class 6th | Integer | Test

Integers

1. Use + or – sign to represent the following:

(a) 5 kg decrease in weight

(b) 1000 m above sea level

(d) A withdrawal of 2300 from the bank.

(e) A submarine is moving at a depth of five hundred metre below sea level.

(f) Gaining a weight of 2 kg.

(g) Going 600 metre above sea level.

(h) Temperature six degree Celsius above 0 degree Celsius.

(i) An aeroplane is flying at a height three thousand five hundred metre above the ground.

(j) Increase in weight 8kg

(k) 30 km north

(l) 80 m east

(m) Loss of Rs 700

(n) 100 m above sea level

(o) An aeroplane is flying at a height two thousand metre above the ground.

(p) A submarine is moving at a depth, eight hundred metre below the sea level.

(q) A deposit of rupees two hundred.

(r) Withdrawal of rupees seven hundred.

(s) Profit of 20

(t) Second floor below the ground level.

(u) Going 4 km towards east.

2. Find the additive inverse of the following.

(a) 16 (b) – 25 (c) 7

(d) –86 (e) + 52 (f) –75

3. Arrange the integers

(a) Arrange in increasing order: 3, 0, –3, 5, –1

(b) Arrange in decreasing order: 23, 15, 5, 2, –25

(d) Arrange in decreasing order: 13,21, 17, 15, 15, 10

4. Add the given integers.

(a) – 410 and +172

(b) +120 and –10

(d) +200 and –75

(e) +11 and +5

(f) –6 and –14

(g) +114 and + 400

(h) 137 and – 354

(i)52 and 52

(j) 312, 39 and 192

(k)50, 200 and 300

5. Subtract the given integers.

(a) +11 from +5

(b) –6 from –14

(d) – 410 from +172

(e) +120 from –10

(f) – 88 from –43

(g) +200 from –75

6. Find the answers of the following additions:

Find the solution of the following:

(a) (– 11) + (– 12)

(b) (10) + (4)

(d) (23) + (40)

(e) (– 7) + (8)

(f) (– 9) + (13)

(g) (7) + (– 10)

(h) (12) + (– 7)

(i) (7) + (– 11)

(j) (– 13) + (10)

(k) (– 7) + (9)

(l) (10) + (– 5)

(m) 11+ (–7)

(n) (– 10) + (19)

(o) (– 380) + (– 270)

(p) (– 13) + (18)

(q) (– 250) + (150)

(r) (– 217) + (– 100)

(s) –81 – (–22)

(t) –36 –(–17)

(u) 117 + (–117)

7. Add the following using properties of integers.

Solve the following using the appropriate properties.

(a) (–7) + (–9) + 4

(b) (37) + (–65) + (–8)

(d) (13) – 8 –1

(e) (– 7) + (– 8) + (– 90)

(f) (–42) + (–28) + 70

(g) (–15) + 9 + 21

(h) 50 – (– 40) – (– 2)

(i) –12 –3 – (–5)

(j) (– 7) – 8 – (– 25)

(k) 26 + 34 + (–16)

8. Find the sum:

(a) (–7) + (–9) + 4 + 16

(b) (37) + (2) + (–65) + (–8)

(d) (13) + 32 – 8 –1

(e) (– 7) + (– 8) + (– 90)

(f) 26 + 34 + (–16) + 4

(g) (–42) + (–28) + 70 –30

(h) (–15) + 9 + 21 –45

(i) 50 – (– 40) – (– 2) –(–8)

(j) –12 –3 – (–5) –(–8)

(k) (– 7) – 8 – (– 25)–(–18)

(l) 26 + 34 + (–16)–(–81)

9. Find the sum:

(a) Find the sum of (– 9) + (+ 4) + (– 6) + (+ 3)

(b) Find the value of (30) + (– 23) + (– 63) + (+ 55)

(d) Find the sum of: (–5) –(6) –(–16) + (16)

(e) Find the sum of: (–10 )+ (18) + (–28) + (–6)

(f) Find the sum of: (–7) + (–9) + (4) + (16)

10. Solve the following

(a) Subtract 211 from the difference obtained by subtracting – 120 from – 57.

(b) Subtract (104) from the sum of 38 and (–27).

(d) Add –41 to the difference obtained by subtracting –176 from –200.

(e) The sum of two integers is –210. If one of the integers is 120, find the other.

(f) The sum of two integers is 188. If one of the integers is – 28, find the other.

(g)The sum of two integers is (– 26). If one of them is 43, then find the other integer.

(h) a = (–8) b = (– 6) and c = 6 then find the value of a + b – c

(i) The difference of an integer P and (–5) is 4. Find the value of P.

(j) What must be subtracted from (–3) to get (–8)?

11. Fill in the blanks.

(a) (– 8) + [.....] = 0

(b) 13 + [.....] = 0

(d) (– 4) + [.....] = –12

(e) [.....] + 15 = –10

(f) (–42) +13 = ....... +(–42)

(g) (–10)+10 = .......

(h) (–11) – 3= .......

(i) – 6 – 0= .......

(j) [(–71) + (–27)] +15 = ....... + [15 + ( ....... )]

12. Fill in the blanks with >, < or = sign.

(a) (–3)+(–6) [.....] (– 3) – (– 6)

(b) (–21)–(–10) [.....] (– 31) + (– 11)

(d) (–25)–(–42) [.....] (– 42) – (– 25)

(e) (–3)+(–4) [.....] (– 4) – (– 4)

(f) (–21)–(–19) [.....] (– 31) + (– 11)

(g) 45–(–15) [.....] 57 + (– 47)

(h) (–25)–(–42) [.....] (– 42) – (– 25)

Number Line

1. Mark the following integers on a number line.

Represent the following numbers on a number line:

(a) – 5

(b) 7

(d) – 6

(e) – 4

(f) 8

(g) 12

(h) – 9

(i) 5

(j) 0

(k) 19

(l) 6

(m) +3

(n) – 10

(o) – 8

(p) – 1

(q) – 7

2. Observe the given line and find the integers for the following:

(a) Find the integer for C

(b) Find the integer for J

(d) Find the integer for C + J

(e) Find the integer for B + M

(f) Find the integer for C + H

(f) Find the integer for C– H

(f) Find the integer for H – C

(f) Find the integer for O – A

(f) Find the integer for C × H

(f) Find the integer for B × K

(f) Find the integer for A × H

(f) Find the integer for C ÷ H

(f) Find the integer for H ÷ C

(f) Find the integer for O ÷ A

(g) Find the integer of successor for C

(h) Find the preceding integer of I

(h) Find the preceding integer of K

(h) Find the preceding integer of M

3. Using the number line, write the integer which is: (Use separate number line for each question)

(a) 4 more than – 1

(b) 5 less than 3

(d) 3 more than 5

(e) 5 more than –5

(f) 6 less than 2

(g) 3 less than –2

(h) 13 more than 5

(i) 15 more than –5

(j) 16 less than 2

(k) 13 less than –2

4. 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

(d) –11, 10

(e) –6, 6

(f) 1, –100

5. Use number line and add the following integers: (Use separate number line for each question)

(A)

(a) 9 + (+ 6)

(b) (–1) + (–7)

(d) (–5) + (–7)

(e) (–8) + 7

(f) – 9 + (–6)

(g) (–2) + (–5)

(h) (–5) + 9

(i) 9 + (–6)

(B)

(a) (–2) + 8 + (– 4)

(b) (–1) + (– 2) + (– 3)

(d) (–1) + (– 2) + (– 3)

(e) (–2) + 8 + (– 4)

(f) (–1) + (– 2) + (– 3)

(g) (–2) + 8 + (– 4)

(h) (–1) + (– 2) + (– 3)

(i) (–2) + 8 + (– 4)

(C)

(b) 5 + (–11) + 5 + (–1)

Exercise 4.2

Concept and Skills

Example: 12+(-18)=

(-16)+(-9)

3. Fill in the blanks.

8. Write five distinct integers whose sum is 5.

9. Find three integers of different signs whose difference is – 25.

10. During a week-long hiking trip in the mountains, the temperature fluctuated. On Monday, the temperature was 5 °C. On Tuesday, the temperature dropped by 7 °C, and on Wednesday, it increased by 12 °C. On Thursday, the temperature dropped again by 3 °C, and on Friday, it increased by 8 °C. What was the temperature on Friday? 11.

8. What is the sum of the largest negative integer and the smallest positive integer?

Exercise 4.1

Concept and Skills

1. State true or false.

(a) There are four even integers between – 11 and 12.

(b) Integers with the same absolute value are equal.

(d) The more the number of zeros at the end of a negative integer, the smaller is the number.

EXERCISE 6.1

1. Write opposites of the following:

(a) Increase in weight 8kg

(b) 30 km north

(d) Loss of Rs 700

(e) 100 m above sea level

2. Represent the following numbers as integers with appropriate signs.

3. Represent the following numbers on a number line:

(a) +5

(b) – 10

(d) - 1

(e) – 6

4. 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?

(d) Write the names of the places where temperatures are above 10°C.

7. Write all the integers between the given pairs (write them in the increasing order.)

(a) 0 and –7

(b) – 4 and 4

(d) 30 and – 23

(a) Write four negative integers greater than -20.

(b) Write four integers less than - 10.

9. 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.

(b) 100 is to the right of - 50 on a number line.

(d) - 26 is greater than - 25.

Try These

1. Find the solution of the following additions using a number line :

(a) (-2) + 6

(b) (-6) + 2

Make two such questions and solve them using the number line.

2. Find the solution of the following without using number line :

(a) (7) + (- 11)

(b) (- 13) + (10)

(d) (10) + (- 5)

Make five such questions and solve them.

EXERCISE 6.2

1. Using the number line write the integer which is :

(a) 3 more than 5

(b) 5 more than -5

(d) 3 less than -2

2. Use number line and add the following integers:

(a) 9+(-6)

(b) 5+(-11) 5 + (-1

(d) (-5)+10

(e) (- 1) + (- 2) + (- 3)

(f) (- 2) + 8 + (- 4)

3. Add without using number line :

(a) 11+ (-7)

(e) (- 380) + (- 270)

(b) (- 13) + (18)

(d) (- 250) + (150)

(f) (- 217) + (- 100)

4. Find the sum of:

EXERCISE 6.3

1. Find

(a) 35-(20)

(b) 72-(90)

(d) (- 20) - (13)

(e) 23(-12)

(f) (- 32) - (- 40)

4. Find

(a) (- 7) - 8 - (- 25)

(b) (13) +32-8-1

(d) 50 - (- 40) - (- 2)

Questions:

1. Find the greatest negative integer.

2. Find the smallest integer which is smaller than all the positive integers.

3. Find the integer which is neither positive nor negative.

4. Find the opposite of the following and represent with signs:

(i) Profit of 20

(ii) Second floor below the ground level.

(iii) Going 4 km towards east.

5. Find additive inverse of 6.

6. Subtract (123) from (–456).

7. less than (–5). 7.

8. 5 more than (–2).

9. What is the succeeding number of the number zero?

10. What is the preceding number of the number zero?

11. What is the succeeding number of the number (–1)?

12. What is the preceding number of the number (–4)?

13. Fill in the box:

(i) (–1) + [ ] = 0

(ii) [ ] – 4 = – 2

Observe the given line and find the integers for the following: (Q. No. 14 to Q. No. 21)

14. Find the integer for C

15. Find the integer for J

16. Find the integer for M

17. Find the integer for C+ J

18. Find the integer for B+ M

19. Find the integer for C– H

20. Find the integer of successor for C

21. Find the preceding integer of K

22. Arrange in increasing order: 3, 0, –3, 5, –1

23. Arrange in decreasing order: 23, 15, 5, 2, –25

24. Arrange in increasing order: 5, –6, –4, 0, 8, 6

25. Arrange in decreasing order: 13,21, 17, 15, 15, 10

26. Find the value of 2 – (–1) – 2 –(–3).

27. Find the value of 5 – {(12 –(10–8)}

28. If you are at (3) on the number line, in which direction should you move to reach (–8)?

29. If you are at (–5) on the number line, in which direction should you move to reach at 2?

30. Subtract (104) from the sum of 38 and (–27).

31. Subtract the sum of (100) and 225 from 50.

32. Find: (–5) –(6) –(–16)

33. Find: (–10 )+ (18) + (–28) + (–6)

34. Find: (–7) + (–9) + (4) + (16)

Represent the following integers with appropriate sign: (Q. No. 35 to Q. No. 40)

35. A withdrawal of 2300 from the bank.

36. A submarine is moving at a depth of five hundred metre below sea level.

37. Gaining a weight of 2 kg.

38. Going 600 metre above sea level.

39. Temperature six degree Celsius above 0 degree Celsius.

40. An aeroplane is flying at a height three thousand five hundred metre above the ground.

41. Shekhar scores 25 runs less than his previous score.

42. The sum of two integers is (– 26). If one of them is 43, then find the other integer.

43. a = (-–8) b = (– 6) and c = 6 then find the value of a + b – c

44. The difference of an integer P and (–5) is 4. Find the value of P.

45. What must be subtracted from (–3) to get (–8)?

46. A bucket contains 35 litres of water. Due to a small hole in the bucket, the quantity of water is decreasing at the rate of 2 litres every hour. Find the quantity of water in the bucket after 10 hours.

47. An insect crawls 10 cm every second on a 90 cm vertical rod and then falls down 4 cm over the next second. How many seconds will it take to climb the rod?

48. In a class test containing 20 questions. 5 marks are given for every correct answer, (2) marks is given for every incorrect answer. Heena attempts all questions and 14 of her answers are correct. What is her total score?

49. In a class test containing 20 questions, 5 marks are given for every correct answer, (1) mark is given for every incorrect answer and 0 mark for each unattempted question. Ravi gets 4 correct and 4 incorrect answers. Find his score.

50. A certain freezing process requires that room temperature be lowered from 40° C at the rate of 6° C per hour. What will be room temperature 10 hours after the process begins?

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