The Other Side of Zero — Mastery

Q1. Which of the following everyday situations naturally needs a number 'less than 0'?

• A. Counting the books on a shelf.
• B. Recording a temperature of 5 degrees below zero in Shimla.
• C. Counting the pages of a notebook.
• D. Listing the integer numbers between 2 and 7.

Q2. What is the central question that the chapter 'The Other Side of Zero' sets out to investigate?

• A. How to multiply large numbers quickly.
• B. How to draw a perfect circle.
• C. Whether there exist numbers to the left of 0 on the number line.
• D. How to count atoms in a glass of water.

Q3. In Bela's Building of Fun, the Toy Store is on Floor −1 and the Book Store is on Floor +3. Which of the following is correct?

• A. Both are above the ground floor.
• B. Both are below the ground floor.
• C. Toy Store is one floor below ground; Book Store is three floors above ground.
• D. Toy Store is three floors below ground; Book Store is one floor above ground.

Q4. Bela's Building of Fun has 6 floors above the ground and 5 floors below. Including the ground floor, what is the range of floor numbers in the building?

• A. 0 to +11.
• B. −5 to +6.
• C. −6 to +5.
• D. −11 to +11.

Q5. Evaluate 0 + (+2) using the Building of Fun.

• A. −2
• B. 0
• C. +2
• D. +20

Q6. According to Brahmagupta's Rule of Addition, the sum of two positive numbers is

• A. Always negative.
• B. Sometimes positive, sometimes zero.
• C. Always positive.
• D. Always zero.

Q7. What is the additive inverse of −543?

• A. −543
• B. 0
• C. +543
• D. +1086

Q8. Match each number with its additive inverse: +5, −7, −8, +9. Which set of inverses is correct?

• A. −5, +7, +8, −9.
• B. +5, −7, −8, +9.
• C. −5, −7, +8, −9.
• D. +5, +7, −8, +9.

Q9. Compare −2 and +5: which is greater?

• A. −2 > +5, because 2 is smaller than 5.
• B. −2 = +5.
• C. −2 < +5, because every positive is greater than every negative.
• D. Cannot be compared.

Q10. Three statements about the integer number line: I. Smaller numbers lie to the left of larger numbers. II. −3 < 2 because −3 is to the left of 2. III. −5 < −3 because −5 is to the left of −3. Which are correct?

• A. I and II only.
• B. II and III only.
• C. I and III only.
• D. All three.

Q11. Subtraction in this chapter is defined as 'finding the missing number to be added'. Which of these subtractions matches this meaning?

• A. 10 − 6 = ? matches the question '6 + ? = 10', so ? = 4.
• B. 10 − 6 = ? matches '10 + ? = 6', so ? = −4.
• C. 10 − 6 = ? matches '10 × ? = 6', so ? = 0.6.
• D. 10 − 6 = ? matches '6 × ? = 10', so ? = 1.67.

Q12. On the number line, if you wish to travel from 5 to 9, how far must you go?

• A. 4 steps forward (to the right).
• B. 4 steps backward (to the left).
• C. 14 steps forward.
• D. 9 steps backward.

Q13. On the number line, you wish to travel from 9 to 3. How far must you move, and what subtraction does this match?

• A. +6, and 3 − 9 = 6.
• B. −6, and 3 − 9 = −6.
• C. +12, and 9 − 3 = 12.
• D. 0, and 9 − 3 = 0.

Q14. On the number line, you wish to travel from 3 to −2. How many steps and in which direction?

• A. 5 steps to the right.
• B. 5 steps to the left.
• C. 1 step to the left.
• D. 1 step to the right.

Q15. The lift attendant's pocket has 5 green tokens and 3 red tokens. Using the token model, on which floor is he?

• A. Floor +8.
• B. Floor −2.
• C. Floor +2.
• D. Floor −8.

Q16. In the token model, why do we sometimes add an extra zero pair before performing a subtraction?

• A. Because the value changes when we add a zero pair.
• B. Because the teacher wants more colourful tokens on the table.
• C. Because there may not be enough tokens of the right colour to take away, and a zero pair adds no value.
• D. Because subtraction is impossible without zero pairs.

Q17. In a geographical cross section, a point P lies 500 m below sea level. What integer should we write next to P?

• A. +500 m
• B. 0 m
• C. +1000 m
• D. −500 m

Q18. On a November day in Leh, the temperature readings were 14 °C, 8 °C, −2 °C and −4 °C. Which reading is the coldest?

• A. 14 °C
• B. 8 °C
• C. −2 °C
• D. −4 °C

Q19. On a winter morning in Shimla, the temperature was −3 °C. By afternoon it rose by 5 °C. What is the afternoon temperature?

• A. −8 °C
• B. +2 °C
• C. +8 °C
• D. +5 °C

Q20. Mount Everest is about 8,848 m above sea level. The Mariana Trench has a deepest point about 11,000 m below sea level. As integer heights, which pair is correct?

• A. +8848 m and +11000 m.
• B. +8848 m and −11000 m.
• C. −8848 m and −11000 m.
• D. −8848 m and +11000 m.

Q21. Brahmagupta's rules for arithmetic on positive numbers, negative numbers and zero appear in which work?

• A. Aryabhatiya.
• B. Lilavati.
• C. Brahma-sphuta-siddhanta.
• D. Bijaganita.

Q22. Brahmagupta's Rule 4 of Addition states that the sum of a number and its inverse is zero. Which calculation illustrates this rule?

• A. 2 + 3 = 5
• B. −2 + (−3) = −5
• C. −5 + 3 = −2
• D. 2 + (−2) = 0

Q23. A Class 6 student writes (−5) + (−3) = −2 and explains that '5 is bigger than 3, so we keep the minus and subtract'. What is the best response from the teacher?

• A. Praise the student; both signs were '−' so subtraction is right.
• B. Mark it correct because (−5) − (−3) does give −2.
• C. Explain that two negatives add (Brahmagupta's Rule 2): 5 + 3 = 8, place '−' to get −8.
• D. Tell the student that integer addition has no rule; any answer is acceptable.

Q24. Ms. Priya wants to introduce negative numbers to her Class 6 students for the first time. According to the NCF-2023 chapter, which is the best opening activity?

• A. Write the rule '(−) + (−) = (−)' on the board and ask students to memorise it.
• B. Use Bela's Building of Fun (or any lift) and ask students how to label floors above and below the ground.
• C. Begin with Brahmagupta's five abstract rules and solve sums.
• D. Skip the introduction and go straight to the unmarked-number-line examples on

Q25. In a mine, a truck is at the level −50 m (50 m below the ground). It then rises by +200 m. What is its new level?

• A. −250 m
• B. +250 m
• C. +150 m
• D. −150 m

Q26. By Brahmagupta's Rule of Addition, the sum of two negative numbers is

• A. Always positive.
• B. Always zero.
• C. Always negative.
• D. Sometimes positive, sometimes negative.

Q27. Evaluate 10 − 20 using the integer rules of the chapter.

• A. +10
• B. +30
• C. −30
• D. −10

Q28. Using an unmarked number line, evaluate (−125) + (−30).

• A. +155
• B. −95
• C. +95
• D. −155

Q29. Aman's bank account had ₹30 in it. The bank then processed a debit of ₹50. What is the new balance?

• A. +₹80
• B. +₹20
• C. −₹20
• D. −₹80

Q30. Which statement about the history of negative numbers is supported by the chapter?

• A. Negative numbers were invented in Europe in the 18th century.
• B. Negative numbers were used in India long before they were accepted in Europe.
• C. Brahmagupta rejected the idea of negative numbers.
• D. Negative numbers were only accepted by Lazare Carnot.