Open App

Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1)

Operations On Rational Numbers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


 
 
 
 
 
 
 
Exercise 5.1         Page No: 5.4 
 
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) 
Page 2


 
 
 
 
 
 
 
Exercise 5.1         Page No: 5.4 
 
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) 
Page 3


 
 
 
 
 
 
 
Exercise 5.1         Page No: 5.4 
 
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)
Page 4


 
 
 
 
 
 
 
Exercise 5.1         Page No: 5.4 
 
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
= 1 9/10
(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
= -8 13/24

	Mathematics (Maths) Class 7 76 videos\|344 docs\|39 tests

Mathematics (Maths) Class 7

76 videos|344 docs|39 tests

Join Course for Free

Top Courses for Class 7

View all

Related Exams

Class 7

About this Document

	4.98/5 Rating
	Dec 22, 2024 Last updated

Document Description: RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) for Class 7 2024 is part of Mathematics (Maths) Class 7 preparation. The notes and questions for RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) have been prepared according to the Class 7 exam syllabus. Information about RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) covers topics like and RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Example, for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1).

Introduction of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) in English is available as part of our Mathematics (Maths) Class 7 for Class 7 & RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) in Hindi for Mathematics (Maths) Class 7 course. Download more important topics related with notes, lectures and mock test series for Class 7 Exam by signing up for free. Class 7: Operations On Rational Numbers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 7

Description

Full syllabus notes, lecture & questions for Operations On Rational Numbers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 7 - Class 7 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 7 | Best notes, free PDF download

Information about RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1)

In this doc you can find the meaning of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) defined & explained in the simplest way possible. Besides explaining types of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) tests, examples and also practice Class 7 tests

	Mathematics (Maths) Class 7 76 videos\|344 docs\|39 tests

Mathematics (Maths) Class 7

76 videos|344 docs|39 tests

Join Course for Free

Download as PDF

Explore Courses for Class 7 exam

Top Courses for Class 7

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Semester Notes

Previous Year Questions with Solutions

Summary

mock tests for examination

Free

study material

video lectures

pdf

Objective type Questions

Operations On Rational Numbers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 7

Important questions

shortcuts and tricks

practice quizzes

Extra Questions

Viva Questions

Operations On Rational Numbers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 7

MCQs

past year papers

Exam

ppt

Sample Paper

;

Additional Information about RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) for Class 7 Preparation

RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Free PDF Download

The RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) is an invaluable resource that delves deep into the core of the Class 7 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) now and kickstart your journey towards success in the Class 7 exam.

Importance of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1)

The importance of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) cannot be overstated, especially for Class 7 aspirants. This document holds the key to success in the Class 7 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Notes

RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1). It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Notes on EduRev are your ultimate resource for success.

RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Class 7 Questions

The "RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) on the App

Students of Class 7 can study RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1), students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.1) is prepared as per the latest Class 7 syllabus.

Education Revolution