RD Sharma solution class 7 chapter 4 Rational numbers Exercise 4.1

Exercise 4.1

Page-4.3

Question 1:

Write down the numerator of each of the following rational numbers:
(i) $\frac{-7}{5}$
(ii) $\frac{15}{-4}$
(iii) $\frac{-17}{-21}$
(iv) $\frac{8}{9}$
(v) 5

Answer 1:

Numerators are:
(i) $-$7
(ii) 15
(iii) $-$17
(iv) 8
(v) 5

Question 2:

Write down the denominator of each of the following rational numbers:
(i) $\frac{-4}{5}$
(ii) $\frac{11}{-34}$
(iii) $\frac{-15}{-82}$
(iv) 15
(v) 0

Answer 2:

Denominators are:
(i) 5
(ii) $-$34
(iii) $-$82
(iv) 1
(v) 1

Question 3:

Write down the rational number whose numerator is (−3) × 4, and whose denominator is (34 − 23) × (7 − 4).

Answer 3:

According to the question:

Numerator = ($-$3) × 4 = $-$12

Denominator = (34 $-$ 23) × (7 $-$ ​4) = 11 × 3 = 33

∴ Rational number = $\frac{-12}{33}$

Question 4:

Write the following rational numbers as integers:
$\frac{7}{1}, \frac{-12}{1}, \frac{34}{1}, \frac{-73}{1}, \frac{95}{1}$

Answer 4:

Integers are 7, $-$12, 34, $-$73 and 95.

Question 5:

Write the following integers as rational numbers with denominator 1:
$-15, 17, 85, -100$

Answer 5:

Rational numbers of given integers with denominator 1 are:

$$\begin{gathered} \frac{-15}{1}, \\ \frac{17}{1}, \\ \frac{85}{1}, \\ \frac{-100}{1} \end{gathered}$$

Question 6:

Write down the rational number whose numerator is the smallest three digit number and denominator is the largest four digit number.

Answer 6:

Smallest three-digit number = 100

Largest four-digit number = 9999

∴ Required rational number = $\frac{100}{9999}$

Question 7:

Separate positive and negative rational numbers from the following rational numbers:

$\frac{-5}{-7}, \frac{12}{-5}, \frac{7}{4}, \frac{13}{-9}, 0, \frac{-18}{-7}, \frac{-95}{116}, \frac{-1}{-9}$

Answer 7:

Given rational numbers can be rewritten as:

$\frac{5}{7}. -\frac{12}{5}, \frac{7}{4}, -\frac{13}{9}, 0 , \frac{18}{7}, -\frac{95}{116}, \frac{1}{9}$

Thus, positive rational numbers are:

$\frac{5}{7}, \frac{7}{4}, \frac{18}{7},\frac{1}{9}$
or, $\frac{-5}{-7}, \frac{7}{4}, 0, \frac{-18}{-7}. \frac{-6}{-9}$

Negative rational numbers are:

$-\frac{12}{5}, -\frac{13}{9}, -\frac{95}{116}$
or, $\frac{12}{-5}, \frac{13}{-9}, \frac{-95}{116}$

Page-4.4

Question 8:

Which of the following rational numbers are positive:
(i) $\frac{-8}{7}$
(ii) $\frac{9}{8}$
(iii) $\frac{-19}{-13}$
(iv) $\frac{-21}{13}$

Answer 8:

The numbers can be rewritten as:

 $$\begin{gathered} \left(i\right) -\frac{8}{7} \\ \left(ii\right) \frac{9}{8} \\ \left(iii\right) \frac{19}{13} \\ \left(iv\right) -\frac{21}{13} \end{gathered}$$

Positive rational numbers are (ii) and (iii), i.e., $\frac{9}{8} \mathrm{and} \frac{-19}{-13}$.

Question 9:

Which of the following rational numbers are negative?
(i) $\frac{-3}{7}$
(ii) $\frac{-5}{-8}$
(iii) $\frac{9}{-83}$
(iv) $\frac{-115}{-197}$

Answer 9:

The  numbers can be rewritten as:
$$\begin{gathered} \left(i\right) -\frac{3}{7} \\ \left(ii\right) \frac{5}{8} \\ \left(iii\right) -\frac{9}{83} \\ \left(iv\right) \frac{115}{197} \end{gathered}$$

Negative rational numbers are (i) and (iii).