# Blackberry publication class 8 maths chapter rational number

### RATIONAL NUMBERS

#### EXERCISE 2(A)

1.Using properties find:
(a) ​$$\dfrac{-4}{7}+\dfrac{-3}{8}+\dfrac{-6}{7}+\dfrac{-14}{14}+\dfrac{1}{56}$$
(b) ​$$\dfrac{-12}{5}+\dfrac{1}{7}+\dfrac{-1}{10}+\dfrac{3}{14}+\dfrac{-7}{20}$$
(c) ​$$\dfrac{-4}{7}+\dfrac{2}{9}+\dfrac{-5}{4}+\dfrac{8}{21}$$
(d) ​$$\dfrac{-3}{16}+\dfrac{14}{8}+\dfrac{-3}{4}+\dfrac{-2}{32}+(-1)$$
(e) ​$$\dfrac{-5}{8}+\dfrac{2}{7}+\dfrac{-5}{2}+\dfrac{8}{56}$$
(f) ​$$\dfrac{-4}{5}\times\dfrac{5}{7}\times\Big(\dfrac{-8}{9}\Big)\times\dfrac{8}{9}\times\dfrac{4}{7}$$
(g) ​$$\dfrac{-3}{2}\times\dfrac{-6}{5}+\dfrac{2}{3}+\dfrac{5}{6}\div\dfrac{7}{6}$$
(h) ​$$\dfrac{-2}{3}\times\Bigg[\dfrac{3}{5}\div\dfrac{-5}{7}\Bigg]$$

2.Write the additive inverse of the following :
(a) ​$$\dfrac{6}{7}$$
(b) ​$$\dfrac{-9}{15}$$
(c) ​$$\dfrac{5}{-26}$$
(d) 0
(e) -1
(f) ​$$\dfrac{-19}{117}$$
(g) $$\dfrac{112}{-133}$$
(h) $$\dfrac{-5}{8}$$

3.Find the reciprocal of :

(a) 43

(b) -8

(c) $$\dfrac{-9}{6}$$

(d) $$\dfrac{5}{-7}$$

(e) $$\dfrac{4}{-7}\times\dfrac{-17}{8}$$

4.The sum of two rational numbers is $$\dfrac{-1}{3}$$.If one number is $$\dfrac{7}{8}$$then find the additive inverse of the other.

5.What should be added to the additive inverse of ​$$\dfrac{9}{8}$$​to get 1 ?

6.What should be added to the additive inverse of ​$$\dfrac{-6}{5}$$​ to get ​$$\dfrac{13}{7}$$

7.The sum of two rational number is -1 .If one number is ​$$\dfrac{-4}{11}$$​, find the other.

8.What should be added to ​$$\dfrac{-5}{4}$$​ to get ​$$\dfrac{2}{3}$$​?

9.What should be added to ​$$\dfrac{3}{7}$$​ to get 0 ?

10.What should be added to -1 to get ​$$\dfrac{5}{9}$$​ ?

11.Verify the following :

(a)​$$\dfrac{-3}{5}\times\dfrac{15}{25}=\dfrac{15}{25}\times\dfrac{-3}{15}$$

(b)​$$\dfrac{1}{3}\times\Bigg[\dfrac{-2}{5}+\dfrac{-3}{7}\Bigg]=\Bigg[\dfrac{1}{3}\times\dfrac{-2}{5}\Bigg]+\Bigg[\dfrac{1}{3}\times\dfrac{-3}{7}\Bigg]$$

(c)​$$\dfrac{4}{5}\times\Bigg[\dfrac{11}{4}\times\dfrac{-5}{25}\Bigg]=\Bigg[\dfrac{4}{5}\times\dfrac{11}{4}\Bigg]\times\dfrac{-5}{25}$$

12.Write the suitable property for that following :

(a) ​$$\dfrac{-14}{9}\times\dfrac{-12}{7}=\dfrac{-12}{7}\times\dfrac{-14}{9}$$

(b) ​$$\dfrac{-3}{5}\times\Bigg[\dfrac{-7}{9}+\dfrac{8}{9}\Bigg]=\Bigg[\dfrac{-3}{5}\times\dfrac{-7}{6}\Bigg]+\Bigg[\dfrac{-3}{5}\times\dfrac{8}{9}\Bigg]$$

(c) ​$$\dfrac{-12}{19}\times\dfrac{19}{-12}=\Bigg[\dfrac{1}{1}\Bigg]$$

(d) ​$$\dfrac{-4}{9}\times0=0$$

(e) ​$$\Bigg[\dfrac{-2}{3}\times\dfrac{7}{5}\Bigg]\times\dfrac{-9}{8}=\dfrac{-2}{3}\times\Bigg[\dfrac{7}{5}\times\dfrac{-9}{8}\Bigg]$$

(f) ​$$\Bigg[\dfrac{-2}{7}\times\dfrac{1}{3}\Bigg]+\Bigg[\dfrac{-2}{7}\times\dfrac{-6}{8}\Bigg]=\dfrac{-2}{7}\times\Bigg[\dfrac{1}{3}+\dfrac{-6}{8}\Bigg]$$

#### EXERCISE 2(B)

1.Represent the following rational numbers on the number line :
(a) ​$$\dfrac{2}{7}$$
(b) ​$$\dfrac{3}{5}$$
(c) ​$$\dfrac{-3}{8}$$
(d) ​$$\dfrac{4}{9}$$
(e) ​$$\dfrac{9}{4}$$
(f) ​$$\dfrac{3}{4}$$
(g) ​$$\dfrac{1}{2}$$

2.Find three rational number between :
(a)  ​$$\dfrac{-1}{3}$$​and  ​$$\dfrac{-4}{7}$$
(b)   ​$$\dfrac{7}{10}$$​and  ​$$\dfrac{1}{3}$$
(c)   ​$$\dfrac{1}{3}$$​and  ​$$\dfrac{1}{2}$$
(d)   ​$$\dfrac{-10}{7}$$​and  ​$$\dfrac{-10}{11}$$

3.Find four rational number between :
(a) 3 and 4
(b)  ​$$\dfrac{2}{9}$$​and  ​$$\dfrac{5}{8}$$
(c) -3 and 2
(d)   ​$$\dfrac{5}{9}$$​and  ​$$\dfrac{2}{9}$$

4.Find five rational number between   ​$$\dfrac{-1}{3}$$​and  ​$$\dfrac{1}{3}$$

5.Find six rational number between   ​$$\dfrac{2}{3}$$​and  ​$$\dfrac{2}{5}$$

6.Find nine rational number between   ​$$\dfrac{1}{8}$$​and  ​$$\dfrac{1}{12}$$

7.Find four rational numbers greater than -3.

8.Find six rational numbers less than -6.