RD Sharma Solutions Class 7 Rational Numbers Exercise 4.2

RD Sharma Solutions Class 7 Chapter 4 Exercise 4.2

RD Sharma Class 7 Solutions Chapter 4 Ex 4.2 PDF Free Download

Exercise 4.2

Q 1 . Express each of the following as rational number with positive denominator :

(i) . \(\frac{-15}{-28}\)

(ii) . \(\frac{6}{-9}\)

(iii) . \(\frac{-28}{-11}\)

(iv) . \(\frac{19}{-7}\)

SOLUTION :

Rational number with positive denominators :

(i) Multiplying the number by -1, we get : -15-28 = -15 x -1-28 x-1 = 1528

(ii) Multiplying the number by -1, we get :  6-9 = 6x-1-9x-1 = -69

(iii) Multiplying the number by -1, we get :  -28-11 = -28 x-1-11 x-1=2811

(iv) Multiplying the number by -1, we get : 19-7 = 19 x-1-7 x-1 = -197

Q 2 . Express \(\frac{3}{5}\) as a rational number with numerator :

(i) 6

(ii) -15

(iii) 21

(iv) -27

SOLUTION :

Rational number with numerator :

(i) 6 is :

\(\frac{3\times 2}{5\times 2}\) = \(\frac{6}{10}\) (multiplying numerator and denominator by 2)

(ii) -15 is :

\(\frac{3\times -5}{5\times -5}\) = –\(\frac{-15}{-25}\)  (multiplying numerator and denominator by -5)

(iii) 21 is :

\(\frac{3\times 7}{5\times 7}\)  = \(\frac{21}{35}\)  (multiplying numerator and denominator by 7)

(iv) -27 is :

\(\frac{3\times -9}{5\times -9}\)  = \(\frac{-27}{-45}\) (multiplying numerator and denominator by -9)

Q 3 . Express \(\frac{5}{7}\) as a rational number with denominator :

(i) -14

(ii) 70

(iii) -28

(iv) -84

SOLUTION :

\(\frac{5}{7}\) as a rational number with denominator :

(1) -14 is :

\(\frac{5\times -2}{7\times -2}\)  = \(\frac{-20}{-14}\) (Multiplying numerator and denominator by -2)

(ii) 70 is :

\(\frac{5\times 10}{7\times 10}\)   = \(\frac{50}{70}\) (Multiplying numerator and denominator by 10)

(iii) -28 is :

\(\frac{5\times -4}{7\times -4}\)   = \(\frac{-20}{-28}\) (Multiplying numerator and denominator by -4)

(iv) -84 is :

\(\frac{5\times -12}{7\times -12}\)   = \(\frac{-60}{-84}\) (Multiplying numerator and denominator by -12)

Q 4 . Express \(\frac{3}{4}\) as a rational number with denominator :

(i) 20

(ii) 36

(iii) 44

(iv) -80

SOLUTION :

\(\frac{3}{4}\)  as rational number with denominator:

(i) 20 is :

\(\frac{3\times 5}{4\times 5 }\)   =\(\frac{15}{20}\)  (multiplying numerator and denominator by 5)

(ii) 36 is :

\(\frac{3\times9 }{4\times 9}\)    = \(\frac{27}{36}\)  (multiplying numerator and denominator by 9)

(iii) 44 is :

\(\frac{3\times 11}{4\times 11}\)    = \(\frac{33}{44}\) (multiplying numerator and denominator by 11)

(iv) -80 is :

\(\frac{3\times -20}{4\times -20}\)   = \(\frac{-60}{-80}\) (multiplying numerator and denominator by -20)

Q 5 . Express \(\frac{2}{5}\) as a rational number with numerator :

(i) -56

(ii) 154

(iii) -750

(iv) -80

SOLUTION :

2/5 as a rational number with numerator :

(i) . -56 is :

\(\frac{2\times -28}{5\times-28 }\)    = \(\frac{-56}{-140}\)  (multiplying numerator and denominator by -28)

(ii) 154 is :

\(\frac{2\times 77}{5\times 77}\)    = \(\frac{154}{385}\)  (multiplying numerator and denominator by 77)

(iii) -750 is :

\(\frac{2\times -375}{5\times -375}\)  = \(\frac{-750}{-1875}\) (multiplying numerator and denominator by -375)

(iv) 500 is :

\(\frac{2\times 250}{5\times 250}\)     = \(\frac{500}{1250}\)  (multiplying numerator and denominator by 250)

Q 6 . Express \(\frac{-192}{108}\) as a rational number with numerator :

(i) 64

(ii) -16

(iii) 32

(iv) -48

SOLUTION :

Rational number with numerator :

(i)  64 as numerator :

-192/-3 & 108/-3 =64/-36 (Dividing the numerator and denomintor by -3)

(ii) -16 as numerator :

-192/12 & 108/12 = -16/9 (Dividing the numerator and denomintor by 12)

(iii) 32 as numerator :

-192/-6 & 108/-6 = 32/-18 (Dividing the numerator and denomintor by -6)

(iv) -48 as numerator :

-192/4 & 108/4 = -48/27 (Dividing the numerator and denomintor by 4)

Q 7 .Express \(\frac{168}{-294}\) as a rational number with denominator :

(i) 14

(ii) -7

(iii) -49

(iv) 1470

SOLUTION :

Rational number with denominator:

(i) 14 as denominator :

168/-21 & -294/-21 = -8/14 (Dividing the numerator and denomintor by -21)

(ii) -7 as denominator :

168/42 & -294/42 = 4/-7 (Dividing the numerator and denomintor by 42)

(iii) -49 as denominator :

168/6 & -294/6 = 28/-49 (Dividing the numerator and denomintor by 6)

(iv) 1470 as denominator :

\(\frac{168\times -5}{-294\times -5}\)  = -840/1470 (Multiplying the numerator and denomintor by -5)

Q 8 . Write \(\frac{-14}{42}\) in a form so that numerator is equal to :

(i) -2

(ii)  7

(iii) 42

(iv) -70

SOLUTION :

Rational number with numerator :

(i) -2 is :

-14/7 & 42/7 = -26 ( Dividing numerator and denominator by 7)

(ii) 7 is :

-14/-2 & 42/-2 = 7/-21 ( Dividing numerator and denominator by -2)

(iii) 42 is :

-14x-3 & 42x-3 = 42/-126 ( Multiplying numerator and denominator by -3)

(iv) -70 is :

-14×5 & 42×5 = -70/210 ( Multiplying numerator and denominator by 5)

Q 9 . Select those rational numbers which can be written as a rational number with numerator 6 :

\(\frac{1}{22}\) , \(\frac{2}{3}\) , \(\frac{3}{4}\) , \(\frac{4}{-5}\) , \(\frac{5}{6}\) , \(\frac{-6}{7}\) , \(\frac{-7}{8}\)

SOLUTION :

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

Q  10 . Select those rational numbers which can be written as a rational number with denominator 4 :

\(\frac{7}{8}\) , \(\frac{64}{16}\) , \(\frac{36}{-12}\) , \(\frac{-16}{17}\) , \(\frac{5}{-4}\) , \(\frac{-140}{28}\).

SOLUTION :

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

Q 11 . In each of the following , find an equivalent form of the rational number having common denominator :

(i) \(\frac{3}{4}\) and \(\frac{5}{12}\)

(ii) \(\frac{2}{3}\) , \(\frac{7}{6}\) and \(\frac{11}{12}\)

(iii) \(\frac{5}{7}\) , \(\frac{3}{8}\) , \(\frac{9}{14}\) and \(\frac{20}{21}\)<

SOLUTION :

Equivalent forms of the rational number having common denominator are :

(i) 3/4 = (3×3)/(4×3) = 9/12 and 512.

(ii) 2/3 = (2×4)/(3×4) = 8/12 and 7/6 = (7×2)/(6×2) = 14/12 and 11/12

Forms are 8/12 , 14/12 and 11/12

(iii) 5/7 = (5×24)/(7×24) = 120/168 , 3/8 = (3×21)/(8×21) = 63/168 , 9/14 = (9×12)/(14×12) = 108/168 and 20/21 = (20×8)/(21×8) = 160/168

Forms are 120/168 , 63/168 , 108/168 and 160/168.

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