Ex - 4.2, Rational Numbers, Class 7, Math RD Sharma Solutions | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

Express each of the following as a rational number with positive denominator:

Answer 1:

Rational number with positive denominators:

(i) Multiplying the number by −-1, we get:

(ii) Multiplying the number by −-1, we get: 

(iii) Multiplying the number by −-1, we get:

(iv) Multiplying the number by −-1, we get:

Question 2:

Express 3/5 as a rational number with numerator:
(i) 6
(ii) −15
(iii) 21
(iv) −27

Answer 2:

Rational number with numerator:

(i) 6 is:

(multiplying numerator and denominator by 2 )

(ii)

(multiplying numerator and denominator by -5)

(iii)

(multiplying numerator and denominator by 7)

(iv)

(multiplying numerator and denominator by -9)

Question 3:

Express 5757 as a rational number with denominator:
(i) −14
(ii) 70
(iii) −28
(iv) −84

Answer 3:

5/7 as a rational number with denominator:
(i) −14 is:

  (multiplying numerator and denominator by -2)

(ii) 70 is :

 (multiplying numerator and denominator by 10)

(iii) −28 is:

 (multiplying numerator and denominator by -4)

(iv) −84 is:

(multiplying numerator and denominator by -12)

Question 4:

Express 3/4 as a rational number with denominator:
(i) 20
(ii) 36
(iii) 44
(iv) −80

Answer 4:

3/4 as rational number with denominator:

(i)
20 is:

 (multiplying numerator and denominator by 5)

(ii)
36 is:

(multiplying numerator and denominator by 9)

(iii)
44 is:

 (multiplying numerator and denominator by 11)

(iv)
−80 is:

 (multiplying numerator and denominator by -20)

Question 5:

Express 2/5 as a rational number with numerator:
(i) −56
(ii) 154
(iii) −750
(iv) 500

Answer 5:

2/5 as a rational number with numerator:

(i)
−56 is:

 (multiplying numerator and denominator by -28)

(ii)
154 is:

 (multiplying numerator and denominator by 77)

(iii)
−750 is:

(multiplying numerator and denominator by -375)

(iv)
500 is:

 (multiplying numerator and denominator by 250)

Question 6:

Express −192/108 as a rational number with numerator:
(i) 64
(ii) −16
(iii) 32
(iv) −48

Answer 6:

Rational number with numerator:

(i) (Dividing the numerator and denomintor by −3)

(ii) (Dividing the numerator and denomintor by 12)

(iii)  (Dividing the numerator and denomintor by −6)

(iv)  (Dividing the numerator and denomintor by 4)

Question 7:

Express 168 / −294 as a rational number with denominator:
(i) 14
(ii) −7
(iii) −49
(iv) 1470

Answer 7:

Rational number with denominator:

(i)  (Dividing the numerator and denomintor by −21)

(ii)  (Dividing the numerator and denomintor by 42)

(iii)  (Dividing the numerator and denomintor by 6)

(iv)  (Dividing the numerator and denomintor by −5)

Question 8:

Write −14/42 in a form so that the numerator is equal to:
(i) −2
(ii) 7
(iii) 42
(iv) −70

Answer 8:

Rational number with numerator:

(i)   ( Dividing numerator and denominator by 7)

(ii)   ( Dividing numerator and denominator by -2)

(iii)   ( Dividing numerator and denominator by -3)

(iv)   ( Dividing numerator and denominator by 5)

Question 9:

Select those rational numbers which can be written as a rational number with numerator 6:

Answer 9:

Given rational numbers that can be written as a rational number with numerator 6 are:

1/22 (On multiplying by 6) = 6/132

2/3 (On multiplying by 3) = 6/9

3/4 (On multiplying by 2) = 6/8

−6/7 (On multiplying by −1) = 6/−7

Question 10:

Select those rational numbers which can be written as a rational number with denominator 4:

Answer 10:

Given rational numbers that can be written as a rational number with denominator 4 are:

7/8 (On dividing by 2) = 3.5/4

64/16 (On dividing by 4) =16/4

36/−12(On dividing by 3) =12/−4 = −12/4

−16/17 can't be expressed with a denominator 4.

5/−4(On multiplying by −1) =−5/4

140/28(On dividing by 7) =20/4

Question 11:

In each of the following, find an equivalent form of the rational number having a common denominator:

Answer 11:

Equivalent forms of the rational number having common denominator are:

(ii) 

(iii)

Forms are