The Other Side of Zero — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "The Other Side of Zero" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "The Other Side of Zero" — 8 important questions with detailed answers for CBSE boar…
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NCERT Solutions for Class 6 Mathematics — The Other Side of Zero. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
The Other Side of Zero — All 8 Questions Solved
Q1. What are integers? Give examples of positive and negative integers.
Integers are whole numbers including zero, positive numbers, and negative numbers
Step 1: Positive integers: 1, 2, 3, 4, 5, ... (greater than zero)
Step 2: Negative integers: -1, -2, -3, -4, -5, ... (less than zero)
Step 3: Zero: 0 (neither positive nor negative)
Step 4: Integers can be represented on a number line
Step 5: Set of integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}
Final Answer: Integers include positive integers (1,2,3...), negative integers (-1,-2,-3...), and zero
Q2. On a number line, which is greater: -5 or -2?
Comparing integers on a number line
Step 1: On a number line, numbers to the right are greater
Step 2: Locate -5 on the left side
Step 3: Locate -2 on the right side of -5
Step 4: Since -2 is to the right of -5, -2 is greater
Step 5: -2 > -5 (Read as: minus 2 is greater than minus 5)
Final Answer: -2 is greater than -5
Q3. What do we use negative numbers for in daily life?
Applications of negative numbers in real life
Step 1: Temperature: Below zero is represented as negative (e.g., -5°C)
Step 2: Bank accounts: Overdraft or debt is shown as negative balance
Step 3: Height: Depth below sea level is negative (e.g., -100 m)
Step 4: Time: Before a reference point can be negative (e.g., -3 seconds before event)
Step 5: Profit/Loss: Loss in business is shown as negative
Final Answer: Negative numbers represent: temperatures below zero, debts, depths below reference, and losses
Q4. Add: 5 + (-3)
Adding a positive and negative integer
Step 1: We need to add 5 and -3
Step 2: On number line, start at 0
Step 3: Move 5 steps to the right (for +5)
Step 4: Then move 3 steps to the left (for -3)
Step 5: Final position is 2
Step 6: 5 + (-3) = 2
Final Answer: 2
Q5. Subtract: 3 - (-2)
Subtracting a negative integer
Step 1: We need to calculate 3 - (-2)
Step 2: Subtracting a negative is the same as adding its positive
Step 3: 3 - (-2) = 3 + 2
Step 4: 3 + 2 = 5
Final Answer: 5
Q6. Arrange the integers in order from smallest to largest: -3, 2, -5, 0, 4
Ordering integers using number line
Step 1: Identify each integer: -3, 2, -5, 0, 4
Step 2: On a number line, leftmost numbers are smallest
Step 3: -5 is the smallest (farthest left)
Step 4: Then -3
Step 5: Then 0
Step 6: Then 2
Step 7: Then 4 (farthest right)
Step 8: Order: -5 < -3 < 0 < 2 < 4
Final Answer: -5, -3, 0, 2, 4
Q7. What is the opposite (additive inverse) of -7?
Finding the additive inverse of a negative integer
Step 1: The additive inverse of a number is what you add to it to get 0
Step 2: For -7, we need to find a number that when added gives 0
Step 3: -7 + ? = 0
Step 4: ? = 7
Step 5: Verification: -7 + 7 = 0 ✓
Step 6: The additive inverse of -7 is +7 or simply 7
Final Answer: 7
Q8. On a number line, show -4 and 4. What is their relationship?
Showing opposite integers on a number line
Step 1: Draw a number line with 0 at the centre
Step 2: Mark 4 at 4 units to the right of 0
Step 3: Mark -4 at 4 units to the left of 0
Step 4: Both are equidistant from 0 (same distance: 4 units)
Step 5: -4 and 4 are opposite integers
Step 6: They are on opposite sides of 0
Step 7: -4 + 4 = 0
Final Answer: -4 and 4 are opposite integers, equidistant from 0 on either side
The Other Side of Zero — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. If a temperature of 5 degrees Celsius *below zero* is represented as -5°C, how would a temperature of 10 degrees Celsius *above zero* be represented?
- A. -10°C
- B. 0°C
- C. 10°C
- D. 5°C
Answer: C. 10°C — Numbers below zero are represented by negative integers, and numbers above zero are represented by positive integers. So, 10 degrees Celsius above zero is +10°C.
MCQ 2. Which of the following numbers is an integer?
- A. 1/2
- B. 0.5
- C. -7
- D. π
Answer: C. -7 — Integers are whole numbers, including positive whole numbers, negative whole numbers, and zero. Fractions and decimals (unless they represent a whole number) are not integers.
MCQ 3. On a number line, which integer is located to the *left* of -3?
- A. -2
- B. 0
- C. -4
- D. 1
Answer: C. -4 — On a number line, numbers decrease as you move to the left. Therefore, -4 is to the left of -3 and is smaller than -3.
MCQ 4. Arrange the following integers in *ascending* order: 5, -2, 0, -7, 3.
- A. -7, -2, 0, 3, 5
- B. 5, 3, 0, -2, -7
- C. 0, -2, 3, -7, 5
- D. -2, -7, 0, 3, 5
Answer: A. -7, -2, 0, 3, 5 — Ascending order means arranging numbers from smallest to largest. Negative numbers are smaller than zero and positive numbers. The further a negative number is from zero, the smaller it is.
MCQ 5. What is the successor of -5?
- A. -6
- B. -4
- C. 0
- D. 5
Answer: B. -4 — The successor of a number is the number immediately following it on the number line, obtained by adding 1. So, the successor of -5 is -5 + 1 = -4.
MCQ 6. A submarine is at 200 meters below sea level. If '0' represents sea level, how would you represent the submarine's position?
- A. 200 m
- B. 0 m
- C. -200 m
- D. 100 m
Answer: C. -200 m — Positions below a reference point (like sea level or zero) are represented by negative numbers. Therefore, 200 meters below sea level is -200 m.
MCQ 7. What is the value of (-8) + 3?
- A. 11
- B. -11
- C. 5
- D. -5
Answer: D. -5 — When adding integers with different signs, find the difference between their absolute values (8 - 3 = 5) and use the sign of the number with the larger absolute value (which is -8, so the result is negative).
MCQ 8. In a quiz, Team A scored -15, 20, 10 in three rounds, and Team B scored 10, -5, 15. Which team scored more?
- A. Team A
- B. Team B
- C. Both scored equally
- D. Cannot be determined
Answer: B. Team B — Team A's total score = -15 + 20 + 10 = 15. Team B's total score = 10 + (-5) + 15 = 20. Since 20 is greater than 15, Team B scored more.
MCQ 9. Which of the following statements is TRUE?
- A. Every positive integer is greater than every negative integer.
- B. Zero is a positive integer.
- C. The greatest negative integer is -10.
- D. The smallest positive integer is 0.
Answer: A. Every positive integer is greater than every negative integer. — Positive numbers are always greater than negative numbers. Zero is neither positive nor negative. The greatest negative integer is -1, and the smallest positive integer is 1.
MCQ 10. A bird is flying at an altitude of 100 meters above sea level. A fish is swimming at a depth of 50 meters below sea level. What is the vertical distance between the bird and the fish?
- A. 50 meters
- B. 100 meters
- C. 150 meters
- D. 200 meters
Answer: C. 150 meters — The bird is at +100 m and the fish is at -50 m. The vertical distance is the difference between their positions: 100 - (-50) = 100 + 50 = 150 meters.
MCQ 11. What is the result of 5 - (-2)?
- A. 3
- B. -3
- C. 7
- D. -7
Answer: C. 7 — Subtracting a negative number is equivalent to adding its positive counterpart. So, 5 - (-2) = 5 + 2 = 7.
MCQ 12. Which number is the additive inverse of 7?
- A. 1/7
- B. 7
- C. -7
- D. 0
Answer: C. -7 — The additive inverse of a number is the number that, when added to the original number, results in zero. For 7, the additive inverse is -7, because 7 + (-7) = 0.
MCQ 13. Starting from -4, if you move 6 units to the right on a number line, and then 3 units to the left, what integer do you reach?
- A. -1
- B. 5
- C. 1
- D. -7
Answer: A. -1 — Starting at -4, moving 6 units to the right means adding 6: -4 + 6 = 2. Then, moving 3 units to the left means subtracting 3: 2 - 3 = -1.
MCQ 14. Compare -10 and -1. Which of the following is correct?
- A. -10 > -1
- B. -10 = -1
- C. -10 < -1
- D. Cannot compare
Answer: C. -10 < -1 — On a number line, numbers increase as you move to the right. Since -1 is to the right of -10, -1 is greater than -10, meaning -10 is less than -1.
MCQ 15. If the current temperature is -3°C and it drops by 5°C, what will be the new temperature?
- A. 2°C
- B. -2°C
- C. 8°C
- D. -8°C
Answer: D. -8°C — A drop in temperature means subtraction. So, the new temperature will be -3°C - 5°C = -8°C.
MCQ 16. In mathematics, what does the term "The Other Side of Zero" primarily refer to?
- A. Positive numbers
- B. Fractions
- C. Negative numbers
- D. Decimal numbers
Answer: C. Negative numbers — "The Other Side of Zero" refers to the numbers located to the left of zero on the number line, which are negative numbers.
MCQ 17. Which integer correctly represents a temperature of 15 degrees Celsius below zero?
- A. 15
- B. -15
- C. 0
- D. 1/15
Answer: B. -15 — Below zero indicates a negative value, so 15 degrees Celsius below zero is represented as -15°C.
MCQ 18. A diver is 25 meters below sea level. How would you represent his position using an integer?
- A. 25
- B. -25
- C. 0
- D. 250
Answer: B. -25 — Positions below sea level are considered negative values, so 25 meters below sea level is represented as -25.
MCQ 19. On a number line, where are negative integers located relative to zero?
- A. To the right of zero
- B. To the left of zero
- C. At zero
- D. Above zero
Answer: B. To the left of zero — By convention, negative integers are placed to the left of zero on a horizontal number line.
MCQ 20. Which of the following represents a loss of ₹750 in a business transaction?
- A. ₹750
- B. -₹750
- C. ₹0
- D. ₹1/750
Answer: B. -₹750 — A loss is represented by a negative integer, so a loss of ₹750 is represented as -₹750.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.