RD Sharma Solutions for Class 6 Maths Chapter 5 Exercise 5.1: Chapter 5 of RD Sharma Class 6 Maths introduces students to the concept of negative numbers and integers, which are crucial for understanding higher-level arithmetic and algebra. Exercise 5.1 covers basic identification, representation on the number line, and comparison of integers.
These concepts align well with the exam pattern and are frequently tested in school assessments. Referring to this exercise helps students strengthen their foundation as per the latest syllabus. Solving RD Sharma and previous year papers ensures better practice, conceptual clarity, and improved exam performance.
What is Covered in Exercise 5.1?
Exercise 5.1 introduces students to the basics of integers, especially focusing on negative numbers. Here’s a detailed breakdown of what is covered:
-
Introduction to Integers
-
Understanding the concept of positive and negative numbers.
-
Real-life examples where negative numbers are used (e.g., temperature, debts, sea level).
-
Number Line Representation
-
Placement of integers (both positive and negative) on a number line.
-
Understanding the position of 0 as the origin or central point.
-
Movement to the right (positive integers) and left (negative integers).
-
Comparing Integers
-
Identifying which integer is greater or smaller.
-
Rules for comparison (e.g., numbers to the right on the number line are always greater).
-
Use of inequality signs (<, >, =) to compare numbers.
-
Ascending and Descending Order
-
Opposite of a Number
-
Understanding the concept of additive inverses (e.g., opposite of +5 is -5).
-
Identifying the opposite of given numbers.
-
Simple Conceptual Questions
RD Sharma Solutions for Class 6 Chapter Negative Numbers and Integers Exercise 5.1
Below are the detailed solutions for RD Sharma Class 6 Maths Chapter 5 Exercise 5.1. These step-by-step answers help students understand the basics of negative numbers and integers clearly. The solutions are aligned with the latest syllabus and exam pattern, making them ideal for thorough practice and revision.
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:
(i) The opposite of Increase in population is Decrease in population.
(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.
(iii) The opposite of earning money is Spending money.
(iv) The opposite of Going North is Going South.
(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.
(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.
(vii) The opposite of 25 is – 25.
(viii) The opposite of – 15 is 15.
2. Indicate the following by using integers:
(i) 25o above zero
(ii) 5o below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:
(i) 25o above zero is + 25o.
(ii) 5o below zero is – 5o.
(iii) A profit of Rs 800 is + 800.
(iv) A deposit of Rs 2500 is + 2500.
(v) 3km above sea level is + 3.
(vi) 2km below level is – 2.
3. Mark the following integers on a number line:
(i) 7
(ii) -4
(iii) 0
Solution:
The following integers are marked on a number line as given below:
4. Which number in each of the following pairs is smaller?
(i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Solution:
(i) 0 is greater than the negative integers
So we get – 4 < 0
Therefore, – 4 is smaller.
(ii) 12 is greater than -3 on a number line
So we get
-3 < 12
Therefore, – 3 is smaller.
(iii) 13 is greater than 8 on a number line
So we get 8 < 13
Therefore, 8 is smaller.
(iv) – 15 is greater than – 27 on a number line
So we get – 27 < – 15
Therefore, – 27 is smaller.
5. Which number in each of the following pairs is larger?
(i) 3, -4
(ii) – 12, – 8
(iii) 0, 7
(iv) 12, – 18
Solution:
(i) We know that 3 is larger than – 4 on a number line
So we get 3 > – 4
Therefore, 3 is larger.
(ii) We know that – 8 is larger than – 12 on a number line
So we get – 8 > – 12
Therefore, – 8 is larger.
(iii) We know that 7 is larger than 0 on a number line
So we get 7 > 0
Therefore, 7 is larger.
(iv) We know that 12 is larger than – 18 on a number line
So we get 12 > – 18
Therefore, 12 is larger.
6. Write all integers between:
(i) – 7 and 3
(ii) – 2 and 2
(iii) – 4 and 0
(iv) 0 and 3
Solution:
(i) The integers between – 7 and 3 are
– 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2
(ii) The integers between – 2 and 2 are
-1, 0, 1.
(iii) The integers between – 4 and 0 are
-3, -2, -1
(iv) The integers between 0 and 3 are
1, 2.
7. How many integers are between?
(i) – 4 and 3
(ii) 5 and 12
(iii) – 9 and – 2
(iv) 0 and 5
Solution:
(i) The integers between – 4 and 3 are
-3, -2, -1, 0, 1, 2
Therefore, number of integers between – 4 and 3 are 6.
(ii) The integers between 5 and 12 are
6, 7, 8, 9, 10, 11
Therefore, number of integers between 5 and 12 are 6.
(iii) The integers between – 9 and – 2 are
-8, -7, -6, -5, -4, -3
Therefore, number of integers between -9 and -2 are 6.
(iv) The integers between 0 and 5 are
1, 2, 3, 4
Therefore, number of integers between 0 and 5 are 4.
8. Replace * in each of the following by < or > so that the statement is true:
(i) 2 * 5
(ii) 0 * 3
(iii) 0 * – 7
(iv) – 18 * 15
(v) – 235 * – 532
(vi) – 20 * 20
Solution:
(i) 2 < 5
(ii) 0 < 3
(iii) 0 > – 7
(iv) – 18 < 15
(v) – 235 > – 532
(vi) – 20 < 20
9. Write the following integers in increasing order:
(i) – 8, 5, 0, -12, 1, -9, 15
(ii) – 106, 107, – 320, – 7, 185
Solution:
(i) – 8, 5, 0, -12, 1, -9, 15 can be written in increasing order as
– 12, – 9, – 8, 0, 1, 5, 15
(ii) – 106, 107, – 320, – 7, 185 can be written in increasing order as
-320, – 106, – 7, 107, 185.
10. Write the following integers in decreasing order:
(i) – 15, 0, -2, -9, 7, 6, -5, 8
(ii) -154, 123, -205, -89, -74
Solution:
(i) – 15, 0, -2, -9, 7, 6, -5, 8 can be written in decreasing order as
8, 7, 6, 0, -2, -5, -9, -15
(ii) -154, 123, -205, -89, -74 can be written in decreasing order as
123, – 74, – 89, – 154, – 205
11. Using the number line, write the integer which is:
(i) 2 more than 3
(ii) 5 less than 3
(iii) 4 more than – 9
Solution:
(i) 2 more than 3
In order to get the integer 2 more than 3
We draw a number line from 2 and proceed 3 units to the right to obtain 5
Therefore, 2 more than 3 is 5.
(ii) 5 less than 3
In order to get the integer 5 less than 3
We draw a number line from 3 and proceed 5 units to the left to obtain – 2
Therefore, 5 less than 3 is – 2.
(iii) 4 more than – 9
In order to get the integer 4 more than – 9
We draw a number line from – 9 and proceed 4 units to the right to obtain -5
Therefore, 4 more than – 9 is – 5.
12. Write the absolute value of each of the following:
(i) 14
(ii) – 25
(iii) 0
(iv) – 125
(v) – 248
(vi) a – 7, if a is greater than 7
(vii) a – 7, if a – 2 is less than 7
(viii) a + 4, if a is greater than -4
(ix) a + 4 if a is less than – 4
(x) |-3|
(xi) -|-5|
(xii) |12 – 5|
Solution:
(i) The absolute value of 14 is
|14| = 14
(ii) The absolute value of – 25 is
|-25| = 25
(iii) The absolute value of 0 is
|0| = 0
(iv) The absolute value of – 125 is
|-125| = 125
(v) The absolute value of – 248 is
|-248| = 248
(vi) The absolute value of a – 7, if a is greater than 7 is
|a – 7| = a – 7 where a > 7
(vii) The absolute value of a – 7, if a – 2 is less than 7 is
|a – 7| = – (a – 7) where a – 2 < 7
(viii) The absolute value of a + 4, if a is greater than -4 is
|a + 4| = a + 4 where a > – 4
(ix) The absolute value of a + 4 if a is less than – 4 is
|a + 4| = – (a + 4) where a < -4
(x) The absolute value of |-3| is
|-3| = 3
(xi) The absolute value of -|-5| is
-|-5| = 5
(xii) The absolute value of |12 – 5| is
|12 – 5| = 7
13. (i) Write 4 negative integers less than – 10.
(ii) Write 6 negative integers just greater than – 12.
Solution:
(i) The 4 negative integers less than – 10 are
– 11, – 12, – 13, – 14
(ii) The 6 negative integers just greater than – 12 are
-11, – 10, – 9, – 8, – 7, – 6
14. Which of the following statements are true?
(i) The smallest integer is zero.
(ii) The opposite of zero is zero.
(iii) Zero is not an integer.
(iv) 0 is larger than every negative integer.
(v) The absolute value of an integer is greater than the integer.
(vi) A positive integer is greater than its opposite.
(vii) Every negative integer is less than every natural number.
(viii) 0 is the smallest positive integer.
Solution:
(i) False. The smallest integer is 1.
(ii) True. 0 is neither positive nor negative so the opposite is 0.
(iii) False. Zero is an integer which is neither positive nor negative.
(iv) True. 0 is larger than – 1.
(v) False. The absolute value of an integer is the numerical value.
(vi) True. 3 is greater than – 3.
(vii) True. – 3 is less than 1.
(viii) False. 1 is the smallest positive integer.
RD Sharma Solutions for Class 6 Maths Chapter 5 Exercise 5.1 PDF Download
To help students strengthen their understanding of integers and negative numbers, we have provided the detailed RD Sharma Solutions for Class 6 Maths Chapter 5 Exercise 5.1 in PDF format below.
These solutions are designed according to the latest CBSE syllabus and exam pattern, making them an ideal resource for revision and practice. Students can refer to this PDF to clarify doubts, improve accuracy, and prepare effectively for exams using step-by-step solved questions.
