NCERT Solutions for Class 6 – Complete Chapter-wise Study Material
6. Integers is one of the most important chapters in the Class 6 Mathematics English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.
The 6. Integers - Class 6 Mathematics English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.
One of the biggest advantages of studying 6. Integers is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.
Our Class 6 Mathematics NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.
Students preparing for school assessments should carefully study 6. Integers because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.
At ATP Education, we continuously update our Class 6 Mathematics English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying 6. Integers thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.
6. Integers - Class 6 Mathematics English NCERT Solutions
6. Integers
Exercise 6.1
Q1. Write opposites of the following :
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of Rs 700
(e) 100 m above sea level
Solution: Q1.
(a) Increase in weight
Answer : Decrease in weight
(b) 30 km North
Answer : 30 km Sounth
(c) 326 BC
Answer : 326 AD
(d) Loss of Rs 700
Answer : Profit of Rs 700.
(e) 100 m above sea level
Answer : 100 m below sea level.
Q2. Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre 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.
Solution Q2.
(a) An aeroplane is flying at a height two thousand metre above the
ground.
Answer : + 2000 m
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
Answer : - 800 m
(c) A deposit of rupees two hundred.
Answer : + Rs 200
(d) Withdrawal of rupees seven hundred.
Answer : - Rs 700
Q3. Represent the following numbers on a number line :
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
Solution Q3:
(a) + 5
Answer :
(b) – 10
Answer :
(c) + 8
Answer :
(d) – 1
Answer :
(e) – 6
Answer :
Q4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points :
(a) If point D is + 8, then which point is – 8?(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.
Solution Q4.
(a) If point D is + 8, then which point is – 8?
Answer : Point F
(b) Is point G a negative integer or a positive integer?
Answer : Negative integer
(c) Write integers for points B and E.
Answer :
(i) For point B : + 4
(ii) For point E : - 10
(d) Which point marked on this number line has the least value?
Answer : Point E has least value.
(e) Arrange all the points in decreasing order of value.
Answer : D, C, B, A, O, H, G, F, E
Q5. Following is the list of temperatures of five places in India on a particular day of the year.
(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 10°C.
Solution Q5:
(a) Write the temperatures of these places in the form of integers in the blank column.
Answer:
(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?
Answer : The coolest place is Siachin
(d) Write the names of the places where temperatures are above 10°C.
Answer : Delhi and Ahmedabad.
Q6. In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9
(b) – 3, – 8
(c) 0, – 1
(d) – 11, 10
(e) – 6, 6
(f) 1, – 100
Solution Q6:
(a) 9 is right to 2
(b) –3 is right to –8
(c) 0 is right to –1
(d) 10 is right to –11
(e) 6 is right to –6
(f) 1 is right to –100
Q7. Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and – 7
(b) – 4 and 4
(c) – 8 and – 15
(d) – 30 and – 23
Solution Q7:
(a) 0 and – 7
Answer : –6, –5, –4, –3, –2, –1
(b) – 4 and 4
Answer : –3, –2, –1, 0, 1, 2, 3
(c) – 8 and – 15
Answer : –14, –13, –12, –11, –10, –9
(d) – 30 and – 23
Answer : –29, –28, –27, –26, –25, –24
Q8. (a) Write four negative integers greater than – 20.
Solution : –19, –18, –17, –16
(b) Write four negative integers less than – 10.
Solution : –11, –12, –13, –14
Q9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
Solution : True (T)
(b) – 100 is to the right of – 50 on a number line.
Solution : False (F)
(c) Smallest negative integer is – 1.
Solution: False (F)
(d) – 26 is greater than – 25.
Solution: False (F)
Q10. Draw a number line and answer the following :
(a) Which number will we reach if we move 4 numbers to the right of – 2.
Solution :
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?
Solution: We should move to left side.
(d) If we are at – 6 on the number line, in which direction should we move to reach – 1?
Solution: We should move to right side.
6. Integers
Exercise 6.2
Q1. Using the number line write the integer which is :
(a) 3 more than 5
Solution:
(b) 5 more than –5
Solution :
(c) 6 less than 2
Solution :
(d) 3 less than –2
Solution :
Q2. Use number line and add the following integers :
(a) 9 + (– 6)
(b) 5 + (– 11)
(c) (– 1) + (– 7)
(d) (– 5) + 10
(e) (– 1) + (– 2) + (– 3)
(f) (– 2) + 8 + (– 4)
Solution Q2:
(a) 9 + (– 6)
Solution:
(b) 5 + (– 11)
Solution :
(c) (– 1) + (– 7)
Solution :
(d) (– 5) + 10
Solution :
(e) (– 1) + (– 2) + (– 3)
Solution :
(f) (– 2) + 8 + (– 4)
Solution :
Q3. Add without using number line :
(a) 11 + (– 7)
(b) (– 13) + (+ 18)
(c) (– 10) + (+ 19)
(d) (– 250) + (+ 150)
(e) (– 380) + (– 270)
(f) (– 217) + (– 100)
Q4. Find the sum of :
(a) 137 and – 354
(b) – 52 and 52
(c) – 312, 39 and 192
(d) – 50, – 200 and 300
Solution:
(a) 137 and – 354
137 + (-354)
= 137 - 354
= – 217 Answer
Solution:
(b) – 52 and 52
= (- 52) + 52
= 0 Answer
Solution:
(c) – 312, 39 and 192
(– 312) + 39 + 192
= - 312 + 231
= - 81 Answer
Solution:
(d) – 50, – 200 and 300
(– 50) + (– 200) + 300
= (- 250) + 300
= 50 Answer
Q5. Find the sum :
(a) (– 7) + (– 9) + 4 + 16
(b) (37) + (– 2) + (– 65) + (– 8)
Solution:
(a) (– 7) + (– 9) + 4 + 16
= (- 16) + 20
= 4 Answer
Solution :
(b) (37) + (– 2) + (– 65) + (– 8)
= (37) + (- 75)
= 37 - 57
= – 38 Answer
6. Integers
Exercise 6.3
Q1. Find
(a) 35 – (20)
(b) 72 – (90)
(c) (– 15) – (– 18)
(d) (–20) – (13)
(e) 23 – (– 12)
(f) (–32) – (– 40)
Solution:
(a) 35 – (20)
= 15 Answer
(b) 72 – (90)
= - 18 Answer
(c) (– 15) – (– 18)
= - 15 + 18
= 3 Answer
(d) (–20) – (13)
= - 20 - 13
= - 33 Answer
(e) 23 – (– 12)
= 23 + 12
= 35 Answer
(f) (–32) – (– 40)
= - 32 + 40
= 8 Answer
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)
Solution:
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
= - 9 __________ - 3 + 6
= - 9 < 3 Answer
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
= - 21 + 10 ________ - 31 - 11
= - 11 > - 42 Answer
(c) 45 – (– 11) ______ 57 + (– 4)
= 45 + 11 _____ 57 - 4
= 56 > 53 Answer
(d) (– 25) – (– 42) _____ (– 42) – (– 25)
= - 25 + 42 ______ - 42 + 25
= 17 > - 17 Answer
Q3. Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = – 10
Solution :
(a) (– 8) + _____ = 0
= - 8 + 8 = 0
(a) 8 Answer
(b) 13 + _____ = 0
= 13 + (- 13) = 0
(b) - 13 Answer
(c) 12 + (– 12) = ____
= 12 + (-12) = 0
(c) 0 Answer
(d) (– 4) + ____ = – 12
= - 4 + (-8) = - 12
(d) - 8 Answer
(e) ____ – 15 = – 10
= 5 - 15 = - 10
(e) 5 Answer
Q4. Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)
Solution :
(a) (– 7) – 8 – (– 25)
= - 7 - 8 + 25
= - 15 + 25
= 10 Answer
(b) (– 13) + 32 – 8 – 1
= - 13 + 32 - 9
= 32 - 22
= 10 Answer
(c) (– 7) + (– 8) + (– 90)
= - 7 - 8 - 90
= - 105 Answer
(d) 50 – (– 40) – (– 2)
= 50 + 40 + 2
= 92 Answer
NCERT Book Solutions
Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
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Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
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Studying from NCERT Solutions helps students build strong conceptual understanding and improve problem-solving skills. These solutions are especially useful for revision because every answer is written according to the marking scheme followed by CBSE.
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