S.chand publication New Learning Composite mathematics solution of class 7 Chapter 3 Rational numbers Exercise 3A

 Exercise 3A

Question 1 

Which of the following are not rational numbers?

(a) $\frac{2}{-3}$

(b) $\frac{7}{8}$

(c) $\frac{-8}{15}$

(d) 0

(e) $\frac{-7}{-18}$

(f) $\frac{0}{3}$

(g) $\frac{5}{0}$

(h) $\frac{0}{0}$

Sol :

(g) $\frac{5}{0}$ and (h) $\frac{0}{0}$ are not rational numbers

Question 2

Express the following in the form p/q

(a) 4

Sol : $\frac{4}{1}$

(b) $2 \frac{1}{5}$

Sol : $\frac{11}{5}$

(c) -8

Sol : $\frac{-8}{1}$

(d) $-2\frac{3}{7}$

Sol :  $\frac{-17}{11}$

(e) $\frac{0}{1}$

Question 3

Are the rational numbers $\frac{2}{3}, \frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{-10}{-15}, \frac{-42}{-63}$ equivalent?

Sol :

Yes, there rational numbers are equivalent

Question 4

Is the number $\frac{17}{40}$ equivalent to $\frac{-34}{80}$ or $\frac{34}{-80}$?

Sol :

No, $\frac{17}{40}$ is not equivalent to $\frac{-34}{80}$ or $\frac{34}{-80}$

Question 5

Write the following rational numbers in standard form.

(a) $\frac{20}{35}$

Sol : $\frac{4}{7}$

(b) $\frac{-18}{30}$

Sol : $\frac{-3}{5}$

(c) $\frac{190}{-76}$

Sol : $\frac{5}{-2}$

(d) $\frac{-110}{-132}$

Sol : $\frac{5}{6}$

Question 6

Identify the positive and negative rational numbers.

(a) $\frac{5}{13}$

(b) $\frac{11}{-18}$

(c) $\frac{-23}{70}$

(d) $\frac{-15}{-8}$

(e) 0

(f) 7

(g) 7

(h) -12

Sol : 

Positive $\frac{5}{13}, \frac{-15}{-8}, 7$

Negative $\frac{11}{-18}, \frac{-23}{70}, -12$

0 is neither positive nor negative 

Question 7

Write four rational numbers equivalent to each of the following rational numbers.

(a) $\frac{3}{5}$

Sol : $\frac{3}{5}=\frac{6}{10}=\frac{9}{15}=\frac{12}{20}=\frac{15}{25}$

(b) $\frac{-6}{7}$

Sol : $\frac{-6}{7}=\frac{-12}{14}=\frac{-18}{21}=\frac{-24}{28}=\frac{-30}{35}$

(c) $\frac{8}{-9}$

Sol : $\frac{8}{-9}=\frac{16}{-18}=\frac{24}{-27}=\frac{32}{-36}=\frac{40}{-45}$

(d) 2

Sol : $\frac{2}{1}=\frac{4}{2}=\frac{6}{3}=\frac{8}{4}=\frac{10}{5}$

(e) -1

Sol :

$\frac{-1}{1}=\frac{-2}{2}=\frac{-3}{3}=\frac{-4}{4}=\frac{-5}{5}$

Question 8

Express:

(a) $\frac{2}{5}$ as a rational number with denominator 35.

Sol :

$\frac{2}{5}=\frac{2\times 7}{5\times 7}=\frac{14}{35}$

(b) $\frac{-8}{11}$ as a rational number with (i) numerator 16, (ii) denominator 33

Sol : 

$\frac{-8}{11}=\frac{-8 \times -2}{11 \times -2}=\frac{16}{-22}$

$\frac{-8}{11}=\frac{-8 \times 3}{11 \times 3}=\frac{-24}{33}$

(c) $\frac{19}{-5}$ as a rational number with (i) numerator 57, (ii) denominator 20

Sol :

$\frac{19}{-5}=\frac{19\times 3}{-5\times 3}=\frac{57}{-15}$

$\frac{19}{-5}=\frac{19\times -4}{-5 \times -4}=\frac{-76}{20}$

Question 9

Find x so that

(a) $\frac{-2}{15}=\frac{16}{x}$

Sol :

$x=\frac{16\times 15}{-2}$

x=-120

(b) $\frac{8}{-3}=\frac{x}{9}$

Sol :

$x=\frac{8\times 9}{-3}$

x=-24

(c) $\frac{-35}{x}-5$

Sol :

$x=\frac{-35}{-5}$

x=7

Question 10

Which of the following rational numbers are equivalent?

(a) $\frac{5}{8}$ and $\frac{10}{16}$

Sol : are equivalent 

(b) $\frac{-6}{15}$ and $\frac{14}{-35}$

Sol : are equivalent 

(c) $\frac{-9}{-27}$ and $\frac{-3}{8}$

Sol : are not equivalent