VMC VIQ Scholarship Test
ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
NCERT Solutions for Class 6 Maths Chapter 6 provided here. The solutions are prepared by expet team at careers360 keeping in mind the latest CBSE syllabus 2023. Before discussing the integers you must have cleared concepts in NCERT regarding Natural Numbers and Whole Numbers. NCERT Class 6 solution for chapter 6 Integers is covering the solutions of each question of the integer. If you put the negative numbers and the whole numbers together, the new collection of numbers will look like –1, – 2, – 3,–4, –5,...... 0, 1, 2, 3, 4, 5,..., and this collection of numbers is known as Integers.
It is advisable that students must complete NCERT Syllabus for Class 6 Maths in time. This chapter contains a total of 19 questions in 3 exercises. NCERT solutions for Class 6 Maths chapter 6 Integers is covering every question in detail. Students must refer to the NCERT Class 6 Maths Books and solve as many questions as they can. If you need NCERT Solutions for other classes and subjects then you click on the given link.
Integers are numbers like -4, -3, -1, 0, 1, 2, 3, 4, and so on. They include both positive and negative whole numbers.
Positive integers are numbers like 1, 2, 3, 4, 5, and so on. They are greater than zero. Negative integers are numbers like -1, -2, -3, and so on. They are less than zero.
The number 0 is an integer that is neither positive nor negative. It is right in the middle of the number line.
If we imagine a number line, with 0 in the centre, all the numbers to the right of 0 are positive integers, and all the numbers to the left of 0 are negative integers.
Opposite numbers are two integers that have the same distance from 0 on the number line but are on opposite sides. For example, 3 and -3 are opposite numbers.
Integer + Opposite Integer =0
The absolute value of an integer is the numerical value of the integer without considering its sign. If the integer is positive or zero, the absolute value is the same as the number itself. If the integer is negative, the absolute value is its opposite (positive) value.
Operation | Rule | Result |
Addition of integers | Same sign: Add the absolute values and keep the same sign | Integer with the same sign |
Absolute value is the sum of the absolute values | ||
Opposite signs: Take the difference between the absolute values and keep the sign of the greater absolute value | Integer with the sign of the addend (integer) that has a greater absolute value has a greater absolute value | |
Absolute value is the difference between the absolute values |
To subtract an integer b from another integer a, you can change the sign of b and add it to a.
a - b = a + (-b)
If you subtract one integer (b) from another integer (a), the result (a - b) is also an integer.
All the properties that apply to whole numbers also apply to integers. The operations of addition, subtraction, multiplication, and division work the same way for integers as they do for whole numbers.
Negative Numbers: Numbers with a negative sign that represent values below zero on the number line. They are used in various contexts such as temperature scales, water levels, oil levels, debit accounts, and outstanding dues.
Integers: The collection of numbers including negative numbers (e.g., -4, -3, -2, -1) and positive numbers (e.g., 1, 2, 3, 4). Negative integers refer to numbers below zero, and positive integers refer to numbers above zero.
Successor and Predecessor: Adding one to a given number yields its successor, while subtracting one yields its predecessor.
Addition of Integers: a) Same Sign: When adding two integers with the same sign, add them and maintain the same sign. Positive integers added together result in a positive integer, and negative integers added together result in a negative integer. b) Different Signs: When adding one positive and one negative integer, subtract the numbers as whole numbers (ignoring their signs) and use the sign of the integer with the greater absolute value. The bigger integer is determined by ignoring the signs. c) Subtraction: Subtracting an integer is equivalent to adding its additive inverse.
Number Line Representation: Addition and subtraction of integers can be visualized and demonstrated on a number line.
Free download NCERT Solutions for Class 6 Maths Chapter 6 Integers PDF for CBSE Exam.
Q1 Write opposites of the following :
(a) Increase in weight
(b) north
(c) east
(d) Loss of
(e) above sea level
Answer: The opposites are-
(a) Decrease in weight
(b) 30 km south
(c) 326 AD
(d) profit of Rs 700
(e) 100 m below sea level
Q2 Represent the following numbers as integers with appropriate signs.
(a) An airplane is flying at a height two thousand meters above the ground.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.
Answer: (a) An airplane is flying at a height two thousand meters above the ground. So it can be written as-
+2000m
(b) A submarine is moving at a depth, eight hundred meters below the sea level. In integers, it can be written as-
- 800m
(c) A deposit of rupees two hundred. In integer form, it can be written as-
+ Rs 200
(d) Withdrawal of rupees seven hundred. It can be written as-
- Rs 700
Q3 Represent the following numbers on a number line :
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
Answer: Draw a straight line and place a mark on it at a distance of the 1cm unit.
(a) Here A indicates the position of
(b) Here B indicates the position of
(c) Here C represents the position of
(d) Here D represents the
(e) Here E represents the
(a) If point D is , then which point is ?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value
Answer:
(a) If D is a then F represents (by counting on the vertical number line)
(b) G is a negative integer because it is below than point zero (0)
(c) Integers for point B and E are and respectively.
(d) E has the least value of
(e) Decreasing order of all the points are-
Q5: Following is the list of temperatures of five places in India on a particular day of the year
A5: Place Temperature
Siachin below .................
Shimla below .................
Ahmedabad above .................
Delhi above .................
Srinagar below .................
(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above .
Answer: (a)
Place | Temperature | Integer form |
Siachin | below | -10 |
Shimla | below | -2 |
Ahmedabad | above | +30 |
Delhi | above | +20 |
Srinagar | below | -5 |
(b)
(c) The coolest pace is Siachin with -10
(d) The places where the temperature is above 10 are-
(i) Delhi 20
(ii) Ahmedabad 30
Q6 In each of the following pairs, which number is to the right of the other on the number line?
(a)
(b)
(c)
(d)
(e)
(f)
Answer: In a number line, if an integer is greater than another integer, then it is placed on the right side of the number line. So, by this information, we can quickly identify which number is on the right side, in the given following pairs.
(a) 9 is right to the 2 ( )
(b) -3 is right to the - 8 ( )
(c) 0 is right to the -1
(d) 10 is right to the -11
(e) 6 is right to the -6
(f) 1 is right to the -100
Q7 Write all the integers between the given pairs (write them in the increasing order.)
(a)
(b)
(c)
(d)
Answer: (a) The integers between are;
(b) Integers between are;
(c) Integers between are;
(d) Integers between are;
Q8 (a) Write four negative integers greater than
(b) Write four integers less than
Answer: (a) four negative integers greater than are;
(all negative integers wg=ho comes before -20)
(b) four integers less than are;
(integers which comes after the -10)
(a) is to the right of on a number line.
(b) is to the right of on a number line.
(c) A smallest negative integer is .
(d) is greater than
Answer: (a) True, ( is greater than so it comes on the right side)
(b) False. is to the left side of on a number line
(c) False,
Correction-There is no smallest negative integer
(d) False,
Correction; is smaller than
Q10 Draw a number line and answer the following:
(a) Which number will we reach if we move numbers to the right of
(b) Which number will we reach if we move numbers to the left of .
(c) If we are at on the number line, in which direction should we move to reach ?
(d) If we are at on the number line, in which direction should we move to reach
Answer: (a) if we move numbers to the right of we get 2.
(b) if we move numbers to the left of we get -4
(c) If we are at on the number line, we should move 5 number to the left side on the number line.
(d) If we are at on the number line, then we should move 5 number right to the on the number line.
Q1 Using the number line write the integer which is :
(a) more than
(b) more than
(c) less than
(d) less than
Answer: (a) more than
The answer is 5 + 3 = 8
(a) more than The answer is 5 + 3 = 8
Q2 Use number line and add the following integers :
(a)
(b)
(c)
(d)
(e)
(f)
Answer: Addition by using the number line method-
(a)
Initially, move 0 to 9 and then 6 number left to the 9 on the numberline.
Q3 Add without using number line :
(a)
(b)
(c)
(d)
(e)
(f)
Answer: In addition without using the number line, in this method, we have to split one number according to the other number such that .
Now,
(a) = 4 + (7)+ (-7) = 4
(b)
= -13 + (13) + 5
= 5
(c)
= (- 10) + (10) + 9
= 9
(d)
= (- 100) + (- 150) + (150)
= - 100
(e)
= - (380 + 270 )
= - 650
(f)
= - (217 + 100)
= - 317
(a)
(b)
(c)
(d)
Answer: It is known that the sum of .
Therefore,
(a) the sum of
= 137 + (-137) + (- 217)
= - 217
(b) the sum of
= -52 + 52 = 0
(c) the sum of
= (- 231) + (81) + (39 + 192 )
= (- 81) + (- 231) + (231)
= - 81
(d) the sum of
= - (50 + 200 ) + (300)
= - 250 + (250) + 50
= 50
(a)
(b)
Answer: It is known that the sum of .
Therefore,
(a)
= - (9 + 7) + 4 + 16
= (- 16) + 4 + 16
= 4
Also we can split the 16 into (- 9 and -7 ).
(b)
= 37 + (- 37) + (- 28) + (-2) + (- 8)
= 0 - (37 + 28 + 8)
= - 73
Q1 Find
(a)
(b)
(c)
(d)
(e)
(f)
Answer: It is known that the sum of .
So, we have to split the number in order to cancel out with other numbers.
(a)
= 15 + (- 20) + 20
= 15 + 0 = 15
(b)
= 72 - (72) - 18
= 0 - 18 = -18
(c)
= (- 15) + 18
= (- 15) + (15) + 3
= 0 + 3 = 3
(d)
= - (20 + 13 )
= -33
(e)
= 23 + 12
= 35
(f)
= (- 32) + 40
= (- 32) + (32) + 8
= 0 + 8
= 8
Q2 Fill in the blanks with or sign.
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
(c) 45 – (– 11) ______ 57 + (– 4)
(d) (– 25) – (– 42) _____ (– 42) – (– 25)
Answer: (a) (– 3) + (– 6) ______ (– 3) – (– 6)
LHS - 3 - 6 = -9
RHS - 3 + 6 = +3
Hence LHS < RHS
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
LHS - 21 +10 = -11
RHS -31 - 11 = -42
Hence LHS > RHS
(c) 45 – (– 11) ______ 57 + (– 4)
LHS 45 + 11 = 66
RHS 57 - 4 =53
Hence LHS > RHS
(d) (– 25) – (– 42) _____ (– 42) – (– 25)
LHS - 25 + 42 = 17
RHS -42 + 25 = -17
Hence LHS > RHS
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = – 10
Answer: a) (– 8) + _____ = 0
Since we know that, . Therefore, the blank space should be + 8.
(b) 13 + _____ = 0
The sum is zero. Therefore it should be additive inverse of 13. -13( is the answer)
(c) 12 + (– 12) = ____
Since we know that, So, the answer is Zero (0)
(d) (– 4) + ____ = – 12
The integer in blank space should be -8
(e) ____ – 15 = – 10
The integer in blank space should be +5
Q4 Find
(a)
(b)
(c)
(d)
Answer: We already know that the sum of the additive inverse is Zero ( )
(a)
(b)
(c)
(d)
Also Check -
NCERT Books and NCERT Syllabus here:
Chapters No. | Chapters Name |
Chapter - 1 | |
Chapter - 2 | |
Chapter - 3 | |
Chapter - 4 | |
Chapter - 5 | |
Chapter - 6 | Integers |
Chapter - 7 | |
Chapter - 8 | |
Chapter - 9 | |
Chapter -10 | |
Chapter -11 | |
Chapter -12 | |
Chapter -13 | |
Chapter -14 |
Thoroughly Designed Solutions: The NCERT Solutions for Class 6 Maths Chapter 6 are meticulously crafted to offer comprehensive and step-by-step explanations for every problem and concept addressed in the chapter.
Enhanced Conceptual Clarity: The main objective of NCERT Maths Class 6 Chapter 6 solutions is to enhance the students' conceptual clarity by presenting intricate concepts in a simplified manner, making it easier for them to grasp.
Inclusive Topic Coverage: The solutions for Maths Class 6 Chapter 6 encompass all essential topics and subtopics, leaving no aspect of the chapter unaddressed. This comprehensive approach ensures that students gain a thorough understanding of the entire chapter.
Focus on Exam Preparedness: With a focused approach towards exam preparation, the NCERT Class 6 Maths chapter number 6 solutions equip students with the necessary skills and strategies to tackle questions effectively and excel in their exams.
The NCERT questions of Class 6 Mathematics are provided for practising the concepts studied in the chapter and also will help in exams. Also, chapter integers will be helpful in higher studies.
The basic idea of integers and the concept of addition and subtraction of integers are the main concepts covered in the chapter Integers. The questions based on these concepts are solved in the NCERT solutions for Class 6 Maths chapter 6 Integers.
Admit Card Date:04 October,2024 - 29 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Application Date:07 October,2024 - 19 November,2024
Application Date:07 October,2024 - 22 November,2024
Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide
Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 30th NOV'24! Trusted by 3,500+ universities globally
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE