Integers are the set of all positive numbers, negative numbers, and zero, written as ... -4, -3, -2, -1, 0, 1, 2, 3, 4 ... They extend the number line in both directions from zero. Class 6 Maths Chapter 10 The Other Side of Zero introduces integers through real-life models: building floors, bank balances, sea level, and temperature.
CBSE important questions class 6 maths chapter 10 on this page cover every question type from the Ganita Prakash textbook. You get extra questions, worksheet-style practice, short notes, and solutions in one place.
Most students struggle with comparing negative integers and with subtraction involving negatives. A student who knows that -5 is smaller than -2, handles number line questions without losing marks. A student who knows that subtracting a negative is the same as adding the positive solves token model questions in seconds. All questions and solutions are available section by section below.
Key Takeaways
| Topic |
What to Know |
| Integers |
All positive numbers, negative numbers, and zero |
| Zero |
Neither positive nor negative |
| Number Line |
Negative numbers are to the left of zero; positive to the right |
| Additive Inverse |
A number and its inverse always add up to zero |
| Addition |
Starting Position + Movement = Target Position |
| Subtraction |
Target Position - Starting Position = Movement Needed |
| Real-life uses |
Bank credits/debits, sea level heights, temperature in degrees C |
| Brahmagupta |
First to give formal rules for integers (628 CE) |
Introduction to The Other Side of Zero: Class 6 Chapter 10
Before this chapter, students had only seen numbers on the right side of zero: 0, 1, 2, 3 ... But the number line is not a ray. It extends in both directions. Numbers to the left of zero carry a minus sign and are called negative numbers.
The chapter uses Bela's Building of Fun as its opening model. The building has floors above and below the ground. The ground floor is Floor 0. Floors above are +1, +2, +3 and floors below are -1, -2, -3. This model makes negative numbers concrete before any rules are introduced.
Key facts from the Ganita Prakash book: a number with a '+' sign is positive; a number with a '-' sign is negative; zero is neither positive nor negative; integers are ... -4, -3, -2, -1, 0, 1, 2, 3, 4 ...
CBSE Important Questions for Class 6 Maths
Very Short Answer Questions on The Other Side of Zero
One-mark questions are common in class tests and unit assessments. These ncert class 6 maths the other side of zero extra questions test direct recall of definitions and basic operations.
- What is the additive inverse of +7? -7. Because (+7) + (-7) = 0.
- Is zero a positive integer or a negative integer? Zero is neither positive nor negative.
- Which number is smaller: -5 or -2? -5, because it is further to the left on the number line.
- What is (-3) + (+3)? 0. They are additive inverses of each other.
- Write the integer for: 4 floors below the ground. -4.
- What is the additive inverse of 0? 0. Because 0 + 0 = 0.
- On the number line, where do all negative integers lie? To the left of zero.
- If Floor A = -12, Floor D = -1, and Floor E = +1, what are Floors B, C, F, G, and H? B = -9, C = -6, F = +2, G = +6, H = +11.
Short Answer Questions on The Other Side of Zero
These 2-3 mark questions test both concept and calculation. These are the class 6 the other side of zero extra questions that appear most often in school tests and periodic assessments.
1. Determine whether each statement is true or false.
(a) The smallest natural number is zero. (b) Zero is not an integer because it is neither positive nor negative. (c) The sum of two negative integers is always less than both integers. (d) Since 5 > 3, it follows that -5 > -3.
(a) False. The smallest natural number is 1. (b) False. Zero is an integer. Integers include all positive numbers, negative numbers, and zero. (c) True. For example, (-1) + (-10) = -11, which is less than both -1 and -10. (d) False. Since 5 > 3, we get -5 < -3.
2. Fill in the blanks.
(a) On the number line, -15 is positioned to the ____ of zero. (b) The additive inverse of -1 is ____. (c) (-11) + (-2) + (-1) = ____.
(a) Left. (b) +1. (c) -14.
3. List five integers greater than -150 but less than -100. -101, -102, -103, -104, -105 (any five integers from this range are correct).
4. Evaluate.
(a) (+4) + (-3) + (-2) (b) (-1) + (+2) + (-3)
(a) -1. (b) -2.
Extra Questions on The Other Side of Zero Class 6
These the other side of zero class 6 extra questions go beyond the textbook exercises. They are commonly asked in school assessments and periodic tests across CBSE 2026 schools.
1. You start from Floor +2 and press -3 in the lift. Write an expression and find where you reach. (+2) + (-3) = -1. You reach Floor -1, the Toy Store.
2. Starting from different floors, find three movements needed to reach Floor -5. (+1) + (-6) = -5 (-2) + (-3) = -5 0 + (-5) = -5
3. Write all integers between -4 and +4 in increasing order. -3, -2, -1, 0, 1, 2, 3.
4. Give three numbers whose sum is -8. -5, 7, -10. (Other combinations are also correct.)
5. Evaluate.
(a) 8 - 13 (b) (-8) - 13 (c) (-13) - (-8) (d) (-13) + (-8)
(a) -5. (b) -21. (c) -5. (d) -21.
Class 6 Maths The Other Side of Zero Extra Questions: Positive and Negative Numbers
Understanding when a number is positive, negative, or zero is the foundation of this chapter. These extra questions on the other side of zero class 6 test that foundation directly.
1. If profit is considered positive, express these as integers.
(a) Profit of Rs 80. (b) Loss of Rs 66.
(a) +80. (b) -66.
2. If depth is considered positive, express these as integers.
(a) 25 metres deep. (b) 45 metres in height.
(a) +25. (b) -45.
3. The sum of two positive integers is always positive. What about (negative) + (negative)? The sum of two negative integers is always negative. For example, (-3) + (-4) = -7.
4. What is (positive) - (negative)? Always positive. Subtracting a negative is the same as adding the corresponding positive. For example, (+8) - (-2) = (+8) + (+2) = +10.
Important Questions on Integers and Zero
These questions test comparison and computation with integers. They appear in fill-in-the-blank and short-answer formats in the the other side of zero class 6 question paper pattern.
1. Is there a smallest negative integer? No. Negative integers go on infinitely in the negative direction: -1, -2, -3, ...
2. Compare using < or >.
(a) -2 __ +5 (b) -5 __ -3 (c) 0 __ -4 (d) +6 __ -6
(a) -2 < +5. (b) -5 < -3. (c) 0 > -4. (d) +6 > -6.
3. Imagine the Building of Fun with more floors. Fill in < or >.
(a) -10 __ -12 (b) +17 __ -10 (c) -25 __ -7
(a) -10 > -12. (b) +17 > -10. (c) -25 < -7.
4. Evaluate.
(a) -5 + 0 (b) 7 + (-7) (c) -10 + 20 (d) 10 - 20 (e) 7 - (-7) (f) -8 - (-10)
(a) -5. (b) 0. (c) +10. (d) -10. (e) +14. (f) +2.
Important Questions on Bela's Building of Fun
Bela's Building of Fun is the chapter's central model. The ground floor is Floor 0. The lift uses + to go up and - to go down. These class 6 maths chapter 10 the other side of zero extra questions are directly based on the Ganita Prakash textbook model.
1. The Food Court is on Floor +1. You press +2 in the lift. Where do you reach? (+1) + (+2) = +3. You reach the Book Store on Floor +3.
2. You are on the ground floor and by mistake press +3. What do you press to cancel it and return to Floor 0? Press -3. Because (+3) + (-3) = 0. The number -3 is the additive inverse of +3.
3. Complete: Starting Floor + Movement = Target Floor.
(a) (+4) + (-3) = ? (b) (-1) + (+2) = ? (c) 0 + (-2) = ?
(a) +1. (b) +1. (c) -2.
4. Write the inverses of: +4, -4, -3, 0, +2, -1. -4, +4, +3, 0, -2, +1.
Number Line Questions from The Other Side of Zero
The number line is the visual heart of this chapter. These the other side of zero class 6 extra questions with solutions cover movement-based thinking directly from the book.
1. From 5, you wish to go to 9. How many steps must you travel? 4 steps forward. So 5 + 4 = 9.
2. From 9, you wish to go to 3. What is the movement? 3 - 9 = -6. Move 6 steps backward.
3. From 3, you wish to go to -2. What is the movement? -2 - 3 = -5. Move 5 steps backward.
4. Is 2 > -3? Why? Yes. On the number line, 2 is to the right of -3, so 2 > -3.
5. Use an unmarked number line to evaluate.
(a) -125 + (-30) (b) +105 - (-55) (c) +80 - (-150) (d) -99 - (-200)
(a) -155. (b) +160. (c) +230. (d) +101.
Questions on Comparing Integers
1. Write all integers between -8 and -15 in increasing order. -14, -13, -12, -11, -10, -9.
2. Write all integers between 0 and -7 in increasing order. -6, -5, -4, -3, -2, -1.
3. Fill in < or >.
(a) (-11) + (-15) __ 11 + 15 (b) (-71) + (+9) __ (-81) + (-9) (c) -101 __ -102
(a) (-11) + (-15) = -26 and 11 + 15 = 26, so <. (b) (-71) + (+9) = -62 and (-81) + (-9) = -90, so >. (c) -101 > -102.
Questions on Additive Inverse and Zero Pairs
Additive inverse questions appear in every the other side of zero class 6 question paper pattern. These cover both direct recall and application.
- What is the additive inverse of -543? +543. Because (-543) + (+543) = 0.
- Connect each number with its additive inverse: +9, +7, -8, -5 with -9, +8, -7, +5. +9 pairs with -9. +7 pairs with -7. -8 pairs with +8. -5 pairs with +5.
- If Basant is at Floor +4 and presses -4, where does he reach? Floor 0. Because (+4) + (-4) = 0.
- Evaluate: (+3) - (-3). (+3) + (+3) = +6. Subtracting a negative is the same as adding its positive.
Questions on Addition of Integers
These questions cover Brahmagupta's rules for addition as taught in the CBSE 2026 syllabus. The class 6th maths chapter the other side of zero solutions for addition follow these rules exactly.
1. Check whether these are true.
(a) 3 + (0 + 9) = (3 + 0) + 9 (b) 34 + {90 + (-11)} = (34 + 90) + (-11)
(a) LHS = 3 + 9 = 12; RHS = 3 + 9 = 12. True. (b) LHS = 34 + 79 = 113; RHS = 124 + (-11) = 113. True.
2. Evaluate.
(a) 79 - 68 + 28 - (-32) (b) 153 + 218 - {29 - 367}
(a) 79 - 68 + 28 + 32 = 71. (b) 153 + 218 - (-338) = 153 + 218 + 338 = 709.
3. Complete the additions.
(a) (+40) + __ = +200 (b) (+40) + __ = -200 (c) (-50) + __ = +200 (d) (-50) + __ = -200
(a) +160. (b) -240. (c) +250. (d) -150.
Questions on Subtraction of Integers
1. Complete these expressions.
(a) (+1) - (+4) = ? (b) (0) - (+2) = ? (c) (+4) - (-3) = ? (d) (-1) - (+2) = ? (e) (-2) - (-2) = ?
(a) -3. (b) -2. (c) +7. (d) -3. (e) 0.
2. Complete the subtractions.
(a) (-5) - (-7) (b) (+10) - (+13) (c) (+3) - (+8)
(a) +2. (b) -3. (c) -5.
3. Evaluate (-200) - (-40) and (+200) - (+40). (-200) - (-40) = -200 + 40 = -160. (+200) - (+40) = +160.
Token Model Questions and Answers
The token model uses green (+) and red (-) tokens. A positive token and a negative token together form a zero pair and cancel each other. These the other side of zero class 6 extra questions worksheet items directly reflect the textbook's Section 10.2.
1. Complete the additions using tokens.
(a) (+6) + (+4) (b) (-3) + (-2) (c) (+5) + (-7) (d) (-2) + (+6)
(a) +10. Six positive and 4 positive = 10 positive tokens. (b) -5. Three negative and 2 negative = 5 negative tokens. (c) -2. Remove 5 zero pairs, 2 negative remain. (d) +4. Remove 2 zero pairs, 4 positive remain.
2. Evaluate the following using tokens.
(a) (+10) - (+7) (b) (-8) - (-4) (c) (+9) - (+12) (d) (-5) - (-7)
(a) +3. (b) -4. (c) -3. (d) +2.
3. Subtract: -3 - (+5). How many zero pairs do you need to add? Result is -8. You need to add 5 zero pairs before you can take away 5 positive tokens.
4. Evaluate: (+8) - (-7). +15. Add 7 zero pairs, then take away 7 negative tokens. 8 + 7 = 15 positive tokens remain.
The Other Side of Zero Class 6 Worksheet with Answers
This the other side of zero class 6 worksheet with answers section covers mixed question types most commonly seen in school tests and CBSE 2026 assessments.
True or False:
The sum of two negative integers is always negative. True. -5 > -2. False. Zero has no additive inverse. False. The additive inverse of 0 is 0. All negative numbers are to the right of zero on the number line. False.
Fill in the Blanks:
The integers between -4 and 0, in increasing order, are __, __, __. Answer: -3, -2, -1. (-7) - (-9) = __. Answer: +2. The additive inverse of +18 is __. Answer: -18. Starting Floor +3, movement -5, Target Floor = __. Answer: -2.
Match the Following:
| Situation |
Integer |
| 20 metres above sea level |
+20 |
| 15 metres below sea level |
-15 |
| Profit of Rs 50 |
+50 |
| Loss of Rs 30 |
-30 |
| Temperature 5 degrees C below zero |
-5 |
Questions on Bank Balance, Credits and Debits
Section 10.3 of the Ganita Prakash textbook uses banking to show integers in real life. Credits are positive; debits are negative. These are the most application-based the other side of zero class 6 important questions.
- You start with Rs 0. Credits of Rs 30, Rs 40, and Rs 50. Debits of Rs 40, Rs 50, and Rs 60. What is your balance? Credits = Rs 120. Debits = Rs 150. Balance = 120 - 150 = -Rs 30.
- You start with Rs 0. Debits: Rs 1, 2, 4, 8, 16, 32, 64, 128. Then one credit of Rs 256. What is your balance? Total debits = Rs 255. Credit = Rs 256. Balance = Rs 1.
- You open a bank account with Rs 100. Next day you deposit Rs 60. Then you pay Rs 30. Then you make a purchase of Rs 150. What is your balance? After deposit: Rs 100 + Rs 60 = Rs 160. After paying Rs 30: Rs 160 - Rs 30 = Rs 130. After purchase: Rs 130 - Rs 150 = -Rs 20 (negative balance).
- Why is a negative bank balance possible? What happens in this situation? Some banks allow temporary negative balances. The bank charges interest or a fee when the balance goes below zero.
Questions on Heights, Sea Level and Temperature
Geography and temperature questions appear regularly in Class 6 tests. Heights above sea level are positive; heights below are negative. Temperatures above 0 degrees C are positive; below 0 degrees C are negative.
- How would you represent a depth of 20 metres below sea level and an elevation of 15 metres above sea level? 20 metres below sea level = -20 m. 15 metres above sea level = +15 m.
- Write these heights in decreasing order: A = +1500 m, B = -500 m, C = +300 m, D = -1200 m. A, C, B, D.
- Match temperature with time: 14 degrees C at 02:00 p.m., 8 degrees C at 11:00 a.m., -2 degrees C at 11:00 p.m., -4 degrees C at 02:00 a.m. 14 degrees C: 02:00 p.m. 8 degrees C: 11:00 a.m. -2 degrees C: 11:00 p.m. -4 degrees C: 02:00 a.m.
- Name any places in India where temperatures sometimes go below 0 degrees C. Leh, Kargil, Drass, Shimla, Srinagar, and high-altitude areas in Himachal Pradesh and Uttarakhand. These places are at high altitudes where temperatures fall below the freezing point of water in winter.
Brahmagupta's Rules: Important Questions
Brahmagupta was the first mathematician to give clear, formal rules for all integers in his work Brahma-sputa-siddhanta, written in 628 CE. These rules form the basis of modern integer arithmetic taught in the CBSE 2026 syllabus.
Key rules for addition: Sum of two positives is positive: 2 + 3 = 5. Sum of two negatives: add without signs, place minus: (-2) + (-3) = -5. Adding a positive and a negative: subtract the smaller from the larger, keep the sign of the larger: -5 + 3 = -2. A number plus its inverse is zero: 2 + (-2) = 0.
Key rules for subtraction: Subtracting a negative number is the same as adding its positive: 2 - (-3) = 2 + 3 = 5. Subtracting a number from itself gives zero: 2 - 2 = 0.
Practice questions:
- Use Brahmagupta's rules to evaluate: -5 + 3. Subtract smaller (3) from larger (5), keep sign of 5 (negative): -2.
- Use Brahmagupta's rules to evaluate: (+6) - (-9). Subtracting a negative is the same as adding its positive: (+6) + (+9) = +15.
- Why did Brahmagupta's work matter? He was the first to treat positive numbers, negative numbers, and zero as equally valid numbers. His rules are essentially what we still use today.
The Other Side of Zero Class 6 Notes
These the other side of zero class 6 notes are aligned to the CBSE 2026 syllabus and the Ganita Prakash textbook. Use them for last-minute revision before tests.
Integers are all positive numbers, negative numbers, and zero: ... -4, -3, -2, -1, 0, 1, 2, 3, 4 ... Zero is neither positive nor negative. It is the reference point. Number line: smaller numbers are to the left; larger numbers are to the right. So -5 < -3 < 0 < 2 < 5. Additive inverse: for every integer n, its additive inverse is -n, and n + (-n) = 0. Addition rule: Starting Position + Movement = Target Position. Subtraction rule: Target Position - Starting Position = Movement Needed. Converting subtraction to addition: subtracting a number is the same as adding its additive inverse. For example, (+8) - (-2) = (+8) + (+2) = +10.
Real-life applications: Above sea level: positive. Below sea level: negative. Bank credit: positive. Bank debit: negative. Temperature above 0 degrees C: positive. Below 0 degrees C: negative. Floors above ground: positive. Floors below ground: negative.
For geometry-based formula support, visit Geometry Formulas.