## NCERT 6TH CLASS MATHEMATICS CHAPTER INTEGERS

**INTEGERS**

**Temperature :** During the winter season, the minimum temperature on a particular day, say in Chennai, may be 20ºC. This means that the temperature in Chennai is higher than the melting point of ice, which is 0ºC. On the same day, the minimum temperature in Shimla may be 5ºC below 0ºC. How do we represent this? This can be represented as –5ºC, read as minus five degree centigrade.

**=Direction :**If we consider the direction towards North as positive, then 5 metres north would mean 5 metres towards the north, while -5 metres north would mean 5 metres in the opposite direction of north, i.e., 5 metres towards the south. Similarly, the negative of south is the positive of north.

**Profit and Loss :**If a profit of Rs 10 is expressed as Rs (+ 10), then a loss of Rs 20 is expressed as Rs (– 20) profit. We can say that negative profit is positive loss and negative loss is positive Profit.

**ORDERING OF INTEGERS**

**ABSOLUTE VALUE OF INTEGERS**

**OPERATION ON INTEGERS**

**Points to Remember**

**OBJECTIVE TYPE**

Q.16 3 – 5 = 3 + ( ), then ( ) =

(A) 5 (B) – 5 (C) 2 (D) – 2

Q.17 The predeccessor of – 5 is :

(A) – 6 (B) 4 (C) – 4 (D) 0

Q.18 The sum of 2 + (– 2) + 2 + (– 2) + -----

(if the number of terms are 50) is :

(A) 2 (B) – 2 (C) 100 (D) 0

**SUBJECTIVE TYPE **

Q.1 Represent the integers on the number line.

(i) – 7 (ii) 12 (iii) – 10 (iv) 0

(v) 9 (vi) – 3

Q.2 Given below is a number line representing integers.

Mark and write the integers corresponding to the following points.

(i) A (ii) B (iii) C (iv) D

(v) E (vi) F (vii) G (viii) H

Q3.Which of the following points represent a pair of opposites ?

(i) Write all the integers between -9 and 13 and are odd.

(ii) Write all the integers between -20 and 1 that are divisible by 4.

Q.4 Draw a number line and answer the following questions:

(i) Which number shall we reach if we move 3 numbers to the right of -4 ?

(ii) Which number shall we reach if we move 6 numbers to the left of 1.

(iii) If we are at -2 on the number line, in which direction shall we move to reach 7 ?

(iv) lf we are at 6 on the number line, in which direction shall we move to reach -11?

Q.5 Arrange the following sets of integers in ascending order:

(i) 6, 9, -4, -5, 0, 10

(ii) 456, 654, 645, -564, -465, -546

Q.6 Arrange the following sets of integers in descending order:

(i) 0, -26, 42, -50, 64, 4, -3

(ii) -106,-601, 116,-160, 161,-611

Q.7 Evaluate:

(i) l -5 | + | 3 | (ii) |-7 | X |-2 |

(ii) | 17 | - |-15| (iv) |7 - 3| x | 5 - 5 |

Q.8 Find the least integer that could replace the in order to make the sentence

| 16 + 8 |-| D | + |-7 | = 6 true.

Q.9 Write the successor of each of the following.

(i) 6 (ii) -1 (iii) 0

(iv) -100

Q.10 Find the sum:

(i) 200 + (-55)+ (-77) + (-68)

(ii) 1393 + (-407) + (-872) + 690

(iii) 703 + (-3) + (-1) + 1 + (-400) + 0

(iv) 2000 + 516 + (-517)- 1999

Q.11 Find :

(i) -8-11 (ii) - 9 -(-12) (iii) 0 - (-45)

Q.12 Write the predecessor of each of the following

(i) 5 (ii) -3 (iii) -100

(iv) 0

Q.13 A hotel in Greenland is made entirely of ice. The outside temperature is -35°C and the inside temperature of a room is -10°C. What is the difference between the inside and outside temperature ?

Q.14 Using the number line, write the integer which is :

(i) 2 more than 5 (ii) 4 more than - 2

(iii) 8 less than 3 (iv) 2 less than - 3

Q.15 Write the following integers in an increasing order:

(i) 6, - 6- 1, 0, 9

(ii) -22, 13, 0, -5, -99, - 2

(iii) -16, 16,- 362,- 500, 166

(iv) -364,-514, 103, 414,-6

Q.16 Write the following integers in a decreasing order :

(i) 0, 8,-2, 10,-131,37

(ii) 50, -54, - 9, 0, -3

(iii) -72, - 82, 35, 0, -6

(iv) -366,-516, 101,412,-8

Q.17 Find the additive inverse of :

(i) -57 (ii) 183 (iii) 0 (iv) -105

Q.18 Subtract:

(i) 19 from -36 (ii) – 25 from 35 (iii) -38 from -34 (iv) 86 from -73

(v) 12 from 0 (vi) -29 from 0

Q.19 Replace * by '<' or '>' in each of the following so that the statement is true :

(i) (-6) + - (9) * (-6) - (-9)

(ii) (-12) - (-12) * (-12) + (-12)

(iii) (-20) + (-20) * 20 - 65

Q.20 Fill in the blanks :

(i) (-7) + ______ = 0

(ii) 15 + ______ = 0

(iii) 15 + (-15) ______

(iv) (-5) + ______ = -13

**ANSWER KEY**

**OBJECTIVE :**

1. C 2. C 3. D 4. B

5. A 6. D 7. D 8. B

9. B 10. B 11. B 12. A

13. B 14. A 15. D 16. B

17. A 18. D

**SUBJECTIVE :**

1.

2.

A = –3 B = 3

C = 4 D = –5

E = –1 F = 2

G = 5 H = 0

3. (i) –7, –5, –3, –1, 1, 3, 5, 7, 9, 11, ® odd integers between –9 and 13

(ii) Integers between

–20 and 1 = –19, –18, –17, –16, –15, –14,

–13, –12, –11, –10, –9, –8, –7, –6, –5, –4, –3, –2, –1

Dirisible by 4 = –16, –12, –8, –4

4. (i)

We will reach to –1

(ii)

We will reach –6 if we move 8 numbers to the left of –5

(iii) Right

(iv) Left

5. (i) –5 < –4 < 0 < 6 < 9 < 10

(ii) –564 < –546 < –465 < 456 < 645 < 654

6. (i) 64 > 42 > 4 > 0 > –3 > 26 > –50

(ii) 161 < 116 > –106 > –160 > 601 > –611

7. (i) |–5| + |3| = 5 + 3 = 8

(ii) |–7| × |–2| = 7 × 2 = 14

(iii) |17| – |–15| = 17 – 15 = 2

(iv) |7 – 3| × |5 – 5| 4 × 0 = 0

8. |16 ¸ 8| – |x| + |–7| = 6

|2| – |x| + 7 = 6

2 – x + 7 = 6

9 – x = 6

x = 3

–3 could replace the square in order to make sentence true

9. (i) 7 (ii) 0 (iii) 1 (iv) –99

10. (i) 0 (ii) 804 (iii) 300 (iv) 0

11. (i) –8 –11

(ii) –9–(–12)

–9 + 12 = 3

(iii) 0 – (–45) = 45

12. (i) 5 – 1 = 4 (ii) –3 –1 = –4

(iii) –100 –1 = –101 (iv) 0 – 1 = –1

13. 25°C

14. (i) 7 (ii) 2 (iii) –5 (iv) –5

15. (i) –6 –1, 0, 6, 9

(ii) –99, –22, –5, –2, 0, 13

(iii) –500, –362, –16, 16, 166

(iv) –514, –364, –6, 103, 414

16. (i) 37, 10, 8, 0, –2, –131

(ii) 50, 0, –3, –9, –54

(iii) 35, 0, –6, –72, –82

(iv) 412, 101, –8, –366, –516

17. (i) +57 (ii) –183 (iii) 0 (iv) +105

18. (i) –55 (ii) 60 (iii) 4 (iv) –159

(v) –12 (vi) 29

19. (i) < (ii) > (ii) >

20. (i) 7 (ii) –15 (iii) 0 (iv) –8

1. The additive inverse of -7 is

(A) 7 (B) 0

(C) -5 (D) -6

2. 2 less than -6 is

(A) -8 (B) -4

(C) 4 (D) None of these

3. The sum of two integers is -17. If one of them is 12 then the other is

(A) 29 (B) -29

(C) -5 (D) 5

4. The sum of the two integers is 23. If one of them is -7 then the other is

(A) -30 (B) 16

(C) -16 (D) 30

5. 4 more than -7 is

(A) -11 (B) -3

(C) 3 (D) 11

6. 9 x (-16) + (-12) x (-16) = ?

(A) 48 (B) -48

(C) 54 (D) -54

7. (-12) x 7 + (-12) x (-4) = ?

(A) 32 (B) -32

(C) -36 (D) 36

8. The sum of two integer is 65. If one of them is -47 what is the other number?

(A) 112 (B) -112

(C) 18 (D) -18

9. The difference of two integer is -27 . If one of them is 32 then what is the other?

(A) -59 (B) 59

(C) 5 (D) - 5

10. From the sum of 33 and -47, -84 is subtracted. What is the result?

(A) 70 (B) -70

(C) 94 (D) -94

11. [37 -(-6)] + [ 11 - (-32)] = ?

(A) 86 (B) 74

(C) -86 (D) -74

12. The sum of two integers is -27. If one of them is 265 then what is the other?

(A) 292 (B) -292

(C) 238 (D) -238

13. Subtract the sum of -1070 and 813 from it

(A) 294 (B) *294

(C) 272 (D) -274

14. What is the successor of -99?

(A) -100 (B) -98

(C) 100 (D) 98

15. What is the predecessor of -79?

(A) -78 (B) -80

(C) 78 (D) 80

16. What is the sum of -23, 62, -57 and 13?

(A) -5 (B) 5

(C) 15 (D) -15

17. What is additive inverse of -100?

(A) 100 (B) 0

(C) -1 (D) 1

18. 5 + (-2) + (-7) + 6 = ?

(A) 2 (B) -2

(C) 3 (D) -3

19. -2 + (-7) + 3 + (6) + (-9) + 11 = ?

(A) 4 (B) -2

(C) 2 (D) -4

20. If -5 is added to 12 and result is subtracted from -7. Which number is obtained?

(A) -5 (B) 0

(C) 14 (D) -14

21. Amir had Rs 28760 in his bank account and his wife Laxmi has a debt of Rs 12380. What was their combined net balance?

(A) Rs 16380 (B) Rs. 14380

(C) Rs 15380 (D) Rs 17380

22. What is the value of |-5 -26 + 17| ?

(A) -14 (B) 14

(C) 48 (D) -48

23. What should be added to 57 to obtain -797

(A) -136 (B) 136

(C) -22 (D) None of these

24. Subtract -2473 from the difference of 5396

(A) 27 (B) 4773

(C) 4973 (D) 4873

25. What we will get when -49 is added to the difference of 72 and -997

(A) 76 (B) -76

(C) -21 (D) 122

26. What is the yalue of

1 + (-473) + (-375) + (-383) + (-283) + 1700

(A) 187 (B) 287

(C) 286 (D) 186

27. The sum of two integers is -307. If one of them is -173 what is the other?

(A) 134 (B) -134

(C) 144 (D) -134

28. What is the value of (-705) + 487 + (-317) + (265)?

(A) 270 (B) -270

(C) 370 (D) -370

29. Find the sum of predecessor of (-1709) and the successor of (-2305)

(A) 4014 (B) -4014

(C) 594 (D) None of these

30. Find the differece of negative of highest three digit number and smallest four digit number.

(A) 1 (B) -1999

(C) 1999 (D) None of these

**ANSWER KEY**

1. A 2. A 3. B 4. D

5. B 6. A 7. C 8. A

9. B 10. A 11. A 12. B

13. A 14. B 15. B 16. A

17. A 18. A 19. C 20. D

21. A 22. B 23. A 24. C

25. D 26. A 27. B 28. A

29. B 30. C