The main objective of providing exercise-wise solutions in PDF is to help students boost their exam preparation. The solutions are designed based on the latest CBSE syllabus and exam pattern. Students can refer to and download the RD Sharma Solutions for Class 7 Chapter 5 Operations on Rational Numbers Exercise 5.1 from the link provided here. Our subject experts formulate these exercises to help students with their exam preparation to achieve good marks in Maths. This exercise contains four questions with many sub-questions, and all are based on basic concepts related to operations on rational numbers. By practising RD Sharma Solutions for Class 7, students will be able to grasp the concepts effortlessly.
RD Sharma Solutions for Class 7 Maths Chapter 5 – Operations on Rational Numbers Exercise 5.1
Access answers to Maths RD Sharma Solutions for Class 7 Chapter 5 – Operations on Rational Numbers Exercise 5.1
1. Add the following rational numbers:
(i) (-5/7) and (3/7)
(ii) (-15/4) and (7/4)
(iii) (-8/11) and (-4/11)
(iv) (6/13) and (-9/13)
Solution:
(i) Given (-5/7) and (3/7)
= (-5/7) + (3/7)
Here denominators are same so add the numerator
= ((-5+3)/7)
= (-2/7)
(ii) Given (-15/4) and (7/4)
= (-15/4) + (7/4)
Here denominators are same so add the numerator
= ((-15 + 7)/4)
= (-8/4)
On simplifying
= -2
(iii) Given (-8/11) and (-4/11)
= (-8/11) + (-4/11)
Here denominators are same so add the numerator
= (-8 + (-4))/11
= (-12/11)
(iv) Given (6/13) and (-9/13)
= (6/13) + (-9/13)
Here denominators are same so add the numerator
= (6 + (-9))/13
= (-3/13)
2. Add the following rational numbers:
(i) (3/4) and (-3/5)
(ii) -3 and (3/5)
(iii) (-7/27) and (11/18)
(iv) (31/-4) and (-5/8)
Solution:
(i) Given (3/4) and (-3/5)
If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then
(p/q) + (r/s) = (p × s + r × q)/ (q × s)
(3/4) + (-3/5) = (3 × 5 + (-3) × 4)/ (4 × 5)
= (15 – 12)/ 20
= (3/20)
(ii) Given -3 and (3/5)
If p/q and r/s are two rational numbers such that q and s do not have a common factor other than one, then
(p/q) + (r/s) = (p × s + r × q)/ (q × s)
(-3/1) + (3/5) = (-3 × 5 + 3 × 1)/ (1 × 5)
= (-15 + 3)/ 5
= (-12/5)
(iii) Given (-7/27) and (11/18)
LCM of 27 and 18 is 54
(-7/27) = (-7/27) × (2/2) = (-14/54)
(11/18) = (11/18) × (3/3) = (33/54)
(-7/27) + (11/18) = (-14 + 33)/54
= (19/54)
(iv) Given (31/-4) and (-5/8)
LCM of -4 and 8 is 8
(31/-4) = (31/-4) × (2/2) = (62/-8)
(31/-4) + (-5/8) = (-62 – 5)/8
= (-67/8)
3. Simplify:
(i) (8/9) + (-11/6)
(ii) (-5/16) + (7/24)
(iii) (1/-12) + (2/-15)
(iv) (-8/19) + (-4/57)
Solution:
(i) Given (8/9) + (-11/6)
The LCM of 9 and 6 is 18
(8/9) = (8/9) × (2/2) = (16/18)
(-11/6) = (-11/6) × (3/3) = (-33/18)
= (16 – 33)/18
= (-17/18)
(ii) Given (-5/16) + (7/24)
The LCM of 16 and 24 is 48
Now (-5/16) = (-5/16) × (3/3) = (-15/48)
Consider (7/24) = (7/24) × (2/2) = (14/48)
(-5/16) + (7/24) = (-15/48) + (14/48)
= (14 – 15) /48
= (-1/48)
(iii) Given (1/-12) + (2/-15)
The LCM of 12 and 15 is 60
Consider (-1/12) = (-1/12) × (5/5) = (-5/60)
Now (2/-15) = (-2/15) × (4/4) = (-8/60)
(1/-12) + (2/-15) = (-5/60) + (-8/60)
= (-5 – 8)/60
= (-13/60)
(iv) Given (-8/19) + (-4/57)
The LCM of 19 and 57 is 57
Consider (-8/57) = (-8/57) × (3/3) = (-24/57)
(-8/19) + (-4/57) = (-24/57) + (-4/57)
= (-24 – 4)/57
= (-28/57)
4. Add and express the sum as mixed fraction:
(i) (-12/5) + (43/10)
(ii) (24/7) + (-11/4)
(iii) (-31/6) + (-27/8)
Solution:
(i) Given (-12/5) + (43/10)
The LCM of 5 and 10 is 10
Consider (-12/5) = (-12/5) × (2/2) = (-24/10)
(-12/5) + (43/10) = (-24/10) + (43/10)
= (-24 + 43)/10
= (19/10)
Now converting it into mixed fraction
=
(ii) Given (24/7) + (-11/4)
The LCM of 7 and 4 is 28
Consider (24/7) = (24/7) × (4/4) = (96/28)
Again (-11/4) = (-11/4) × (7/7) = (-77/28)
(24/7) + (-11/4) = (96/28) + (-77/28)
= (96 – 77)/28
= (19/28)
(iii) Given (-31/6) + (-27/8)
The LCM of 6 and 8 is 24
Consider (-31/6) = (-31/6) × (4/4) = (-124/24)
Again (-27/8) = (-27/8) × (3/3) = (-81/24)
(-31/6) + (-27/8) = (-124/24) + (-81/24)
= (-124 – 81)/24
= (-205/24)
Now converting it into mixed fraction
=
RD Sharma Solutions for Class 7 Maths Exercise 5.1 Chapter – 5 Operations on Rational Numbers
RD Sharma Solutions for Class 7 Maths Chapter 5 Operations on Rational Numbers Exercise 5.1 have problems that are based on the addition of rational numbers. Some of the topics focused on prior to Exercise 5.1 are listed below.
- Addition of rational numbers
- Rational numbers with the same denominator
- Rational numbers with distinct denominators
Comments