RD Sharma Solutions Class 7 Rational Numbers Exercise 4.1

Exercise 4.1

Q 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

SOLUTION :

Numerators are :

(i). -7

(ii) . 15

(iii) . -17

(iv) . 8

(v) . 5

Q 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

SOLUTION :

Denominators are :

(i) . 5

(ii) . -34

(iii). -82

(iv). 1

(v). 1

Q 3 . Write down the rational number whose numerator is (-3) \(\times\)4 , and whose denominator is (34 – 23) \(\times\)(7 – 4).

SOLUTION :

According to the question :

Numerator = (-3) x 4 = -12

Denominator = (34 – 23) x (7 – 4) = 11 x 3 = 33

Therefore , Rational number = \(\frac{-12}{32}\)

Q 4 .Write the following rational numbers as integers :

\(\frac{7}{1}\) , \(\frac{-12}{1}\) , \(\frac{34}{1}\) , \(\frac{-73}{1}\) , \(\frac{95}{1}\)

SOLUTION :

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

Q 5 .Write the following integers as rational numbers with denominator 1 :

-15 , 17 , 85 , -100

SOLUTION :

Rational numbers of given integers with denominator 1 are :

\(\frac{-15}{1}\) , \(\frac{17}{1}\) , \(\frac{85}{1}\) , \(\frac{-100}{1}\)

Q 6 .Write down the rational whose numerator is the smallest three digit number and denominator is the largest four digit number .

SOLUTION :

Smallest three digit number = 100

Largest four digit number = 9999

Therefore rational number = \(\frac{100}{9999}\)

Q 7 .Seperate positive and negative rational numbers from the following rational numbers :

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

SOLUTION :

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 :

\(\frac{5}{7}\) , \(\frac{7}{4}\)  , \(\frac{18}{7}\) , \(\frac{1}{9}\)

Negative rational numbers are :

\(\frac{-12}{5}\) , \(\frac{-13}{9}\) , \(\frac{-95}{116}\)

Q 8 .Which of the following rational numbers are positive :

(i) .\(\frac{-8}{7}\)

(ii) . \(\frac{9}{8}\)

(iii) . \(\frac{-19}{-13}\)

(iv) . \(\frac{-21}{13}\)

SOLUTION :

The numbers can be rewritten as :

(i) . \(\frac{-8}{7}\)

(ii) .\(\frac{9}{8}\)

(iii) . \(\frac{19}{13}\)

(iv) . \(\frac{-21}{13}\)

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

Q 9 .Which of the following rational numbers are negative ?

(i) . \(\frac{-3}{7}\)

(ii) . \(\frac{-5}{-8}\)

(iii) . \(\frac{9}{-83}\)

(iv) . \(\frac{-115}{-197}\)

SOLUTION :

The numbers can be rewritten as :

(i) . \(\frac{-3}{7}\)

(ii) . \(\frac{5}{8}\)

(iii) . \(\frac{-9}{83}\)

(iv) . \(\frac{115}{197}\)

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