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.

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