Haryana Board Class 6 Maths Solutions For Chapter 6 Integers

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers

• The collection of all positive numbers, zero and negative numbers together are called ‘Integers’.
  The set of Integers is denoted by the symbol Z. Z = {………….. -4, -3, -2, -1, 0, 1, 2, 3, 4 …}
• The number without any sign is considered positive number only.
  Eg: 3 is considered + 3
• Brahmagupta (598 AD-670 AD) first used a special sign (-) for negative numbers and stated the rules for dealing with positive and negative quantities.
• The letter “Z” was first used by the Germans because the word for Integers in the Ger- man language is “Zehlen”, which means “Number”.
• Natural numbers, (1,2,3,4,…) are also called positive integers and Whole numbers. {0,1,2,3,4,…) are also called non-negative integers.
  Negative numbers are important to represent just opposite numbers for positive numbers.
• Every integer can be represented on a number line horizontally or vertically.
• Addition and subtraction of integers can be done on number line.
• Every negative integer is always lesser than zero.
• The smallest and the biggest positive integers are +1 and positive infinite (+∞).
• The smallest and the biggest negative integers are negative infinite (-∞) and -1
• The sum of two negative integers is always a negative integer. Eg: -2 + (-3) = -5
• The sum of two positive integers is always a positive integer. Eg: 5 + 7 = 12
• The sum of two integers, one of which is positive and the other is negative, then the sum may be either positive, negative or zero.
  Eg: 12 + (-9) = 3;-12 + 9 = -3;-3 + 3 = 0
• For any integer a, -(-a) = a
• We add the opposite of an integer (additive inverse) to an integer in subtraction.
• Integers are widely used in our daily life i.e., business, engineering, games, temperatures, medicine etc……
• Integers are closed under addition and sub- traction.
• Integers are commutative and associative under addition.
• Integers are not commutative and associative under subtraction.
• We use negative numbers to represent debit, temperature below the 0°C, past periods of time depth below sea level.
• Number Line:

• The numbers on the left side of zero (i.e., less than zero) are called ‘negative numbers’.
• The numbers on the right side of zero (i.e., greater than zero) are called ‘positive numbers’.
• We can show the addition and subtraction of integers on the number line.
• ‘O’ is neither positive nor negative.
• Any two distinct numbers that give zero when added to each other are additive inverse of each other.
  Eg. : 3 and -3
  3 + (-3) = 0
• The subtraction of integers is the same as the addition of their additive inverse.
  Eg. The additive inverse of 7 is -7
  The additive inverse of -8 is 8
• Numbers with a negtative sign are called negative numbers. They are less than zero.
• If we add ‘1’ (one) to a given number we get successor.
• If we subtract ‘one’ from a given number we get predecessor.
• If we move right side of a given number on a number line the value of the number increases and to the left the value decreases.
• If we add a positive number and a negative number we must do subtraction and put the sign of the bigger number.
• The addition of two integers is zero then each one is called additive inverse of the other.

Suppose David and Mohan have started walking from zero position in opposite directions. Let the steps to the right of zero be represented by ‘+’ sign and to the left of zero represented by “” sign. If Mohan moves 5 steps to the right of zero it can be represented as +5 and if David moves 5 steps to the left of zero it can be represented as -5. Now represent the following positions with +or – sign:

a) 8 steps to the left of zero.

Answer. -8

b) 7 steps to the right of zero.

Answer. +7

c) 11 steps to the right of zero.

Answer. +11

d) 6 steps to the left of zero.

Answer. -6

Write the succeeding number of the following:

Write the preceeding number of the following:

Write the following numbers with appropriate signs:

a. 100 m below sea level.

Solution. -100 m

b. 25°C above 0°C temperature.

Solution. + 25°C

c. 15°C below 0°C temperature.

Solution. -15°C.

d. Five numbers less than 0.

Solution. -1, -2, -3, -4, -5

Mark 3, 7,-4,-8,- 1 and 3 on the number line.

Solution.

Compare the following pairs of numbers using > or <.

0 _ 8

-1 _ -15

5 _ -5

11 _ 15

0 _ 6

– 20 _ 2

Solution.

0 > 8

-1 > -15

5 > -5

11 < 15

0 < 6

-20 < 2

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Exercise – 6.1

Question 1. Write the opposites of the following:

a) Increase in weight

b) 30 km north

c) 80 m east

d) Loss of Rs. 700

e) 100 m above sea level

Solution. a) decrease in weight

b) 30 km south

c) 80 m west

d) Profit of Rs. 700

e) 100 m below sea level

Haryana Board Class 6 Maths Integers solutions

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

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

Solution. +2000 metre

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

Solution. -800 metere

c) A deposit of rupees two hundred.

Solution. +Rs. 200

d) Withdrawal of rupees seven hundred.

Solution. -Rs. 700

Question 3. Represent the following numbers on a number line.

a) +5

b) -10

c) +8

d) -1

e) -6

Addition and subtraction of integers Class 6 HBSE

Question 4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:

a. If the point D is + 8, then which point is -8?

Solution. Point F.

b. Is point G is a negative integer or a positive integer?

Solution. It is a negative integer.

c. Write integers for points B and E.

Solution. Integer for point B = +4

Integer for point E = -10.

d. Which point marked on this number line has the least value?

Solution. Point E.

e. Arrange all the points in decreasing order of value.

Solution. D, C, B, A, O, H, G, F, E.

Question 5. Following is the list of temperatures of five places in India, on a particular day of the

a) Write the temperatures of these places in the form of integers in blank column.

Solution.

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?

Solution. Siachin is the coolest place.

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

Solution. Delhi and Ahmedabad.

Question 6. In each of the following pairs, which number is to the right of the other on the number line?

a) 2,9

Solution. The number 9 is to the right of the number 2.

b) -3, -8

Solution. The number -3 is to the right of the number -8.

c) 0,-1

Solution. The number ‘0’(zero) is to the right of the number -1.

d) -11, 10

Solution. The number 10 is to the right of the number -11.

e) -6,6

Solution. The number 6 is to the right of the number -6.

f) 1, -100

Solution. The number 1 is to the right of the

Multiplication and division of integers Class 6

Question 7. Write all the integers between the given pairs (write them in the increasing or

a. 0 and -7.

Solution. -6,-5,-4,-3,-2 and -1.

b. -4 and 4.

Solution. -3, -2, -1, 0, 1, 2 and 3.

C. -8 and -15.

Solution. -14,13,12,-11,-10 and -9.

d. 30 and -23.

Solution. -29,-28,-27,-26,-25 and -24.

Question 8. a. Write four negative integers greater than 20.

Solution. 19, -18,-17 and – 16..

b. Write four negative integers less than -10.

Solution. 11, 12, 13, and – 14.

Question 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.

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)

Question 10. 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. We reach the number ‘2’.

b. Which number will we reach if we move 5 numbers to the left of 1?

Solution. We reach the number – 4.

c. If we are at 8 on the number line, in which direction should we move to reach – 13?

Solution. We should move in the left direction.

d. If we are at 6 on the number line, in which direction should we move to reach – 1?

Solution. We should move in the right direction.

Question 11. Draw a figure on the ground in the form of a horizontal number line as shown below. Frame questions as given in the said example and ask your friends.

1) Which is greater (-2) or (-1)?

Solution. 1.

2) Which is smaller among – 6 and 3?

Solution. -6.

3) Which is the nearest positive integer to zero ?

Solution. 1.

4) Which integer is neither positive nor negative ?

Solution. ‘O’ is neither positive nor negative.

5) How many negative numbers you will find on left side of zero?

Solution. Infinite

6) Write three integers greater than -2.

Solution. -1,0,1.

7) Write five integers lesser than -1.

Solution. -2,-3,-4,-5, -6.

8) Which is the nearest positive integer to -1?

Solution. +1.

Integer number line Class 6 Haryana Board

Question 12. Take two different coloured buttons like white and black. Let us denote one white button by (+1) and one black button by (-1). A pair of one white button (+1) and black button (-1) will denoted zero i.e. [1 + (-1) = 0]

In the following table, integers are shown with the help of coloured buttons.

Let us perform additions with the help of the coloured buttons. Observe the following table and complete it.

Question 13. Find the answers of the following additions:

a. (-11)+(-12)

Solution. (-11) + (-12)

= -11 – 12 = -23.

b. (+10) + (+4)

Solution. 10 + 4 = 14.

c. (32) + (-25)

Solution. -32 + (-25)

= -32 – 25 = -57.

d. (+23) + (+40)

Solution. 23 + 40 = 63.

Question 14. Find the solution of the following:

a. (-7) + (+8)

Solution. -7 + (+8)

= -7 + 7 + 1 = 1.

b. (-9) + (+13)

Solution. (-9) + (+13)

= -9 + 9 + 4 = 4.

c. (+7) + (-10)

Solution. +7 + (-10) = +7 – 10

[∴ -10 = -7 – 3]

= 7 – 7 – 3 = -3.

d. (+12) + (-7)

Solution. (+12) + (-7) = 12 – 7

[∴ 12 = 5 + 7]

= 5 + 7 – 7 = 5.

Question 15. Find the solution of the following additions using a number line:

a) (-2) + 6

Solution.

∴ 2 + 6 = 4

b. (-6) + 2

Solution.

∴ -6 + 2 = -4

Question 16. Make two such questions and solve them using the number line.

Solution. 1) (-5) + 3

∴ 5 + 3 = -2

2) -3 + 5

Question 17. Find the solution of the following without using number line.

a) (+7) + (-11)

Solution. 7 – 11 = -4

b) (-13) + (+10)

Solution. 13 + 10 = -3.

c) (-7)+(+9)

Solution. -7 + 9 = 2.

d) (+10)+(-5)

Solution. 10 – 5 = 5.

Make five such questions and solve them.

Question 18. Find the solution of (-7) + (+3) without using the number line.

Solution. (-7) + (+3) = (-4)

Question 2. Find the solution of (+15) + (-9) without using the number line.

Solution. (+15) + (-9) = (+6)

Question 3. Find the solution of (-20) + (+20) without using the number line.

Solution. (-20) + (+20) = 0

Question 4. Find the solution of (+11) + (-11) without using the number line.

Solution. (11) + (-11) = 0

Question 5. Find the solution of (-5) + (+7) without using the number line.

Solution. (-5) + (+7) = (+2)

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Exercise 6.2

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

a) 3 more than 5.

Solution.

∴ 3 more than 5 is 8.

Word problems on integers for Class 6 HBSE

b) 5 more than -5.

Solution.

∴ 5 more than -5 is ‘0’.

c) 6 less than 2.

Solution.

∴ 6 less than 2 is -4.

d) 3 less than -2.

Solution.

∴ 3 less than 2 is -5.

Question 2. Use number line and add the following integers :

a) 9 + (-6)

Solution.

∴ 9 – 6 = 3

b) 5 + (-11)

Solution.

∴ 5 – 11 = -6.

c) (-1) + (-7)

Solution.

∴ -1 – 7 = -8.

d) -5 + 10

Solution.

∴ -5 + 10 =5 .

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

Solution.

∴ -1 – 2 – 3 = -6.

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

Solution.

∴ – 2 + 8 – 4 = 8 – 6 = 2.

Question 3. Add without using number line:

a) 11 + (-7).

Solution. 11 + (-7)

= 11 – 7

= 4 + 7 – 7 [∴ 11 = 4 + 7]

= 4 + 0 = 4

b) (-13) + (+18)

Solution. (-13) + (+18)

= -13 + 18

= -13 + 13 + 5

[∴ 18 = 13 + 5]

= 0 + 5

= 5

c) (-10) + (+19)

Solution. (-10) + (+19) = -10 + 19

= -10 + 10 + 9

= 0 + 9

= 9

d) (-250) + (+150)

Solution. -250 + 150 = -150 – 100 + 150

[∴ – 250 = -150 – 100]

= -150 + 150 – 100

= 0 – 100

= -100

e) (-380) + (-270)

Solution. (-380) + (-270)

= -380 – 270

= -650

f) (-217)+(-100)

Solution. (-217) + (-100)

= -217 – 100

= -317

Question 4. Find the sum of:

a) 137 and -354

Solution. 137 + (-354) = 137 – 137 – 217

[∴ -354 = -137 – 127]

= 0 – 217

= – 217

b) -52 and 52

Solution. -52 + 52 = 0

c) -312, 39 and 192.

Solution. -312, 39 and 192.

= -300 – 12 + 39 + 192

[∴ -312 – 300 – 12]

= -300 – 12 + 39 + 180 + 12

= -300 + 219 – 81.

d) -50 – 200 + 300

Solution. -50 – 200 + 300

= -250 + 300

= -250 + 250 + 50

[∴ 300 = 250 + 50]

= +50

= 50

Question 5. Find the sum?

a) (-7) + (-9) + 4 + 16

Solution. (-7) + (-9) + 4 + 16

= -16 + 20

= -16 + 16 + 4 (20 = 16 + 4)

= 0 + 4 – 4

b) (37) + (-2) + (-65) + (-8)

Solution. 37 + (-2) + (-65) + (-8) = 37 – 75

= 37 – 75

= -38

Chapter 6 Integers Exercise 6.3

Question 1. Find:

a) 35-(20)

Solution. 35 – 20 = 15 + 20 – 20 (35 = 15 + 20)

= 15 + 0

= 15

b) 72 – (90)

Solution. 72 – 90

= 72 – 72 – 18 [∴ -90 = -72 – 18]

=0 – 18

= -18

c) (-15) – (-18)

Solution. -15 – (-18)

= -15 + 18

= -15 + 15 + 3 [∴ 18 = 15 + 3]

= 0 + 3

= 3

d) (-20)-(13)

Solution. -20 – 13

= -33

e) 23 (12)

Solution. 23 – (-12)

= 23 + 12 = 35 [∴ – x – = +]

f)(-32) – (-40)

Solution. (-32) – (-40)

= -32 + 40

= -32 + 32 + 8

[∴ 40 = 32 + 8]

= 0 + 8

= 8.

Question 2. Fill in the blanks with >, < or = sign.

a) (-3)+(-6) ____ (-3)-(-6)

Solution. L.H.S. = -3 – 6 = -9

R.H.S. = -3 – (-6)

= -3 + 6 = 3

∴ (-3) + (-6) < (-3) – (-6)

b) (-21) – (-10) ____ (31) + (-11)

Solution. L.H.S. = -21 – (-10) = -21 + 10 = -11

R.H.S. = -31 + (-11) = -31 – 11 = -42

= (-21) – (-10) > (-31) + (-11)

c) (45)-(-11) ____ 57 + (-4).

Solution. L.H.S. = 45 – (-11) = 45 + 11 = 56

R.H.S. = 57 + (-4) = 57 – 4 = 53

= 45 – (-11) > 57 + (-4)

d) (-25)-(-42) ____ (-42)-(-25)

Solution. L.H.S. = -25 – (-42) = -25 + 42.

= -25 + 25 + 17

= 0 + 17 = 17

R.H.S. = (-42)-(-25) = -42 + 25

= -17 – 25 + 25

= -17 – 0 = -17

∴ (-25) – (-42) > (-42) – (-25)

Question 3. Fill in the blanks:

a) (-8) + ____ = 0

Solution. (-8) + 8= 0

b) 13 + ____ = 0

Solution. 13 + (-13) = 0

c) 12 + (-12) = ____

Solution. 12 + (-12) = 0

d) (-4) + ____ = -12

Solution. (-4) + (-8) = -12.

e) ____ -15 = -10

Solution. (+5) – 15 – 10

Question 4. Find:

a) (-7) – 8 – (-25)

Solution. (-7) -8 -(-25) = 7 – 8 + 25

= -7 – 8 + 7 + 18 [∴ 25 = 7 + 18]

= -8 + 18

= -8 + 8 + 10

= 0 + 10 = 10

b) (-13) + 32 – 8 – 1

Solution. (-13) + 32 – 8 – 1

= -13 + 32 – 9

= -13 + 23 + 9 – 9 [∴ 32 = 23 + 9]

= -13 + 23

= -13 + 13 + 10

= 0 + 10

= 10

c) (-7)+(-8)+(-90)

Solution. (-7) + (-8) + (-90)

= -7 – 8 – 90

= -15 – 90

= -105

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

Solution. 50 – (-40) – (-2)

50 + 40 + 2 = 90 + 2

= 92

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Very Short Answer Questions

Question 1. Put appropriate symbol > or < in the boxes given between the two integers.

1) – 1………. 0

Solution. -1 < 0

2) -3 …….. -7

Solution. -3 > -7

3)-10 ……. +10

Solution. -10 < +10

Question 2. The temperature recorded in Shimla is -4° c and in Kufri is -6°c on the same day. Which place is colder on that day? Why?

Solution. Temperature recorded in Shimla = -4°C;

Kufri = -6°C

Comparing these: -6 < -4

∴ Kufri is colder than Shimla.

Question 3. Find the sum of:

1) 120 and -274

Solution. The sum of 120 and -274 is

= 120 + (-274)

= -154

2) -68 and 28

Solution. The sum of -68 and 28 is

= -68 + 28

= -40

Question 4. Simplify

1) (-6) + (-10) + 5 + 17

Solution. -6 + (-10) + 5 + 17 = -16 + 22

= 6

2) 30 + (-30) = (-60) + (-18)

Solution. 30 + (-30) + (-60) + (-18)

= [30+(-30)] + [(-60)+(-18)]

= 0 + (-78)

= -78

Question 5. Fill in boxes with <, > or = sign.

1) (-4) + (-5) ____ (-5) – (-4)

Solution.-9 < -1

2) (-16)-(-23) ____ (-6) + (-12)

Solution. 7 > -18

3) 44-(-10) ____ 47+ (-3)

Solution. 54 > 44

Question 6. Fill in the blanks:

1) (-13) + …… = 0

Solution. (-13) + 13 = 0

2) (-16) + 16 =

Solution. (-16) + 16 = 0

3) (-5) + …………. = -14

Solution. (-5) + (-9) = -14

4) ……..+ (2 – 16) = -22

Solution. -8 + (2 – 16) = -22 [∴ 2 – 16 = -14]

Question 7. Arrange the following integers in ascending order and descending order. -1000, 10,-1,-100, 0, 1000, 1, -10

Solution. Ascending order: -1000, -100, -10, -1, 0, 10, 1000 (From smallest to greatest)

Descending order: 1000, 10, 0, 1-, -10, – 100,-1000 (From greatest to smallest)

Question 8. The temperature in Nainital is -5° C and in Shimla is -10° C. In which place is the temperature higher ?

Solution.

The temperature in Nainital is -5°C and temperature in Shimla is -10°C – 5°C is greaterthan -10°C.

∴ The temperature in Nainital is higher than the temperature in Shimla.

Question 9. Simplify (-7)+(-12)+5+12

Solution. (-7) + (-12) + 5 + 12 = [-7 – 12] + [5 + 12]

= -19 + 17

= -2

Question 10. Find 25 + (-21) + (-20) + 17 + (-1).

Solution. 25 + (-21) + (-20) + 17 + (-1)

= 25 + 17 + [-21 – 20 – 1]

= 42 + [-42]

= 42 – 42 = 0

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Short Answer Questions

Question 11. Represent the integers on a number line as given below.

1) Integers lie between -7 and -2.

2) Integers lie between -2 and 5.

Solution. 1) The integers lie between -7 and -2 are -6, -5, -4, -3

2) The integers lie between -2 and 5 are -1, 0, 1, 2, 3, 4

Question 12. Write the following integers in increasing and decreasing order:

1) -7,5,-3

Solution. Increasing order: -7,-3,5

Decreasing order: 5, -3, -7

2) -1,3,0

Solution. Increasing order: -1,0,3

Decreasing order: 3, 0, -1

3) 1,3, -6

Solution. Increasing order: -6, 1, 3

Decreasing order: 3, 1, -6

4) -5, -3, -1

Solution. Increasing order: -5, -3, -1

Decreasing order: -1, -3, -5

Question 13. Write True or False, Correct those that are false:

1) Zero is on the right of -3

Solution. True

2) -12 and +12 represent the same integer on the number line.

Solution. False; Correct answer : -12 is a negative integer and +12 is a positive integer.

3) Every positive integer is greater than zero.

Solution. True

4) (-100) > (+100)

Solution. False; Correct answer: -100 < +100.

Question 14. Find the value of the following using a numberline.

1) (-3) + 5

2) (-5) + 3

Make your own two new questions and solve them using the number line.

Solution. 1) (-3) + 5

First move 3 steps to the left of 0 reach – 3 and then from that point we move 5 steps to the right. We reach the number.

∴ (-3) + 5 = 2

Solution. 2) (-5) + 3

First move 5 steps to the left of 0 reach – 5 and then from that point we move 3 steps to the right. We reach the number – 2.

∴ (-5) + 3 = -2.

Question 15. Add without using number line.

1) 10 + (-3)

2) (-10) + (+16)

3) (-8) + (+8)

Solution.

1) 10+ (-3)

= (7 + 3) + (-3)

= 7 + [3+(-3)]

= 7 + 0 = 7

2) (-10) + (+16)

= (-10) + 10 + 6

= [-10 + 10] + 6

= 0 + 6 = 6

3) (-8) + (+8) = 0

Chapter 6 Integers Long Answer Questions

Question 16. Find all integers which lie between the given two integers. Represent them on number line.

1) -1 and 1

2) -5 and 0

3) -6 and -8

4) 0 and -3

1) -1 and 1

Solution. The integer between -1 and 1 is 0.

2) -5 and 0

Solution. The integers between -5 and 0 are -4, -3, -2, -1.

3) -6 and -8

Solution. The integer between -6 and -8 is -7.

4) 0 and -3

Solution. The integers between 0 and -3 are -1, -2

Properties of integers Class 6 HBSE Maths

Question 17. Add the following integers using number line.

(1) 7 + (-6)

(2) (-8) + (-2)

(3) (-6)+(-5)+(+2)

1) 7 + (-6)

Solution.

First move to the right of 0 by 7 steps to each 7, then move 6 steps to the left of 7 we reach 1.

∴ 7 + (-6) = 1

2) (-8) + (-2)

Solution.

First move to the left of 0 by 8 steps to reach -8, then again move 2 steps to the left of -8 we reach -10.

3) (-6)+(-5) + (+2)

Solution.

First move to the left of 0 by 6 steps to reach – 6.

Again move 5 steps to the left of -6 we reach -11.

Now move 2 steps to the right of -11 we reach -9.

∴ (-6) + (-5) + (+2) = -9.

Question 18. In a quiz competition,where negative score for wrong answer is taken,Team A scored +10, -10, 0, -10, 10,-10 and Team B scored 10,10, -10,0,0,10 in 6 rounds successively. Which team wins the competition? How?

Solution. In a quiz, the score made by team A are +10, -10, 0, -10, 10, -10-

The total score made by team A

= 10 + (-10) + 0 + (-10) + 10 + (-10) = -10

The score made by team B are 10, 10, -10, 0, 0, 10

The total score made by team B

= 10 + 10 + (-10) + 0 + 0 + 10 = 20
Team B scored more than team A.

∴ Team B wins the quiz competition.

Question 19. Find the values of (1) (-3)+(-8)+(-5); (2) (-1)+7+ (-3) using number line.

1) (-3) + (-8) + (-5)

Solution.

First move to the left of 0 by 3 steps to reach – 3.

Again move 8 steps to the left of -3 we reach -11.

Now move 5 steps to the left of -11 we reach -16.

∴ (-3) + (-8) + (-5) = -16

2) (-1) + (7) + (-3)

Solution.

First move to the left of 0 by 1 steps to reach – 1.

Again move 7 steps to the right of -1 we reach 6.

Now move 3 steps to the left of -6 we reach 3.

∴ (-1) + 7 + (-3) = 3

Question 20. Represent the following statements using signs of integers :

1) An aeroplane is flying at a height of 3000 meters.

Solution. +3000 meters (height)

2) The fish is 10 meters below the water surface.

Solution. -10 meters (depth)

3) The temperature in Vijayawada is 35°C above 0°C.

Solution. +35° C (+ more),

4) Water freezes at 0°C temperature.

Solution. 0° C (neither ‘+’ nor ‘-‘)

5) The average temperature at the mount Everest in January is 36°C below zero degree.

Solution. -36° C (less)

6) The submarine is 500 meters below the surface of the sea.

Solution. -500 meters (below)

7) The average temperature at Darjeeling in July is 19°C below zero degree.

Solution. -19° C (less)

8) The average low temperature in Vishakapatnam during January is 18°C.

Solution. -18° C (more)

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Objective Type Questions

Choose the correct answer :

Question 1. Set of integers is denoted by

1. N
2. Z
3. W
4. Q

Answer. 2. Z

Question 2. Write all the integers lie between 0 and -3

1. 1, 2
2. -4, -5
3. -1, -2
4. 4, 5

Answer. 3. -1, -2

Question 3. The sum of two negative integers is always

1. negative
2. positive
3. 0
4. None of these

Answer. 1. negative

Question 4. The sum of two integers one of which is positive and the other is negative then the sum may be

1. positive
2. negative
3. zero
4. any one of the above

Answer. 4. any one of the above

Question 5. Subtract +5 from (-5)

1. 0
2. 10
3. -10
4. 5

Answer. 3. -10

Question 6. 18 – 18 + 1 = …..

1. -4
2. -1
3. 3
4. 1

Answer. 4. 1

Question 7. -2 … 1

1. =
2. ⊥
3. <
4. >

Answer. 3. <

Question 8. Sum of 10 and -16 is …….

1. -6
2. 6
3. 12
4. -26

Answer. 1. -6

Question 9. Choose the correct matching:

1. 1 – d, 2 – b, 3 – c, 4 – a
2. 1 – b, 2 – d, 3 – a, 4 – c
3. 1 – b, 2 – d, 3 – c, 4 – a
4. 1 – a, 2 – d, 3 – b, 4 – c

Answer. 2. 1 – b, 2 – d, 3 – a, 4 – c

Question 10. The lest negative integer is

1. 1
2. -1
3. -7
4. does not exist

Answer. 4. does not exist

Question 11. Subract -8 from 8

1. 19
2. 0
3. 11
4. 16

Answer. 4. 16

Question 12. -4 – 4 + (-4) + (-4) =

1. -16
2. -12
3. 13
4. 84

Answer. 1. -16

Question 13. Additive inver of 7 – 3 is

1. 4
2. -4
3. 8
4. -7

Answer. 2. -4

Question 14. -20 – 82 = …

1. 111
2. -200
3. 100
4. -102

Answer. 4. -102

Question 15. Integer between -1 and + 1

1. 1
2. 2
3. 0
4. 4

Answer. 3. 0

Question 16. -131 + ……… = 0

1. -13
2. 131
3. 117
4. 814

Answer. 2. 131

Question 17. 38 – (-40) = …….

1. 31
2. 2
3. 16
4. 78

Answer. 4. 78

Question 18. -3 – (-3) = ………

1. -9
2. 0
3. 1
4. -2

Answer. 2. 0

Question 19. -8 + (-9) + (+17) =

1. -3
2. 11
3. -1
4. 0

Answer. 4. 0

Question 20. The smallest among -7, 0, 1, 5 is

1. 1
2. 5
3. 0
4. -7

Answer. 4. -7

Question 21. The greater negative integer in the following is

1. -1
2. -4
3. -7
4. -6

Answer. 1. -1

Question 22. …… is neither positive nor negative.

1. 3
2. 1
3. 7
4. 0

Answer. 4. 0

Question 23. Identify true statement from the following

1. -7 is to the left of 0
2. -3 is to the right of 1
3. -7 – 3 = -6
4. -1, -2, -3, -4 ….. are positive integers.

Answer. 1. -7 is to the left of 0

Question 24. The fish is 20 meters below the water surface can be denoted as

1. 21 m
2. -10 m
3. -20 m
4. 20 m

Answer. 3. -20 m

Question 25. Number of integers between 2017 and 2018 is

1. 0
2. 1
3. 3
4. does not exist

Answer. 1. 0

Question 26. -6 – 13 + 19 = …….

1. 10
2. -11
3. 0
4. 8

Answer. 3. 0

Question 27. ….. + (-16) = 20

1. 36
2. 20
3. 10
4. 12

Answer. 1. 36

Question 28. The profit of Rs 200/- is represented as

1. +200
2. -200
3. Both A & B
4. None

Answer. 1. +200

Question 29. 4° C below 0° is represented as

1. +4° C
2. -4° C
3. Both A & B
4. None

Answer. 2. -4° C

Question 30. Positive integers are

1. Whole numbers
2. Natural numbers
3. Both A & B
4. None

Answer. 2. Natural numbers

Question 31. Non negative integers are

1. Natural numbers
2. Either natural numbers or whole numbers
3. Whole numbers
4. Both B & C

Answer. 2. Either natural numbers or whole numbers

Question 32. Number of integers between -5 and 5

1. 10
2. 8
3. 9
4. 11

Answer. 3. 9

Question 33. Identify the false statement from the following

1. Zero is the right side of -3
2. Every positive integer is greater than zero
3. There are infinite integers in the number system
4. All integers are whole numbers

Answer. 4. All integers are whole numbers.

Question 34. The sum of two positive numbers is always

1. Positive
2. Negative
3. Either positive nor negative
4. Neither positive nor negative

Answer. 1. Positive

Question 35. The sum of two negative numbers is always

1. Positive
2. Negative
3. Either positive or negative
4. Neither positive nor negative

Answer. 1. Positive

Question 36. The sum of a positive and a negative number is

1. Positive
2. Negative
3. Either positive or negative
4. All above

Answer. 2. Negative

Question 37. a – (-a) =

1. a
2. 2a
3. 0
4. \(a^2\)

Answer. 2. 2a

Question 38. The biggest among -6, 0, 7, 1, -7, -9 is

1. -9
2. -7
3. 7
4. 0

Answer. 3. 7

Question 39. Add (-5) + (-5) + (-5) + 0

1. 15
2. -5
3. 0
4. -15

Answer. 4. -15

Question 40. Add the number 5 to additive inverse of -8 is

1. 11
2. -1
3. 1
4. 0

Answer. 2. -1

Question 41. Subtract 7 from additive inverse of -8 is

1. -1
2. 15
3. 1
4. -15

Answer. 3. 1

Question 42. Add additive inverse of 6 and additive inverse of -5

1. 1
2. -1
3. 11
4. -11

Answer. 2. -1

Question 43. Simplify 30 + (-30) + (-70) + 70 + 0

1. 100
2. 200
3. 0
4. 10

Answer. 3. 200

Question 44. Successor of -7 is ………

1. -4
2. -9
3. -2
4. -6

Answer. 4. -6

Question 45. Predecessor of 12 is ……

1. 1
2. 11
3. 13
4. 10

Answer. 2. 11

Question 46. Five numbers less than ‘0’ is ……

1. -1
2. -3
3. -4
4. -5

Answer. 4. -5

Question 47. The opposite of 2 km south is ………

1. 2 km south
2. 2 km east
3. 2 km north
4. none

Answer. 3. 2 km east

Question 48. 12 + ……… = 12

1. 0
2. 1
3. 4
4. 3

Answer. 1. 0

Question 49. (-4) + (+3) = …….

1. 7
2. 3
3. -1
4. 1

Answer. 3. -1

Question 50. -11 + (-12) = ……

1. -23
2. 23
3. 4
4. 1

Answer. 1. -23

Question 51. (-1) + (0) = ……

1. 4
2. 1
3. 0
4. -1

Answer. 4. -1

Question 52. (-9) + (+4) + (-6) + (+3) = ………

1. 6
2. -8
3. -7
4. 0

Answer. 2. -8

Question 53. -8 – (-10) = ……….

1. 2
2. -2
3. 10
4. 8

Answer. 1. 2

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Fill in the blanks:

Question 54. 3 – 4 – 10 = ……….

Answer. -17

Question 55. a + (-a) ……….

Answer. 0

Question 56. 6 + (-10) + 5 + 17 = ………..

Answer. +6

Question 57. -16 – (-23)…. -6 + (-12) (Use >, < or =)

Answer. >

Question 58. …….. + (-51) = 100

Answer. 151

Question 59. Number of integers lying between-3 and 3 is ………

Answer. 5

Question 60. By arranging the following numbers in descending order, the middle integer is 7,8,0,-6,-5,-4,3 …………

Answer. 0

Question 61. Subtract-10 from – 10, we get ……….

Answer. 0

Question 62. Additive inverse of 17 is ……

Answer. +17

Question 63. ………. is neither positive nor negative integer.

Answer. 0

Question 64. (-4) + 6 …….(7-1) (use > or <)

Answer. <

Question 65. 35 – (20) …………

Answer. 15

Question 66. 12 + (-7) = …………….

Answer. 5

Question 67. (-6) + (-2) = ……….

Answer. -8

Question 68. 5 + (12) + 0 = ……….

Answer. 17

Question 69. ……………… is the successor of 7.

Answer. 8

Question 70. The predecessor of -2 is ………

Answer. -3

Question 71. 0. ………. 8 (use < or >)

Answer. <

Question 72. The collection of numbers 1, 2, 3, 4, …. are called …… numbers.

Answer. natural

Question 73. The sum of 137 and -137 is …………..

Answer. 0

Question 74. (-7) + (-3) + (+3) + (+7) = ……….

Answer. 0

Question 75. The loss of 200 in a business is represented as ……..

Answer. -200

Question 76. At a particular place morning temperature is 30°C. It has increased by 6°C by lunch time. At lunch time the temperature. ……………

Answer. 36°C

Question 77. The temperature recorded in Jammu at 6 o’ clock was 7°C. Every one hour the tempera- ture decreases by 2°C. At 10 o’ clock the temperature is …..

Answer. -1°C

Question 78. 5 + (-2) + (-1)= …….

Answer. 2

Question 79. The nearest positive integer to zero is ……..

Answer. +1

Question 80. Which is greater (-2) or (-1) ……….

Answer. -1

Question 81. Which is smaller 3 and -5 ………

Answer. -5

Question 82. The additive inverse of (-9) is ………

Answer. 9

Question 83. The depth below the sea level is denoted by ……. numbers.

Answer. negative

Question 84. Write the number between the least positive integer and the greatest negative integer is ……..

Answer. 0

Question 85. Use > or < in the box (-4) ……… (-10)

Answer. >

86. The subtraction of integers is the same as the addition of their ………

Answer. additive inverse

Haryana Board Class 6 Maths Solutions For  Chapter 6 Integers Match the following:

Question 87.

Answer. 1-E, 2-D, 3-A, 4-B, 5-C