Rational Numbers (Exercise 4.6) RD Sharma Solutions | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

 Page 1


 
 
 
 
 
 
Exercise 4.6       page no: 4.26 
 
1. Draw the number line and represent following rational number 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: 
(i) We know that (2/3) is greater than 2 and less than 3. 
? it lies between 2 and 3. It can be represented on number line as, 
 
    
 
(ii) We know that (3/4) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iii) We know that (3/8) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iv) We know that (-5/8) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
Page 2


 
 
 
 
 
 
Exercise 4.6       page no: 4.26 
 
1. Draw the number line and represent following rational number 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: 
(i) We know that (2/3) is greater than 2 and less than 3. 
? it lies between 2 and 3. It can be represented on number line as, 
 
    
 
(ii) We know that (3/4) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iii) We know that (3/8) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iv) We know that (-5/8) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
 
 
 
 
 
 
(v) We know that (-3/16) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
(vi) We know that (-7/3) is greater than -3 and less than -2. 
? it lies between -3 and -2. It can be represented on number line as, 
 
 
(vii) We know that (22/-7) is greater than -4 and less than -3. 
? it lies between -3 and -4. It can be represented on number line as, 
 
 
(Viii) We know that (-31/3) is greater than -11 and less than -10. 
? it lies between -10 and -11. It can be represented on number line as, 
 
 
2. Which of the two rational numbers in each of the following pairs of rational number 
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) 
Page 3


 
 
 
 
 
 
Exercise 4.6       page no: 4.26 
 
1. Draw the number line and represent following rational number 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: 
(i) We know that (2/3) is greater than 2 and less than 3. 
? it lies between 2 and 3. It can be represented on number line as, 
 
    
 
(ii) We know that (3/4) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iii) We know that (3/8) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iv) We know that (-5/8) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
 
 
 
 
 
 
(v) We know that (-3/16) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
(vi) We know that (-7/3) is greater than -3 and less than -2. 
? it lies between -3 and -2. It can be represented on number line as, 
 
 
(vii) We know that (22/-7) is greater than -4 and less than -3. 
? it lies between -3 and -4. It can be represented on number line as, 
 
 
(Viii) We know that (-31/3) is greater than -11 and less than -10. 
? it lies between -10 and -11. It can be represented on number line as, 
 
 
2. Which of the two rational numbers in each of the following pairs of rational number 
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) Given (-3/8), 0 
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)  Given (5/2), 0 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero. Thus, (5/2) > 0 
 
(iii) Given (– 4/11), (3/11) 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero, also the denominator is same in given question 
now we have to compare the numerator, thus - 4/11 < 3/11. 
 
(iv) Given (– 7/12), (5/- 8) 
Consider (– 7/12) 
Multiply both numerator and denominator by 2 then we get 
(-7/12) × (2/2) = (-14/24)…… (1) 
Now consider (5/-8) 
Multiply both numerator and denominator by 3 we get  
(5/-8) × (3/3) = (15/-24)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (– 7/12) > (5/- 8) 
 
(v) Given (4/-9), (– 3/- 7) 
Consider (4/-9) 
Multiply both numerator and denominator by 7 then we get 
(4/-9) × (7/7) = (28/-63)…… (1) 
Now consider (-3/-7) 
Multiply both numerator and denominator by 9 we get  
(-3/-7) × (9/9) = (-27/-63)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (4/-9) < (– 3/- 7) 
Page 4


 
 
 
 
 
 
Exercise 4.6       page no: 4.26 
 
1. Draw the number line and represent following rational number 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: 
(i) We know that (2/3) is greater than 2 and less than 3. 
? it lies between 2 and 3. It can be represented on number line as, 
 
    
 
(ii) We know that (3/4) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iii) We know that (3/8) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iv) We know that (-5/8) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
 
 
 
 
 
 
(v) We know that (-3/16) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
(vi) We know that (-7/3) is greater than -3 and less than -2. 
? it lies between -3 and -2. It can be represented on number line as, 
 
 
(vii) We know that (22/-7) is greater than -4 and less than -3. 
? it lies between -3 and -4. It can be represented on number line as, 
 
 
(Viii) We know that (-31/3) is greater than -11 and less than -10. 
? it lies between -10 and -11. It can be represented on number line as, 
 
 
2. Which of the two rational numbers in each of the following pairs of rational number 
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) Given (-3/8), 0 
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)  Given (5/2), 0 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero. Thus, (5/2) > 0 
 
(iii) Given (– 4/11), (3/11) 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero, also the denominator is same in given question 
now we have to compare the numerator, thus - 4/11 < 3/11. 
 
(iv) Given (– 7/12), (5/- 8) 
Consider (– 7/12) 
Multiply both numerator and denominator by 2 then we get 
(-7/12) × (2/2) = (-14/24)…… (1) 
Now consider (5/-8) 
Multiply both numerator and denominator by 3 we get  
(5/-8) × (3/3) = (15/-24)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (– 7/12) > (5/- 8) 
 
(v) Given (4/-9), (– 3/- 7) 
Consider (4/-9) 
Multiply both numerator and denominator by 7 then we get 
(4/-9) × (7/7) = (28/-63)…… (1) 
Now consider (-3/-7) 
Multiply both numerator and denominator by 9 we get  
(-3/-7) × (9/9) = (-27/-63)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (4/-9) < (– 3/- 7) 
 
 
 
 
 
 
 
(vi) Given (– 5/8), (3/- 4) 
Now consider (3/-4) 
Multiply both numerator and denominator by 2 we get  
(3/-4) × (2/2) = (6/-8) 
The denominator is same in above equation now we have to compare the numerator, 
thus (– 5/8) > (3/- 4) 
 
(vii) Given (5/9), (-3/- 8) 
Consider (5/9)  
Multiply both numerator and denominator by 8 then we get 
(5/9) × (8/8) = (40/72)…… (1) 
Now consider (5/-8) 
Multiply both numerator and denominator by 9 we get  
(-3/-8) × (9/9) = (-27/-72)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (5/9) > (-3/- 8) 
 
(viii) Given (5/- 8), (-7/12) 
Consider (5/-8)  
Multiply both numerator and denominator by 3 then we get 
(5/-8) × (3/3) = (15/-24)…… (1) 
Now consider (-7/12) 
Multiply both numerator and denominator by 2 we get  
(-7/12) × (2/2) = (-14/24)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (5/- 8) < (-7/12) 
 
3. Which of the two rational numbers in each of the following pairs of rational 
numbers is smaller? 
(i) (-6/-13), (7/13) 
(ii) (16/-5), 3 
(iii) (-4/3), (8/-7) 
(iv) (-12/5), (-3) 
 
Solution: 
(i) Given (-6/-13), (7/13) 
Page 5


 
 
 
 
 
 
Exercise 4.6       page no: 4.26 
 
1. Draw the number line and represent following rational number 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: 
(i) We know that (2/3) is greater than 2 and less than 3. 
? it lies between 2 and 3. It can be represented on number line as, 
 
    
 
(ii) We know that (3/4) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iii) We know that (3/8) is greater than 0 and less than 1. 
? it lies between 0 and 1. It can be represented on number line as, 
 
 
(iv) We know that (-5/8) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
 
 
 
 
 
 
(v) We know that (-3/16) is greater than -1 and less than 0. 
? it lies between 0 and -1. It can be represented on number line as, 
 
 
(vi) We know that (-7/3) is greater than -3 and less than -2. 
? it lies between -3 and -2. It can be represented on number line as, 
 
 
(vii) We know that (22/-7) is greater than -4 and less than -3. 
? it lies between -3 and -4. It can be represented on number line as, 
 
 
(Viii) We know that (-31/3) is greater than -11 and less than -10. 
? it lies between -10 and -11. It can be represented on number line as, 
 
 
2. Which of the two rational numbers in each of the following pairs of rational number 
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) Given (-3/8), 0 
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)  Given (5/2), 0 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero. Thus, (5/2) > 0 
 
(iii) Given (– 4/11), (3/11) 
We know that every positive rational number is greater than zero and every negative 
rational number is smaller than zero, also the denominator is same in given question 
now we have to compare the numerator, thus - 4/11 < 3/11. 
 
(iv) Given (– 7/12), (5/- 8) 
Consider (– 7/12) 
Multiply both numerator and denominator by 2 then we get 
(-7/12) × (2/2) = (-14/24)…… (1) 
Now consider (5/-8) 
Multiply both numerator and denominator by 3 we get  
(5/-8) × (3/3) = (15/-24)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (– 7/12) > (5/- 8) 
 
(v) Given (4/-9), (– 3/- 7) 
Consider (4/-9) 
Multiply both numerator and denominator by 7 then we get 
(4/-9) × (7/7) = (28/-63)…… (1) 
Now consider (-3/-7) 
Multiply both numerator and denominator by 9 we get  
(-3/-7) × (9/9) = (-27/-63)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (4/-9) < (– 3/- 7) 
 
 
 
 
 
 
 
(vi) Given (– 5/8), (3/- 4) 
Now consider (3/-4) 
Multiply both numerator and denominator by 2 we get  
(3/-4) × (2/2) = (6/-8) 
The denominator is same in above equation now we have to compare the numerator, 
thus (– 5/8) > (3/- 4) 
 
(vii) Given (5/9), (-3/- 8) 
Consider (5/9)  
Multiply both numerator and denominator by 8 then we get 
(5/9) × (8/8) = (40/72)…… (1) 
Now consider (5/-8) 
Multiply both numerator and denominator by 9 we get  
(-3/-8) × (9/9) = (-27/-72)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (5/9) > (-3/- 8) 
 
(viii) Given (5/- 8), (-7/12) 
Consider (5/-8)  
Multiply both numerator and denominator by 3 then we get 
(5/-8) × (3/3) = (15/-24)…… (1) 
Now consider (-7/12) 
Multiply both numerator and denominator by 2 we get  
(-7/12) × (2/2) = (-14/24)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (5/- 8) < (-7/12) 
 
3. Which of the two rational numbers in each of the following pairs of rational 
numbers is smaller? 
(i) (-6/-13), (7/13) 
(ii) (16/-5), 3 
(iii) (-4/3), (8/-7) 
(iv) (-12/5), (-3) 
 
Solution: 
(i) Given (-6/-13), (7/13) 
 
 
 
 
 
 
Here denominator is same therefore compare the numerator, 
Thus (-6/-13) < (7/13) 
 
(ii) Given (16/-5), 3 
We know that 3 is a whole number with positive sign 
Therefore (16/-5) < 3 
 
(iii) Given (-4/3), (8/-7) 
Consider (-4/3)  
Multiply both numerator and denominator by 7 then we get 
(-4/3) × (7/7) = (-28/21)…… (1) 
Now consider (8/-7) 
Multiply both numerator and denominator by 3 we get  
(8/-7) × (3/3) = (-24/21)…… (2) 
The denominator is same in equation (1) and (2) now we have to compare the 
numerator, thus (-4/3) < (8/-7) 
 
(iv) Given (-12/5), (-3) 
Now consider (-3/1) 
Multiply both numerator and denominator by 5 we get  
(-3/1) × (5/5) = (-15/5) 
The denominator is same in above equation, now we have to compare the numerator, 
thus (-12/5) > (-3) 
 
4. Fill in the blanks by the correct symbol out of >, =, or <: 
(i) (-6/7) …. (7/13) 
(ii) (-3/5) …. (-5/6) 
(iii) (-2/3) …. (5/-8) 
(iv) 0 …. (-2/5) 
 
Solution: 
(i) (- 6/7) < (7/13) 
 
Explanation: 
Because every positive number is greater than a negative number. 
 
(ii) (-3/5) > (-5/6)