RD Sharma Solutions Class 7 Rational Numbers Exercise 4.6

RD Sharma Solutions Class 7 Chapter 4 Exercise 4.6

RD Sharma Class 7 Solutions Chapter 4 Ex 4.6 PDF Free Download

Exercise 4.6

Q 1 . Draw the number line and represent the following rational numbers on it :

(i) 2/3

(ii) 3/4

(iii) 3/8

(iv) -5/8

(v) -3/16

(vi) -7/3

(vii) 22/-7

(viii) -31/3

SOLUTION :

Q 2 . Which of the two rational numbers in each of the following pairs of rational numbers is greater ?

(i) -3/8 , 0

(ii) 5/2 , 0

(iii) -4/11 , 3/11

(iv) -7/12 , 5/-8

(v) 4/9 , -3/-7

(vi) -5/8 , 3/-4

(vii) 5/9 , -3/-8

(viii) 5/-8 , -7/12

SOLUTION :

(i) We know that every positive rational number is greater than zero and every negative rational number is smaller than zero . Thus , -3/8>0

(ii) 5/2>0 . Because every positive rational number is greater than zero and every negative rational number is smaller than zero .

(iii) -4/11<3/11. Because every positive rational number is greater than zero and every negative rational number is smaller than zero .

(iv) -7/12 = (-7×2)/(12×2) = -14/24 and 5/-8 = (-5×3)/(8×3) = -15/24

Therefore -7/12>5/-8

(v) 4/-9 = (-4×7)/(9×7) = -28/63 and -3/-7 = (3×7)/(7×9) = 21/63

Therefore , 4/-9<-3/-7

(vi) -5/8 and 3/-4 = (-3×2)/(4×2) = -6/8

Therefore , -5/8>3/-4

(vii) 5/9 = (5×8)/(9×8) = 40/72 and -3/-8 = (3×9)/(8×9) = 27/72

Therefore , 5/9>-3/-8

(viii) -7/12 = (-7×2)/(12×2) = -14/24 and 5/-8 = (-5×3)/(8×3) = -15/24

Therefore , 7/12 >5/-8

Q 3. Fill in the blanks by the correct symbol out > , = , or < :

(i) $\frac{-6}{-13}$ , $\frac{7}{13}$

(ii) $\frac{16}{-5}$ , 3

(iii) $\frac{-4}{3}$ , $\frac{8}{-7}$

(iv) $\frac{-12}{5}$ , -3

SOLUTION :

(i)-6/-13 = 6/13<7/13

(ii) 16/-5<3

(iii) -4/3 = (-4×7)/(3×7) = -28/21 and 8/-7 = (-8×3)/(7×3) = -24/21

Therefore , -4/3<8/-7

(iv) -12/5 and -3 = (-3×5)/(1×5) = -15/5

Therefore -12/5>-3

Q 4 .Fill in the blanks by the correct symbol out of >, = , or < :

(i) $\frac{6}{7}….\frac{7}{13}$

(ii) $\frac{-3}{5}….\frac{-5}{6}$

(iii) $\frac{2}{3}….\frac{5}{-8}$

(iv) $0….\frac{-2}{5}$

SOLUTION :

(i) Because every positive number is greater than a negative number , -6/7<7/13 .

(ii) On multiplying -3/5 by 6/6 , we get -18/30 .

On multiplying -5/6 by 5/5 , we get -25/30 .

Because -18> -25 , -35>-56

(iii) On multiplying -2/3 by 8/8 , we get -16/24 .

On multiplying 5/-8 by 3/3 , we get 15/-24 = -15/24 .

Because -15 >-16 , -2/3<5/-8.

(iv) Because every positive number is greater than a negative number , 0>-2/5 .

Q 5 . Arrange the following rational numbers in ascending order :

(i) $\frac{3}{5}$ , $\frac{-17}{-30}$ , $\frac{8}{-15}$ , $\frac{-7}{10}$

(ii) $\frac{-4}{9}$ , $\frac{5}{-12}$ , $\frac{7}{-18}$ , $\frac{2}{-3}$

SOLUTION :

(i) Ascending order:

Since , LCM of 5 , -30 , -15 , 10 is 30 .

Multiplying the numerators and denominators to get the denominator equal to the LCM 3/5 = (3×6)/(5×6) = 18/30 , 17/30 = (17×1)/(30×1) = 17/30 , 8/- 15 = (-8×2)/(15×2) = -16/30 , -7/10 = (-7×3)/(10×3) = -21/30 .

0rder is -21 <-16<17<8 .

0rder is -7/10<8/-15<17/30<3/5.

(ii) Since , LCM of 9 , -12 , -18 , 3 is 36 .

Multiplying the numerators and denominators to get the denominator to get the denominator equal to the LCM ,

-4/9 = (-4×4)/(9×4) = -16/36 , 5/-12 = (-5×3)/(12×3) = -15/36 , 7/-18 = (-7×2)/(8×2) = -14/36 , 2/-3 = (-2×12)/(3×12) = -24/36 .

0rder is -24 <-16<-15<-14.0rder is 2/-3<-4/9<5/-12<7/-18.

Q 6 . Arrange the following rational numbers in descending order :

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

(ii) $\frac{-3}{10}$ , $\frac{17}{-30}$ , $\frac{7}{-15}$ , $\frac{-11}{20}$

SOLUTION :

We have to arrange them in descending order.

(i) Since , LCM of 8 , 16 , -12 , -4 , 28 is 336 .

Multiplying the numerators and denominators , to get the denominator equal to the LCM , 7/8 = (7×42)/(8×42) = 294/336 , 64/16 = (64×21)/(16×21) = 1344/336 , 36/-12 = (-36×28)/(12×28) = -1008/336 , 5/- 4 = (-5×84)/(4×84) = -420/336 , 140/28 = (140×12)/(28×12) = 1680/336 .

Order is 1680> 1344 >294 >-420>-1008.Order is 4>36-12.

Order is 140/28> 64/16>7/8>5/-4>36/-12

(ii) Since , LCM of 10 , -30 , -15 , 20 is 60 .

Multiplying the numerators and denominators , to get the denominator equal to LCM ,

-3/10 = (-3×6)/(10×6) = -18/60 , 17/-30 = (-17×2)/(30×2) = -34/60 , 7/- 15 = (-7×4)/(15×4) = -28/60 , -11/20 = (-11×3)/(20×3) = -33/60 .

Order is, -18>-28>-33>-34.

Order is -3/10>7/-15>-11/20>17/-30.

Q 7 . Which of the following statements are true :

(i) The rational number $\frac{29}{23}$ lies to the left of zero on the number line .

(ii) The rational number $\frac{-12}{-17}$ lies to the left of zero on the number line .

(iii) The rational number $\frac{3}{4}$ lies to the right of zero on the number line .

(iv) The rational number $\frac{-12}{-5}$ and $\frac{-7}{-17}$ are on the opposite side of zero on the number line .

(v) The rational number $\frac{-21}{5}$ and $\frac{7}{-31}$ are on the opposite side of zero on the number line .

(vi) The rational number $\frac{-3}{-5}$ is on the right of $\frac{-4}{7}$ on the number line .

SOLUTION :

(i) False ; it lies to the right of zero because it is a positive number .

(ii) False ; it lies to the right of zero because it is a positive number .

(iii) True

(iv) True ; they are of opposite signs .

(v) False ; they both are of same signs .

(vi) True ; they both are of opposite signs and positive number is greater than the negative number. Thus , it is on the right of the negative number .