numbers lying between 1 3 and 3 5 are 51 15 , 52 15 , 53 15 , 54 15 . . . 87 15 , 88 15 , 89 15 . Hence, any thirty rational numbers out of these may be taken.

Find hundred rational numbers between - 3 11 and 5 11 .

Given: Two rational numbers - 3 11 and 5 11 . To find any hundred rational numbers lying between - 3 11 and 5 11 . ∵ Denominators are equal, we have to multiply and divide each of them by 100 . Now, - 3 11 = - 3 11 × 100 100 = - 300 1100 and 5 11 = 5 11 × 100 100 = 500 1100 . ∴ Rational numbers lying between - 3 11 and 5 11 are - 299 1100 , - 298 1100 , - 297 1100 , - 296 1100 , . . . , 497 1100 , 498 1100 , 499 1100 . Hence, any hundred rational numbers out of these may be taken.

E M B I B E

Number Magic a textbook of Mathematics 8>Chapter 1 - Rational Numbers>EXERCISE

Monica Capoor Solutions for Chapter: Rational Numbers, Exercise 9: EXERCISE

Author:Monica Capoor

Monica Capoor Mathematics Solutions for Exercise - Monica Capoor Solutions for Chapter: Rational Numbers, Exercise 9: EXERCISE

Attempt the practice questions on Chapter 1: Rational Numbers, Exercise 9: EXERCISE with hints and solutions to strengthen your understanding. Number Magic a textbook of Mathematics 8 solutions are prepared by Experienced Embibe Experts.