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

 Exercise 1A

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

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Question 1

Write four rational numbers equivalent to each of the following numbers

(a) $\frac{2}{9}$

Sol :

$\frac{4}{18},\frac{6}{27},\frac{8}{36},\frac{10}{45}$

(b) $-\frac{3}{5}$

Sol :

$\frac{-6}{10},\frac{-9}{15},\frac{-12}{20},\frac{-15}{25}$

(c) $-\frac{7}{11}$

Sol :

$\frac{14}{-22},\frac{21}{-33},\frac{28}{-44},\frac{35}{-55}$

(d) $\frac{-6}{-13}$

Sol :

$\frac{-12}{-26},\frac{-18}{-39},\frac{-24}{-52},\frac{-30}{-65}$

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

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Question 2

Write the following rational numbers in standard form.

$\frac{15}{20},\frac{64}{72},\frac{-54}{-63},\frac{88}{-99},\frac{-87}{156}$

Sol :

$\frac{15}{20}=\frac{3}{4}$ 

$\frac{64}{72}=\frac{8}{9}$

$\frac{-54}{-63}=\frac{6}{7}$

$\frac{88}{-99}=\frac{8}{-9}\times \frac{-1}{-1}$

$\frac{-87}{156}=-\frac{29}{52}$

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

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Question 3

Write the absolute value value of each of the following.

$\frac{17}{24},\frac{-6}{35},\frac{-11}{-17},0,\frac{28}{-45}$

Sol :

$\frac{17}{24}=\frac{17}{24}$

$\frac{-6}{35}=\frac{6}{35}$

$\frac{-11}{-17}=\frac{11}{7}$

0=0

$\frac{28}{-45}=\frac{28}{45}$

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

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Question 4

Write the rational numbers whose absolute value is $\frac{5}{6}$

Sol :

$+\frac{5}{6},-\frac{5}{6}$

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Q5 | Ex-1A |Class 8 |Rational Numbers | S.Chand | New Learning | Composite mathematics | myhelper

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Question 5

(a) -1<$\frac{-1}{2}$

(b) 1>-2

(c) 0>-3

(d) -5<-4

(e) $3\frac{3}{4}>1\frac{2}{5}$

(f) -4<$4\frac{2}{3}$

(g) $-3\frac{4}{5}>-4$

(h) $-\frac{1}{2}>-1\frac{5}{5}$

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Q6 | Ex-1A |Class 8 |Rational Numbers | S.Chand | New Learning | Composite mathematics | myhelper

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Question 6

Which pairs of rational numbers are not equivalent?

(a) $\frac{15}{19},\frac{-15}{-19}$

Sol :

$\frac{15\times -19}{-15\times 19}=\frac{-285}{-285}$

(b) $\frac{28}{-49},\frac{-4}{7}$

Sol : 

$=\frac{-4}{7}=\frac{-4\times 7}{-7\times 4}=\frac{-28}{-28}$

(c) $\frac{16}{17},\frac{26}{27}$

Sol :

$\frac{16\times 27}{17\times 26}=\frac{432}{442}$

⇒432<442 (not equivalent)

(d) $\frac{27}{99},\frac{51}{187}$

Sol :

$\frac{3}{11},\frac{3}{11}$ 

$=\frac{3\times 11}{3\times 11}=\frac{33}{33}$

(e) $\frac{16}{20},\frac{4}{-5}$

Sol :

$=\frac{4}{5},\frac{4}{-5}=\frac{4\times -5}{5\times 5}=\frac{-20}{20}$

=-2 (not equivalent)

(c) and (e) are not equivalent

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Q7 | Ex-1A |Class 8 |Rational Numbers | S.Chand | New Learning | Composite mathematics | myhelper

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Question 7

Compare. Write <, > or = in the blanks to make a true statement.

(a) $-\frac{8}{15}< -\frac{7}{30}$

(b) $-\frac{1}{5}>-\frac{1}{4}$

(c) $\frac{3}{10}< \frac{5}{12}$

(d) $\frac{5}{6}=\frac{15}{18}$

(e) $\frac{1}{-25}<\frac{1}{50}$

(f) $\frac{17}{40}<0.519$

(g) -8.9<$\frac{-33}{4}$

(h) $\frac{-1}{8}=\frac{4}{-32}$

(i) $\frac{18}{-19}<\frac{-10}{11}$

(j) $\frac{-16}{25}>\frac{17}{-21}$

(k) $\frac{-5}{3}<\frac{40}{27}$

(l) $\frac{15}{-16}<\frac{-9}{10}$

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Q8 | Ex-1A |Class 8 |Rational Numbers | S.Chand | New Learning | Composite mathematics | myhelper

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Question 8

Arrange the following groups of rational numbers in ascending order.

(a) $\frac{-1}{4},\frac{1}{2},\frac{7}{8},\frac{15}{6},\frac{-9}{40}$

Sol :

$\frac{-1}{4},\frac{-9}{40},\frac{1}{2},\frac{7}{8},\frac{15}{6},$

(b) $\frac{5}{7},\frac{-7}{25},\frac{-9}{-4},\frac{-6}{5},\frac{8}{11}$

Sol :

$\frac{-9}{-4},\frac{-6}{5},\frac{-7}{25},\frac{5}{7},\frac{8}{11}$

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Q9 | Ex-1A |Class 8 |Rational Numbers | S.Chand | New Learning | Composite mathematics | myhelper

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Question 9

Arrange the following groups of rational numbers in descending order.

(a) $-\frac{13}{8},\frac{23}{12},\frac{-27}{16},\frac{17}{9},\frac{-11}{6}$

Sol :

$\frac{23}{12}>\frac{17}{9}>\frac{-13}{8}>\frac{-27}{16}>\frac{-11}{16}$

(b) $\frac{-7}{16},\frac{-1}{4},\frac{1}{8},\frac{9}{32},\frac{18}{25}$

Sol :

$\frac{18}{25}>\frac{9}{32}>\frac{1}{8}>\frac{-1}{4}>\frac{-7}{16}$