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) \(\times\)
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 :
\(\frac{7}{1}\)
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 :
\(\frac{-15}{1}\)
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 :
\(\frac{-5}{-7}\)
SOLUTION :
Given rational numbers can be rewritten as :
\(\frac{5}{7}\)
Thus , positive rational numbers are :
\(\frac{5}{7}\)
Negative rational numbers are :
\(\frac{-12}{5}\)
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., \(\frac{9}{8}\)
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) .