CBSE Important Questions Class 6 Maths Chapter 6

Important Questions Class 6 Maths Chapter 6 – Integers

Maths is not a subject that is only required in schools but is needed in real life too. In our daily life, we deal with numbers. Numbers can be classified into different groups according to different features.

Chapter 6 of Class 6 Maths is about integers. Integers include 0, natural numbers and negative natural numbers. Integers can be of two types- positive integers (2,5,8 etc.) and negative integers (-2, -5, -8 etc.). Students must practise questions from the chapter to clarify their understanding of the concepts in integers.

Extramarks is a reputed educational company that provides different kinds of study material related to CBSE and NCERT. The subject experts at Extramarks believe in practice, and for this purpose, they have made the document Important Questions Class 6 Maths Chapter 6. It includes several questions related to integers and their solutions. Students may follow the questions and answers to improve their exam preparation.

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Integers Questions for Class 6 Maths CBSE – With Solutions

Experts have collected all the questions from different sources. They have taken help from the textbook, CBSE sample papers, NCERT exemplar and past years’ question papers. Apart from this, they have also solved the questions for the benefit of students. Experienced professionals have further checked the solutions to ensure the best quality for students. So, you can go through the Important Questions Class 6 Maths Chapter 6 to solve the following questions.  

Q1. Write the opposites in the following values given below:

(a) An increase in weight

(b) Distance of 30 km north

(c) Distance of 80 m east

(d) Loss of Rupees 700

(e) 100 metres above sea level

Answer 1

(a) The opposite of the term increase in weight is the decrease in weight.

(b) The opposite of the distance 30 km north is 30 km south.

(c) The opposite of the distance 80 m east is 80 m west.

(d) The opposite of a loss of Rs 700 is the gain of Rs 700.

(e) The opposite of 100 metres above sea level is 100 metres below sea level.

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

(a) An aeroplane is flying at the height of two thousand metres above the surface.

(b) A submarine is travelling at a depth of eight hundred metres below sea level.

(c) A deposit of rupees two hundred.

(d) A withdrawal of rupees seven hundred.

Answer 2 

(a) + 2000 m

(b) – 800 m

(c) + Rs 200

(d) – Rs 700

Question 3. Find the answers to the following terms:

(a) 35 – (20) 

(b) 72 – (90)

(c) (-15) – (-18)

(d) (-20) – (13)

(e) 23 – (-12)

(f) (-32) – (-40)

Answer 3 

(a) 35 – (20) is equal to 15 + (20) – (20)

= 15 + 0 = 15 [(+a) + (-a) = 0]

(b) 72 – 90 can also be represented as, 

72 – (72 + 18), which is equal to,

= 72 – 72 – 18

= So, 0 – 18 = – 18 [a + (- a) = 0]

(c) The (- 15) – (- 18) is also represented as, 

= (- 15) + (as the additive inverse of – 18)

= (-15) + (18) = 3

(d) (- 20) – (13) is equal to,

(- 20) – (13) = – [20 + 13] = – 33

(e) 23 – (- 12) is equal to 23,

23 – (- 12) = 23 + (as the additive inverse of – 12)

= 23 + 12 = 35

(f) (- 32) – (- 40)

(- 32) + (additive inverse of – 40)

= (- 32) + 40 = 8

Question 4.

Fill in the following blanks with >, < or = sign (greater, lesser or equal sign)

(a) (-3) + (-6), (-3) – (-6)

(b) (-21) – (-10), (- 31) + (-11)

(c) 45 – (-11), 57 + (-4)

(d) (-25) – (-42), (-42) – (-25)

Answer 4:

(a) (-3) + (-6) can also be written as – [3 + 6] = – 9 and in, (-3) – (-6) = (-3) + 6 = 3

Here, – 9 is less than 3, So

∴ (- 3) + (- 6) < (- 3) – (- 6)

(b) (-21) – (-10) can also be written as (-21) + 10 = -11 and in, (-31) + (-11) = – (31 + 11) = – 42

Hence, -42 < -11 or -11 > -42 ∴ (-21) , -(-10) >(-31)+ (-11)

(c) 45 – (-11) can also be written as 45 + 11 = 56 and in, 57 + (-4) = 57 -4 = 53

Here, 56 >53

∴ 45 – (-11) > 57 + ( -4)

(d) (-25) – (-42) = -25 + 42 = 17

and in, (-42) – (-25) = -42 + 25 = -17

Here, 17 > -17

∴ (-25) – (-42) > (-42) – (-25).

Question 5. Solve the following terms:

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

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

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

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

Answer 5- 

(a) (- 7) – 8 – (- 25)

(- 7) – 8 – (- 25)

= (- 7) + (the additive inverse of 8) – (- 25)

= (- 7) + (- 8) – (- 25)

= – 15-(-25)

= – 15 + (the additive inverse of – 25)

= -15+ (+25)

= – 15 + (+ 15) + (+ 10)

= 0 + (+ 10) = 10

(b) (- 13) + 32 – 8 – 1

(-13)+ 32-8-1

= (-13)+ 32-9

= (- 13) + 32 + (the additive inverse of 9)

= (- 13) + 32 + (- 9)

= (- 13) + 23 + 9 + (- 9)

= (-13)+ 23 + 0

= (- 13)+ 23

= (-13)+13+10

= 0+ 10 = 10

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

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

= (-15)+ (-90)

= -105

(d) 50-(-40)-(-2) 

= 50 – (-40) – (-2)

= 50 + (the additive inverse of – 40) – (-2)

= 50+ (40)-(-2)

= 90-(-2)

= 90 + (additive inverse of – 2)

= 90 + 2 = 92

Question 6. Write the opposite 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

Answer 6

(a) Decrease in weight

(b) 30 km south

(c) 326 AD

(d) Gain of Rs. 700

(e) 100 m below sea level

Question 7. If we denote the height of a place above the sea level with a positive integer and depth below the sea level with a negative integer, answer the following statements using integers with their appropriate signs: 

(a) 200 m above sea level

(b) 100 m below sea level 

(c) 10 m above sea level

(d) sea level 

Answer 7

 (a) 200 m above sea level = +20 

(b) 100 m below sea level = 100 

(c) 10 m above sea level = +10 

(d) sea level = 0

Question 8. Write all the integers present between the given pairs (also write them in increasing order):

(a) 0 and – 7 (negative)

(b) – 4 and 4

(c) – 8 and – 15

(d) – 30 and – 23.

Answer 8 

(a) 0 and – 7

The integers that occur between the numbers 0 and – 7 in increasing order are: – 6, – 5, – 4, – 3, – 2 and – 1.

(b) – 4 and 4

The integers that occur between the numbers – 4 and 4 in increasing order are: – 3, – 2, – 1, 0, 1, 2 and 3.

(c) – 8 and – 15

The integers present between the numbers – 8 and – 15 in increasing order are: – 14, – 13, – 12, – 11, – 10 and – 9.

(d) – 30 and – 23

The integers present between the numbers – 30 and – 23 in increasing order are: – 29, – 28, – 27, – 26, – 25 and – 24.

Question 9. Write four negative integers which are greater than – 20.

(b) Write four negative integers which are less than -10.

Answer 9 

(a) The four negative integers which are greater than the number 20 are: – 19, – 18, – 17 and – 16.

(b) Four negative integers which are less than – 10 are: 11,- 12,- 13 and -14.

Question 10.

For the below following statements, write True (T) or False (F). If the statement is false, then correct the state­ment.

(a) -8 is present to the right of- 50 on a number line.

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

(c) The smallest negative integer is said to be – 1.

(d) – 26 is larger than the number -25.

Answer 10

(a) The statement is True (T).

(b) The statement is False (F); – 100 is to the left of – 50 on a number line.

(c) The statement is False (F); the greatest negative integer is – 1.

(d) The statement is False (F); – 26 is smaller than – 25.

Question 11. Draw a number line and then answer the following:

(a) Which number will we reach in the number line if we move four numbers to the right of the number -2?

(b) Which number will we reach in the number line if we move five numbers to the left of the number 1?

(c) If we are present at the number -8 on the number line, then in which direction should we move to reach the number -13?

(d) If we are at number -6 on the number line, then in which direction should we move to reach -1 on the number line?

Answer 11

(a) We will reach number 2 if we move four numbers to the right of the number -2.

(b) We will reach the number – 4 if we move five numbers to the left of 1.

(c) We should travel in the left direction to reach the number -13.

(d) We should travel in the right direction to reach -1 on the number line.

Question 12. Amar and Amulya visited two places, A and B, respectively, in the city of Kashmir and recorded the minimum temperatures on a very particular day as –4°C at A and –1°C at point B. Based on this information, which of the following given statement is true?

(A) Point A is cooler than Point B.

(B) Point B is cooler than Point A.

(C) There is a difference of almost two °C in the temperature.

(D) The temperature at A is four °C higher than that at B.

Answer 12

(A) A is cooler than B.

Explanation – We know that, in the case of a negative integer, the big number is smaller.

Question 13. When a following negative integer is subtracted from another negative integer, the sign of the result

(A) is always negative. (B) is always positive.

(C) is never negative. (D) depends on the numerical value of the integers.

Answer 13

The correct option is (D) 

Explanation – It depends on the numerical value of the integers like for example in: (i) – 4 – (-3) becomes -4 + 3 = – 1

(ii) – 6 – (-9) = – 6 + 9

= 3

Question 14. The statement “When an integer is added to itself, the sum is always greater than the integer itself” is

(A) always true.

(B) never true (false).

(C) true only when the integer is positive in nature.

(D) true for only non-negative integers.

Answer 14

The correct answer is an option (C) 

Explanation – Option c is true only when the integer is positive in nature. This can be understood by this example.

 Consider the positive integer,

 5 = 5 + 5 = 10

In the positive integer given above, the sum is greater than the integer.

But on the other hand, in negative integer 

-4 = -4 + (-4)

= – 4 – 4

= – 8

In the negative integer given above, the sum is less than the integer.

Question 15. Which of the following options shows the maximum rise in temperature?

(A) 0°C to 10°C 

(B) –4°C to 8°C

(C) –15°C to –8°C

 (D) –7°C to 0°C

Answer 15:

The correct answer is option (B) –4°C to 8°C

 Explanation: In the  temperature changes given above, B option has more rise in temperature.

 Because the difference between two temperatures = 8 – (-4)

= 8 + 4

= 12°C

Question 16. Add −9568 and −695.

Answer 16. Adding −9568 and −695,

− 9568 + (− 695) = −10263

Hence, the answer is −10,263.

Question 17. Add: 

(a) −19+36

(b) −49+27

Answer 17: (a) Adding −19 and 36,

−19+36−− 17

Hence, the answer is 17.

(b) Adding −49 and 27,

−49+27−−−22

Hence, the answer is −22.

Question 18

 (−14+6)___(−38−(−9)). Use >, <, =

Answer 18: Solving both sides, we get

(−14+6)__(−38−(−9))

−8>−29 

Question 19. Subtract the following:

(a) −842

 from 0

(b) −2959

 from 8158

Answer 19: (a) Subtracting −842 from 0,

0−(−842)=0+842=842

Hence, the answer is 842.

(b) Subtracting −2959 from 8158,

8158−(−2959)=8158+2959=11117

Hence, the answer is 11,117.

Question 20. The sum of the two integers is – 38. Suppose one of them is 240. Find the other.

Answer 20: We know that, addend+addend=sum

From given,

240+X=−38X=−38−240X=−278

Hence, the other number is −278.

Question 21. Find the product of (−27)×18×30.

Answer 21: The product of (−27)×18×30 is

(−27)×30×18=−810×18=−14580

Hence, the answer is −14,580.

Question 22. A class test contained 25 questions, 4 marks are given to students for each correct answer, and (2) marks are given for every wrong answer. A student attempts all questions and 20 of his answers are correct. What is the total score given to the student?

Answer 22: Total questions in the test is =25

Marks which are given for every correct answer =4

Marks are given for every incorrect answer =2

Marks given for the 20 correct answers =20×4=80

Total incorrect answers =(25 – 20)=5

Marks are given for incorrect answers =5×(2)=10

The total score on the test 

=80+(10)=70

Hence, the total score of the student on the test is 70 marks.

Question 23. The temperature of a place at 12:00 noon was found to be +5°C. The temperature increased by three °C in the first hour and then decreased by one °C in the next hour. What will be the temperature at 2:00 pm?  

Answer 23: Initial temperature at 12:00 noon = +5°C 

The temperature in the first hour increased by = three °C and the temperature in the second hour decreased by = one °C 

Temperature at 2:00 pm: +5°C + 3°C – 1°C = 7°C 

Question 24. Using the number line, how do you compare 

(a) two negative integers? 

(b) two positive integers? 

(c) one positive and one negative integer?

Answer 24 (a) On a number line, negative integers are represented by a – sign and are on the left side of 0. Also, the negative integer on the right side is greater than that on the left side. 

(b) On a number line, positive integers are represented by the + sign and are on the right side of 0. Also, the positive integer on the right side is greater than that on the left side. 

(c) On a number line, positive integers are represented by the + sign and are on the right side of 0, and negative integers are represented by the – sign and are on the left side of 0. Also, positive integers are greater than negative integers. 

Question 25. Solve the terms given below- 

• (- 13) + 32 – 8 – 1

• 72 – 90 

• (- 15) – (- 18)

• − 9568 + (− 695) 

Answer 25 

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

= (-13) + 32-9

= (-13) + 32 + (the additive inverse of 9)

= (-13) + 32 + (- 9)

= (-13) + 23 + 9 + (- 9)

= (-13) + 23 + 0

= (-13) + 23

= (-13) +13+10

= 0 + 10 = 10

(b) 72 – 90 

can also be represented as, 

72 – (72 + 18), which is equal to,

= 72 – 72 – 18

= So, 0 – 18 = – 18 [a + (- a) = 0]

(c) The (- 15) – (- 18) is also represented as, 

= (- 15) + (as the additive inverse of – 18)

= (-15) + (18) = 3

(d) − 9568 + (− 695) = −10263

Hence, the answer is −10,263.

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