CBSE Important Questions Class 6 Maths Chapter 10 – The Other Side of Zero

Class 6 Maths Chapter 10 The Other Side of Zero is part of the new NCERT textbook Ganita Prakash. It introduces students to negative numbers, the numbers that lie on the left of zero on the number line. Students learn to read integers on a number line, compare and order them, add and subtract them, and understand the additive inverse, which is the same number with the opposite sign.

These CBSE important questions for Class 6 Maths Chapter 10 cover number patterns that go below zero, arranging integers in descending order, a lift moving up and down a building, adding and subtracting positive and negative numbers, deciding when a sum is positive, and finding additive inverses. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 6 Maths Chapter 10 – The Other Side of Zero

The Other Side of Zero (New NCERT)
Easy
Q.
Find
(a) 35 – (20)                      (b) 72 – (90)
(c) (– 15) – (– 18)             (d) (–20) – (13)
(e) 23 – (– 12)                   (f) (–32) – (– 40)
The Other Side of Zero (New NCERT)
Medium
Q.
Start from the Food Court and press +2 in the lift Where will you reach? _________
The Other Side of Zero (New NCERT)
Medium
Q.
Use unmarked number lines to evaluate these expressions:
(a) -125 + (-30) = _________
(b) +105 – (-55) = _________
(c) +80 – (-150) = _________
(d) -99 – (-200) = _________
The Other Side of Zero (New NCERT)
Medium
Q.
Think of an ‘infinite lift’. Does it remind you of a number line? In what ways?
The Other Side of Zero (New NCERT)
Medium
Q.
In the other exercises that you did earlier, did you notice that subtracting a negative number was the same as adding the corresponding positive number?
The Other Side of Zero (New NCERT)
Medium
Q.
Try evaluating the following expressions by similarly drawing or imagining a suitable lift:
(a) -125 + (-30)
(b) +105 – (-55)
(c) +105 + (+55)
(d) +80 – (-150)
(e) +80 + (+150)
(f) -99 – (-200)
(g) -99 + (+200)
(h) +1500 – (-1500)
The Other Side of Zero (New NCERT)
Medium
Q.
​Evaluate 15 – 5, 100 – 10, and 74 – 34 from this perspective.​
The Other Side of Zero (New NCERT)
Medium
Q.
​Comparing Numbers using Floors
Who is on the lowest floor?
1. Jay is in the Art Centre. So, he is on Floor +2.
2. Asin is in the Sports Centre. So, she is on Floor ______.
3. Binnu is in the Cinema Centre. So, she is on Floor ______.
4. Aman is in the toy shop. So, he is on ______.
The Other Side of Zero (New NCERT)
Medium
Q.
Connect the inverses by drawing lines.
The Other Side of Zero (New NCERT)
Medium
Q.
​Number all the Floors in the Building of Fun.
The Other Side of Zero (New NCERT)
Medium
Q.
Fill in the blanks with >, < or = sign.
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
(c) 45 – (– 11) ______ 57 + (– 4)
(d) (– 25) – (– 42) _____ (– 42) – (– 25)
The Other Side of Zero (New NCERT)
Medium
Q.
What do you press to go four floors up? What do you press to go three floors down?
The Other Side of Zero (New NCERT)
Medium
Q.
Can there be a number less than 0? Can you think of any way to have less than 0 of something?
The Other Side of Zero (New NCERT)
Medium
Q.
Give your examples of each rule of Bhramagupta's.
The Other Side of Zero (New NCERT)
Medium
Q.
Can you explain each of Brahmagupta’s rules in terms of Bela’s buildings of fun, or in terms of a number line?
The Other Side of Zero (New NCERT)
Medium
Q.
This string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?
The Other Side of Zero (New NCERT)
Medium
Q.
What could be so special about these grids? Is the magic in the numbers the way they are arranged or both? Can you make more such grids?
The Other Side of Zero (New NCERT)
Medium
Q.
Complete these expressions. Check your answers by thinking about the movement in the mineshaft.
(a) (+40) + _______________ = +200
(b) (+40) + _______________ = -200
(c) (-50)+ _______________ = +200
(d) (-50) + _______________ = -200
(e) (-200) – (-40) = _______________
(f) (+200) – (+40) = _______________
(g) (-200) – (+40) = _______________
The Other Side of Zero (New NCERT)
Easy
Q.
Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
The Other Side of Zero (New NCERT)
Medium
Q.
Give your own examples of each rule.

CBSE Important Questions Class 6 Maths Chapter 10 – The Other Side of Zero

Q1. A sequence follows the pattern: 5, 2, −1, −4, −7, ... If this pattern continues, what will be the sum of the 7th and 8th terms?
(a) 29
(b) −29
(c) 16
(d) −16

Answer: (b) −29
Each term is 3 less than the one before it (5 to 2 is −3, 2 to −1 is −3, and so on).
6th term = −7 − 3 = −10
7th term = −10 − 3 = −13
8th term = −13 − 3 = −16
Sum of the 7th and 8th terms = −13 + (−16) = −29

The sequence 5, 2, -1, -4, -7, -10, -13, -16 marked on a number line

Q2. Four integers P, R and S satisfy the following conditions:
P is 7 more than the inverse of 12.
R is 3 less than the inverse of 4.
S is the sum of the inverses of 6 and 9.
Arrange P, R and S in descending order.
(a) R, P, S
(b) P, S, R
(c) P, R, S
(d) S, P, R

Answer: (c) P, R, S
Here 'inverse' means the additive inverse, that is, the number with the opposite sign.
Additive inverse of 12 = −12, so P = −12 + 7 = −5
Additive inverse of 4 = −4, so R = −4 − 3 = −7
Additive inverses of 6 and 9 are −6 and −9, so S = (−6) + (−9) = −15
On the number line, −5 > −7 > −15.
So the descending order is P, R, S.

P = -5, R = -7 and S = -15 marked on a number line

Q3. A lift starts from the ground floor (0). It goes up 8 floors, then down 12 floors, then up 15 floors, and finally down 6 floors. If the building has 3 basement levels (B1, B2, B3) and 20 floors above ground, on which floor does the lift finally stop?
(a) 3rd floor
(b) B1
(c) 5th floor
(d) B2

Answer: (c) 5th floor
Going up is a positive number and going down is a negative number.
First movement = +8
Second movement = −12
Third movement = +15
Last movement = −6
Net movement = 8 − 12 + 15 − 6 = +5
So the lift finally stops at the 5th floor.

The lift moving up and down and finally stopping at the 5th floor

Q4. In a sequence of integers, each term after the first is obtained by adding (−3) to the previous term. If the 4th term is +5, what is the 2nd term?
(a) −7
(b) −9
(c) 11
(d) 13

Answer: (c) 11
Each term is 3 less than the one before it, so to go backwards we add 3.
4th term = +5
3rd term = 5 + 3 = +8
2nd term = 8 + 3 = +11

Q5. What will you get on subtracting the sum of −4020 and 3040 from −609?
(a) −500
(b) 500
(c) 371
(d) −371

Answer: (c) 371
First find the sum: −4020 + 3040 = −980
Now subtract this sum from −609:
−609 − (−980) = −609 + 980 = 371

Q6. The sum of two integers is 245. If one of them is −139, then the other is
(a) −395
(b) −384
(c) 384
(d) 395

Answer: (c) 384
Let the other number be x.
−139 + x = 245
x = 245 + 139 = 384

Q7. Which sum is positive?
(a) (−56) + (−34)
(b) −59 + 34
(c) −35 + 45
(d) (−57) + 57

Answer: (c) −35 + 45
(a) The sum of two negative integers is always negative: −56 − 34 = −90.
(b) Here the negative number is bigger in value, so the answer is negative: −59 + 34 = −25.
(c) Here the positive number is bigger in value, so the answer is positive: −35 + 45 = +10. ✓
(d) These two are additive inverses of each other, so their sum is 0, which is neither positive nor negative.

Q8. The value of 200 + (−75) + (−88) + 65 is
(a) −102
(b) 102
(c) −28
(d) 28

Answer: (b) 102
Add the positive numbers: 200 + 65 = 265
Add the negative numbers: −75 + (−88) = −163
Now, 265 − 163 = 102

Q9. The value of 105 + (−705) + (−880) + 55 is
(a) 1425
(b) −1425
(c) −1745
(d) 1745

Answer: (b) −1425
Add the positive numbers: 105 + 55 = 160
Add the negative numbers: −705 + (−880) = −1585
Now, 160 − 1585 = −1425

Q10. The additive inverse of the sum of two negative integers is
(a) A negative integer
(b) 0
(c) A positive integer
(d) Neither positive nor negative integer

Answer: (c) A positive integer
The sum of two negative integers is always negative (for example, −3 + (−5) = −8).
The additive inverse of a negative integer is the same number with a positive sign (the additive inverse of −8 is +8).
So the additive inverse will always be a positive integer.

Q11. The additive inverse of the sum of −9854 and 6666 is
(a) 16520
(b) −3188
(c) −16520
(d) 3188

Answer: (d) 3188
First find the sum: −9854 + 6666 = −3188
The additive inverse of −3188 is +3188.

Q12. The additive inverse of the sum of −9853 and 9853 is
(a) 9000
(b) −19706
(c) 0
(d) 19706

Answer: (c) 0
The numbers −9853 and 9853 are additive inverses of each other, so their sum is 0.
The additive inverse of 0 is 0 itself.

Related Study Material on Extramarks

Q.1 A floor is 10 m long and 8 m wide. A square carpet of side 4.5 m is laid on it. Find the area of floor uncovered by the carpet.

Area of rectangular floor = 10m × 8m =80m2Area of square carpet = 4.5m×4.5m =20.25 m2Area of uncovered floor =80m2-20.25 m2 =59.75m2Thus, area of uncovered floor is 59.75 m

Marks:4

Ans

Area of rectangular floor = 10m — 8m =80m2Area of square carpet = 4.5m—4.5m =20.25 m2Area of uncovered floor =80m2-20.25 m2 =59.75m2Thus, area of uncovered floor is 59.75 m2.

Q.2 A rectangular grassy lawn measuring 48 m by 35 m is to be surrounded externally by a path, which is 2.5 m wide. Find the cost of the leveling the path at the rate of 4.50 per sq m.

Let KLMN be a grassy lawn surrounded by the path which is 2.5 m wide.
Area of lawn = 48 ×35
= 1680 m2
Length of lawn including the path = 48 + 2 × 2.5
= 53 m
Breadth of lawn including the path = 35 + 2 × 2.5
= 40 m
Total area of lawn including the path = 53 × 40
= 2120 m2
Area of path = Total area Area of the grassy lawn
= 2120 m2 – 1680 m2
= 440 m2
Cost of leveling the path = 440 × 4.50
Marks:5

Ans

Let KLMN be a grassy lawn surrounded by the path which is 2.5 m wide.
Area of lawn = 48 —35
= 1680 m2
Length of lawn including the path = 48 + 2 — 2.5
= 53 m
Breadth of lawn including the path = 35 + 2 — 2.5
= 40 m
Total area of lawn including the path = 53 — 40
= 2120 m2
Area of path = Total area €“ Area of the grassy lawn
= 2120 m2 – 1680 m2
= 440 m2
Cost of leveling the path = 440 — 4.50
= 1980

Q.3 A marble tile measures 25 cm by 20 cm. To cover a wall of size 4 m by 3 m, the number of required tiles is:

A. 340

B. 270

C. 240

D. 120

Marks:1

Ans

The measure of marble tile = 25 cm by 20 cm
So, area of marble tile = 25 cm × 20 cm
= 500 cm2
Wall size = 4m by 3m

= 4 × 100 cm by 3 × 100 cm
So, wall size = 400 cm by 300 cm
Area of the wall = 400 cm × 300 cm
= 120000 cm2
So, number of tiles = Area of wall/Area of tiles

= 120000/500

= 240

Q.4 Area of a square is 196 cm2. What is its perimeter

A. 14 cm

B. 28 cm

C. 42 cm

D. 56 cm

Marks:1

Ans

Q.5 The perimeter of 12 m wide rectangular field is 104 m. What is its area

A. 240 m2

B. 120 m2

C. 480 m2

D. 160 m2

Marks:1

Ans

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Chapter 1 - Knowing Our Numbers

Chapter 2 - Whole Numbers

Chapter 3 - Playing with Numbers

Chapter 4 - Basic Geometrical Ideas

Chapter 5 - Understanding Elementary Shapes

Chapter 6 - Integers

Chapter 7 - Fractions

Chapter 8 - Decimals

Chapter 9 - Data Handling

Chapter 11 - Algebra

Chapter 12 - Ratio and Proportion

Chapter 13 - Symmetry

Chapter 14 - Practical Geometry

FAQs (Frequently Asked Questions)

The additive inverse of any integer n is -n. When you add a number to its additive inverse, the result is always zero. For example, (+5) + (-5) = 0. In Bela’s Building, pressing +3 and then -3 brings you back to Floor 0. Brahmagupta formalised this property in 628 CE.

Addition moves you in the direction of the number you are adding. Moving right means positive movement; moving left means negative movement. For subtraction, find the movement needed to go from the starting number to the target number using Target Number – Starting Number = Movement Needed.

Each positive token represents +1 and each negative token represents -1. A positive and a negative token together form a zero pair and cancel each other. Combine all tokens, remove all zero pairs, and count what remains. For example, (+5) + (-3): remove 3 zero pairs, 2 positive tokens remain, so the answer is +2.

Exam questions include true/false on integer properties, fill-in-the-blanks on number line position and additive inverse, compare integers using < or >, movement problems using Starting Floor + Movement = Target Floor, word problems on bank balance and temperature, token-based addition and subtraction, and HOTS-level integer grid puzzles.

NCERT textbook exercises focus on direct concept application. Extra questions test inference, multi-step problems, and real-life application in formats like bank balance scenarios, temperature comparisons, and floor movement chains. Practising extra questions prepares students for the higher-order questions that appear in school unit tests and CBSE 2026 assessments.