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Integers Exercise Solutions | KalviGavani

TN Class 6 Maths Integers exercise solutions — positive negative integers number line addition subtraction, MCQ and step-by-step answers.

Updated 12 June 202612 min read

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

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Integers -- Exercise Solutions

Use this page alongside the official Samacheer Kalvi textbook. Solve each exercise first, then check the methods below.

Exercise 2.1 -- Fill in the Blanks (Q1)

1. The potable water available at 100 m below the ground level is denoted as ___ m
Answer-100 -- Below ground level is represented by a negative integer.
2. A swimmer dives to a depth of 7 feet from the ground into the swimming pool. The integer that represents this, is ___ feet
Answer-7 -- Depth below the surface is negative.
3. -46 is to the ___ of -35 on the number line
AnswerLeft -- Since -46 < -35, it lies to the left on the number line.
4. There are ___ integers from -5 to +5 (both inclusive)
Answer11 -- Counting: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 = 11 integers.
5. ___ is an integer which is neither positive nor negative
Answer0 -- Zero is the only integer that is neither positive nor negative.

Exercise 2.1 -- True or False (Q2)

Q2(i). Each of the integers -18, 6, -12, 0 is greater than -20.

AnswerTrue -- Since -18 > -20, 6 > -20, -12 > -20, and 0 > -20, all are greater than -20.

Q2(ii). -1 is to the right of 0.

AnswerFalse -- -1 is to the left of 0 on the number line. Correction: -1 is to the left of 0.

Q2(iii). -10 and 10 are at equal distance from 1.

Answer: False -- Distance from 1 to 10 =10 - 1= 9, but distance from 1 to -10 =1 - (-10)= 11. The distances are not equal.

Q2(iv). All negative integers are greater than zero.

AnswerFalse -- All negative integers are less than zero. Correction: All negative integers are less than zero.

Q2(v). All whole numbers are integers.

AnswerTrue -- Whole numbers {0, 1, 2, 3, ...} are a subset of integers {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Exercise 2.1 -- Number Line Questions (Q3, Q4)

Q3. Mark the numbers 4, -3, 6, -1 and -5 on the number line.

AnswerOn a number line, from left to right: -5, -3, -1, 4, 6 at their respective positions with equal spacing.

Arrange from left to right: -5, -3, -1, 0, 4, 6. Place each integer at equal intervals on the number line.

Q4(i). On the number line, which number is 4 units to the right of -7?

Step-by-step:

  • Moving 4 units to the right means adding 4: -7 + 4 = -3
Answer-3

Q4(ii). On the number line, which number is 5 units to the left of 3?

Step-by-step:

  • Moving 5 units to the left means subtracting 5: 3 - 5 = -2
Answer-2

Exercise 2.1 -- Opposites (Q5)

Find the opposite of each integer:

Sub-questionIntegerOpposite
5(i)44-44
5(ii)-1919
5(iii)00
5(iv)-312312
5(v)789-789

The opposite (additive inverse) of any integer n is -n. Zero is its own opposite.

Exercise 2.1 -- Real-Life Situations (Q6)

Q6. If 15 km east of a place is denoted as +15 km, what is the integer that represents 15 km west of it?

Step-by-step:

  • East is positive (+); west is the opposite direction, so it is negative (-).
  • 15 km west = -15 km
Answer-15

Exercise 2.1 -- Integers Between Given Numbers (Q8)

Q8(i). Write all integers between 7 and 10:
Answer8, 9
Q8(ii). Write all integers between -5 and 4:
Answer-4, -3, -2, -1, 0, 1, 2, 3
Q8(iii). Write all integers between -3 and 3:
Answer-2, -1, 0, 1, 2
Q8(iv). Write all integers between -5 and 0:
Answer-4, -3, -2, -1

The integers "between" exclude the endpoints. Count carefully when negatives are involved.

Exercise 2.1 -- Comparing Integers (Q9)

Put the appropriate sign (<, >, or =):

Sub-questionComparisonAnswerReason
9(i)-7 ? 8-7 < 8Negative < positive
9(ii)-8 ? -7-8 < -7-8 is further left on the number line
9(iii)-999 ? -1000-999 > -1000-999 is closer to zero
9(iv)-111 ? -111-111 = -111Same integer
9(v)0 ? -2000 > -200Zero is greater than any negative

Rule: On the number line, the integer to the right is always greater. Any positive integer is greater than any negative integer.

Exercise 2.1 -- Ascending Order (Q10)

Q10(i). Arrange in ascending order: -11, 12, -13, 14, -15, 16, -17, 18, -19, -20

Step-by-step:

  • Separate negatives: -11, -13, -15, -17, -19, -20
  • Sort negatives ascending: -20, -19, -17, -15, -13, -11
  • Separate positives: 12, 14, 16, 18
  • Sort positives ascending: 12, 14, 16, 18
  • Combine: -20, -19, -17, -15, -13, -11, 12, 14, 16, 18

Q10(ii). Arrange in ascending order: -28, 6, -5, -40, 8, 0, 12, -1, 4, 22

Answer-40, -28, -5, -1, 0, 4, 6, 8, 12, 22

Q10(iii). Arrange in ascending order: -100, 10, -1000, 100, 0, -1, 1000, 1, -10

Answer-1000, -100, -10, -1, 0, 1, 10, 100, 1000

Exercise 2.1 -- Descending Order (Q11)

Q11(i). Arrange in descending order: 14, 27, 15, -14, -9, 0, 11, -17

Answer27, 15, 14, 11, 0, -9, -14, -17

Q11(ii). Arrange in descending order: -99, -120, 65, -46, 78, 400, -600

Answer400, 78, 65, -46, -99, -120, -600

Q11(iii). Arrange in descending order: 111, -222, 333, -444, 555, -666, 7777, -888

Answer7777, 555, 333, 111, -222, -444, -666, -888

Exercise 2.1 -- Objective Type Questions (Q12-Q16)

Q12. There are ___ positive integers from -5 to 6. Positive integers: 1, 2, 3, 4, 5, 6

Answer(b) 6 -- There are 6 positive integers in the range.

Q13. The opposite of 20 units to the left of 0 is: 20 units left of 0 = -20. Opposite of -20 = 20.

Answer(a) 20

Q14. One unit to the right of -7 is: -7 + 1 = -6

Answer(d) -6

Q15. 3 units to the left of 1 is: 1 - 3 = -2

Answer(c) -2

Q16. The number which determines marking the position of any number to its opposite on a number line is: Zero is the reference point from which opposites are measured.

Answer(b) 0

Exercise 2.2 -- Miscellaneous Practice Problems

Q1. Write two different real life situations that represent the integer -3.

Answer
  • (i) A temperature of 3 degrees below 0 degrees Celsius (-3 degrees C)
  • (ii) A loss of Rs. 3 in a business transaction (-3 rupees)
  • (iii) 3 metres below sea level (-3 m)

Q2(i). Mark all integers greater than -7 but less than 7.

Answer-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6

Q2(ii). Mark the opposite of 3.

Answer-3

Q2(iii). 5 units to the left of -1.

Step-by-step:

  • -1 - 5 = -6
Answer-6

Q3. Construct a number line that shows the depth of 10 feet from the ground level and its opposite.

Step-by-step:

  • Ground level = 0
  • Depth of 10 feet = -10
  • Opposite (height above ground) = +10
AnswerMark -10 below 0 and +10 above 0 on the number line.

Q4. Identify the integers that are at a distance of 8 units from -6.

Step-by-step:

  • Going 8 units to the right: -6 + 8 = 2
  • Going 8 units to the left: -6 - 8 = -14
Answer2 and -14

Q7. Find the integers that are 4 units to the left of 0 and 2 units to the right of -3.

Step-by-step:

  • 4 units to the left of 0: 0 - 4 = -4
  • 2 units to the right of -3: -3 + 2 = -1
Answer-4 and -1

Exercise 2.2 -- Challenge Problems

Q8. Is there the smallest and the largest number in the set of integers? Give reason.

AnswerNo. There is no smallest integer because for any integer n, n - 1 is always smaller. There is no largest integer because for any integer n, n + 1 is always larger. Integers extend infinitely in both directions.

Q10. P, Q, R, S puzzle on a number line.

Step-by-step:

  • (ii) R = smallest positive integer = 1
  • (iv) Q = 2 units left of R = 1 - 2 = -1
  • (iii) P and S are at the same distance from 0, so they are opposites
  • (i) S is the least integer = -2, therefore P = 2
AnswerP = 2, Q = -1, R = 1, S = -2. Ascending order: S(-2), Q(-1), R(1), P(2).

Q11. Place mapping on number line (Home = 0):

PlaceCalculationInteger
HomeStarting point0
Bus Stand3 km right3
Library2 km left-2
Dept. Store6 km left-6
Post Office1 km right of Library = -2 + 1-1
Park1 km right of Dept. Store = -6 + 1-5
Railway Station3 km left of Post Office = -1 - 3-4
School8 km right of Railway Station = -4 + 84
PlaygroundOpposite of Library = -(-2)2
Electricity BoardEqual distance from Home as Dept. Store6

Additional Questions

Q1. Write all the integers between -5 and 10.

Answer-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Q2. Write the opposite of each:

  • (a) Profit of Rs. 500 --> Loss of Rs. 500
  • (b) Deposit of Rs. 2000 --> Withdrawal of Rs. 2000
  • (c) 50 km towards south --> 50 km towards north

Q5. Write the following numbers with appropriate signs:

  • (a) 100 m below sea level = -100 m
  • (b) 25 degrees C above 0 degrees C = +25 degrees C
  • (c) Any 3 numbers less than 0 = -1, -2, -3

Q7. Draw a number line and answer:

Step-by-step: -2 + 4 = 2

Step-by-step: 1 - 5 = -4

AnswerLeft -- -13 is smaller than -8, so move left.
AnswerRight -- -1 is greater than -6, so move right.
  • (a) Which number will we reach if we move 4 numbers to the right of -2?
  • (b) Which number will we reach if we move 5 numbers to the left of 1?
  • (c) If we are at -8, in which direction should we move to reach -13?
  • (d) If we are at -6, in which direction should we move to reach -1?

Q8. Write four negative integers greater than -15 and four negative integers less than -5.

  • (a) Four negative integers greater than -15: -11, -10, -5, -1
  • (b) Four negative integers less than -5: -7, -15, -18, -20

Q10. Represent the following as integers:

  • (a) A deposit of rupees two thousand = +2000
  • (b) An aeroplane is flying at a height of three thousand metres above the ground = +3000

Common Mistakes to Avoid

1. Confusing the direction on the number line: On the number line, integers increase to the right and decrease to the left. A common error is treating -7 as greater than -3 because 7 > 3. Remember: -3 > -7.

2. Forgetting zero is an integer: Zero is neither positive nor negative, but it is an integer. When counting "integers from -5 to 5," include 0. Total = 11, not 10.

3. Wrong opposite of negative numbers: The opposite of -5 is 5, not -5. The opposite of a negative integer is positive, and vice versa.

4. Counting endpoints when asked for "between": "Integers between -5 and 5" does NOT include -5 and 5. The answer is -4, -3, -2, -1, 0, 1, 2, 3, 4.

5. Mixing up predecessor and successor: The predecessor of 3 is 2 (3 - 1), not 4. The successor of -5 is -4 (-5 + 1), not -6.

6. Treating "greater" and "more to the right" differently: On the number line, greater always means more to the right. Zero is greater than every negative integer.

7. Forgetting that distance is always positive: The distance between -3 and 5 is5 - (-3)=8= 8, not -8. Distance cannot be negative.

Exam Checklist

  • [ ] Can you define integers and distinguish them from whole numbers and natural numbers?
  • [ ] Can you represent integers on a number line correctly?
  • [ ] Can you find the opposite (additive inverse) of any integer?
  • [ ] Can you compare integers using <, >, and = signs?
  • [ ] Can you arrange integers in ascending and descending order?
  • [ ] Can you find integers between two given integers (inclusive and exclusive)?
  • [ ] Can you move left (subtract) and right (add) on the number line?
  • [ ] Can you represent real-life situations (temperature, altitude, profit/loss) as integers?
  • [ ] Can you find integers at a given distance from another integer?
  • [ ] Can you identify the predecessor and successor of any integer?

Frequently Asked Questions

Integers are the set of whole numbers that include positive numbers, negative numbers, and zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}.