# RD Sharma Solutions Class 7 Rational Numbers Exercise 4.3

## RD Sharma Solutions Class 7 Chapter 4 Exercise 4.3

### RD Sharma Class 7 Solutions Chapter 4 Ex 4.3 PDF Free Download

#### Exercise 4.3

Q 1 . Determine whether the following rational numbers are in the lowest form or not :

(i) $\frac{65}{84}$

(ii) $\frac{-15}{32}$

(iii) $\frac{24}{128}$

(iv) $\frac{-56}{-32}$

SOLUTION :

(i) We observe that 65 and 84 have no common factor their HCF is 1 .

Thus , 65/84 is in its lowest form .

(ii) We observe that -15 and 32 have no common factor i.e., their HCF is 1 .

Thus , -15/32 is in its lowest form .

(iii) HCF of 24 and 128 is not 1 .

Thus , given rational number is not in its simplest form .

(iv) HCF of 56 and 32 is 8 .

Thus , given rational number is not in its simplest form .

Q 2 . Express each of the following numbers to the lowest form :

(i) $\frac{4}{22}$

(ii) $\frac{-36}{180}$

(iii) $\frac{132}{428}$

(iv)  $\frac{-32}{-56}$

SOLUTION :

Lowest form of :

(i)  4/22 is :

4 = 2×2 ,22 = 2×11

HCF of 4 and 22 is 2 .

Dividing the fraction by 2 , we get 2/11.

(ii) -36/180 is :

36 = 3x3x2x2 , 180 = 5x3x3x2x2

HCF of 36 and 180 is 36 .

Dividing the fraction by 36 , we get -1/5 .

(iii) 132/-428 is :

132 = 2x3x2x11 , 428 = 2x2x107

HCF of 132 and 428 is 4 .

Dividing the fraction by 4 , we get 33/-107 .

(iv) -32/-56 is :

32 =2x2x2x2x2 , 56 = 2x2x2x7

HCF of 32 and 56 is 8 .

Dividing the fraction by 8 , we get 4/7 .

Q 3. Fill in the blanks :

(i) $\frac{-5}{7}$ = $\frac{…}{35}$ = $\frac{…}{49}$

(ii) $\frac{-4}{-9}$ = $\frac{…}{18}$ = $\frac{12}{…}$

(iii) $\frac{6}{-13}$ = $\frac{-12}{…}$ = $\frac{24}{…}$

(iv) $\frac{-6}{…}$ = $\frac{3}{11}$ = $\frac{….}{-55}$<

SOLUTION :

(i) Here , (-5×5)/(7×5) = -25/35

Also , (-5×7)/(7×70 = -35/49 .

Therefore , -5/7 = -25/35 = -35/49

(ii) Here, (-4x-2)/(-9x-2) = 8/18

Also , (-4x-3)/(-9x-3) = 12/27

Therefore , -4/-9 = 8/18 = 12/27

(iii) Here , (6x-2)/(-13x-2) = -12/26

Also , (6×4)/(-13×4) = 24/-52

Therefore , 6/-13 = -12/26 = 24/-52

(iv) Here , (-6×2)/(-22×2)  = 3/11

Also , -6/-22 = (3x-5)/(11x-5) = 45/- 55

Therefore , -6/-22 = 3/11 = -15/-55

#### Practise This Question

Which of the following relations in R is an equivalence relatilon?