S.chand publication New Learning Composite mathematics solution of class 8 Chapter 1 Rational numbers Exercise 1E

 Exercise 1E

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Q1| Ex-1D |Class 8 |Rational Numbers | S.Chand | New Learning | Composite maths | myhelper

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Question 1

Find One Rational number between

(a) 6 and 8

Sol :

$=\frac{8+6}{2}=7$

(b) -3 and 9

Sol :

$=\frac{9+(-3)}{2}=\frac{6}{2}=3$

(c) $\frac{1}{3}\text{ and }\frac{1}{4}$

Sol :

$\left(\frac{1}{3}+\frac{1}{4}\right)\div 2=\frac{4+3}{12}\times \frac{1}{2}$

$=\frac{7}{12}\times \frac{1}{2}=\frac{7}{24}$

(d) $\frac{-1}{8}\text{ and }\frac{3}{16}$

Sol :

$\left(\frac{-1}{8}+\frac{3}{16}\right)\div 2=\frac{-2+3}{16}\times \frac{1}{2}$

$=\frac{1}{16}\times \frac{1}{2}=\frac{1}{32}$

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Q2 | Ex-1D |Class 8 |Rational Numbers | S.Chand | New Learning | Composite maths | myhelper

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Question 2

Two rational numbers between

Difference$=\frac{b-a}{n+1}$ ,where b(second term), a(first term) and n(number of terms needed) 

(a) 4 and 7

Sol :

Difference $=\frac{7-4}{2+1}=\frac{3}{3}=1$

1^st rational number=4+1=5

2^nd rational number=4+(2×1)=6

(b) -1 and 6

Sol :

Difference $=\frac{6-(-1)}{2+1}=\frac{6+1}{3}=\frac{7}{3}$

1^st rational number$=-1+\frac{7}{3}=\frac{-3+7}{3}=\frac{4}{3}$

2^nd rational number$=-1+2\times \frac{7}{3}=1+\frac{14}{3}$ $=\frac{-3+14}{3}=\frac{11}{3}$

(c) $\frac{1}{2}\text{ and }\frac{7}{8}$

Sol :

Difference $=\dfrac{\frac{7}{8}-\frac{1}{2}}{2+1}=\dfrac{\frac{2}{3}}{3}$ $=\frac{3}{8}\times \frac{1}{3}=\frac{1}{8}$

1^st rational number$=\left(\frac{1}{2}\right)+\frac{1}{8}=\frac{4+1}{8}=\frac{5}{8}$

2^nd rational number$=\left(\frac{1}{2}\right)+\frac{1}{8}\times 2$ $=\frac{2+1}{4}=\frac{3}{4}$

(d) $\frac{-3}{4}\text{ and }\frac{5}{6}$

Sol :

Difference$=\dfrac{\frac{5}{6}+\frac{3}{4}}{2+1}=\dfrac{\frac{19}{12}}{3}=\frac{19}{36}$

1^st rational number$=\frac{-3}{4}+\left(\frac{19}{36}\right)=\frac{-27+19}{36}=-\frac{2}{9}$

2^nd rational number$=\frac{-3}{4}+2\times \left(\frac{19}{36}\right)=\frac{11}{36}$

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Q3| Ex-1D |Class 8 |Rational Numbers | S.Chand | New Learning | Composite maths | myhelper

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Question 3

Three rational numbers between

(a) -7 and -3

Sol :

Difference $=\frac{-7-(-3)}{3+1}=\frac{-4}{4}$

=-1

1^st rational number=-3+(-1)

=-3-1=-4

2^nd rational number=-3+2(-1)

=-3-2=-5

3^rd rational number=-3+3(-1)

=-3-3=-6

(b) $-\frac{2}{7}\text{ and }\frac{6}{7}$

Sol :

Difference$=\dfrac{\frac{6}{7}-\left(-\frac{2}{7}\right)}{3+1}$ $=\dfrac{\frac{8}{7}}{4}=\frac{2}{7}$

1^st rational number$=-\frac{2}{7}+\frac{2}{7}=0$

2^nd rational number$=-\frac{2}{7}+2\times \frac{2}{7}=\frac{2}{7}$

3^rd rational number$=-\frac{2}{7}+3\times \frac{2}{7}=\frac{4}{7}$

(c) $\frac{3}{8}\text{ and }\frac{5}{12}$

Sol :

Difference$=\dfrac{\frac{5}{12}-\frac{3}{8}}{3+1}=\dfrac{\frac{1}{24}}{4}$

$=\frac{1}{24}\times \frac{1}{4}=\frac{1}{96}$

1^st rational number$=\frac{3}{8}+\frac{1}{96}=\frac{36+1}{96}=\frac{37}{96}$

2^nd rational number$=\frac{3}{8}+2\times \frac{1}{96}=\frac{36+2}{96}=\frac{38}{96}$

3^rd rational number$=\frac{3}{8}+3\times \frac{1}{96}=\frac{36+3}{96}=\frac{13}{32}$ 

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Q4 | Ex-1D |Class 8 |Rational Numbers | S.Chand | New Learning | Composite maths | myhelper

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Question 4

Five rational numbers between

(a) -3 and -8

Sol :

Difference$=\frac{-3-(-8)}{5+1}=\frac{+5}{6}$

1^st rational number$=-8+\frac{5}{6}=\frac{-48+5}{6}=\frac{-43}{6}$

2^nd rational number$=-8+2\times \frac{5}{6}=\frac{-48+10}{6}=\frac{-38}{6}$

3^rd rational number$=-8+3\times \frac{5}{6}=\frac{-48+15}{6}=\frac{-33}{6}$

4^th rational number$=-8+4\times \frac{5}{6}=\frac{-48+20}{6}=-\frac{28}{6}$

5^th rational number$=-8+5\times \frac{5}{6}=\frac{-48+25}{6}=\frac{-23}{6}$

(b) $\frac{3}{5}\text{ and }\frac{4}{5}$

Sol :

Difference$=\dfrac{\frac{4}{5}-\frac{3}{5}}{5+1}=\dfrac{\frac{1}{5}}{6}=\frac{1}{30}$

1^st rational number$=\frac{3}{5}+\frac{1}{30}=\frac{18+1}{30}=\frac{19}{30}$

2^nd rational number$=\frac{3}{5}+\frac{2}{30}=\frac{18+2}{30}=\frac{20}{30}$

3^rd rational number$=\frac{3}{5}+\frac{3}{30}=\frac{18+3}{30}=\frac{21}{30}$

4^th rational number$=\frac{3}{5}+\frac{4}{30}=\frac{18+4}{30}=\frac{22}{30}$

5^th rational number$=\frac{3}{5}+\frac{5}{30}=\frac{18+5}{30}=\frac{23}{30}$

 

(c) $\frac{-1}{6}\text{ and }\frac{5}{9}$

Sol :

Difference$=\dfrac{\frac{5}{9}-\left(-\frac{1}{6}\right)}{5+1}=\frac{13}{108}$

1^st rational number$=\frac{-1}{6}+\frac{13}{108}=\frac{-18+13}{108}=\frac{-5}{108}$

2^nd rational number$=\frac{-1}{6}+2\times \frac{13}{108}=\frac{-18+26}{108}=\frac{8}{108}$

3^rd rational number$=\frac{-1}{6}+3\times \frac{13}{108}=\frac{-18+39}{108}=\frac{21}{108}$

4^th rational number$=\frac{-1}{6}+4\times \frac{13}{108}=\frac{-18+52}{108}=\frac{34}{108}$

5^th rational number$=\frac{-1}{6}+5\times \frac{13}{108}=\frac{-18+65}{108}=\frac{47}{108}$