CBSE Class 6 Mathematics The Other Side of Zero Practice Paper Worksheet Set 02 with Answers

Official Class 6 Mathematics Worksheets: Chapter 10 The Other Side of Zero

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This page gives CBSE Class 6 Maths Ganita Prakash Chapter 10 The Other Side of Zero Practice Paper 22, a 40-mark paper of 20 questions in Sections A to E, with a step-by-step answer under every question. It tests finding the move between two integers, completing balances such as □ + (−18) = −7, comparing negative integers, distance from zero and additive inverses, plus up-and-down journeys of a survey drone, a research submarine and the temperature in a hill station.

Section A: Multiple Choice Questions (1 Mark Each)

Question 1: From −11, what is the least positive move to reach +1?
(a) +10
(b) +11
(c) +12
(d) +13
Show Answer & Explanation

Answer: (c) +12

Explanation:
1. Move needed = final − start = (+1) − (−11).
2. (+1) − (−11) = 1 + 11 = 12.
3. Check: −11 + 12 = +1. The move is +12.

Teacher's Note:
1. A move from a smaller to a bigger integer is always positive.
2. From −11 it takes 11 steps to reach 0 and 1 more step to reach +1.

Question 2: Which integer x satisfies: x − 5 = −9?
(a) −15
(b) −14
(c) −4
(d) −3
Show Answer & Explanation

Answer: (c) −4

Explanation:
1. x − 5 = −9 means: after taking away 5 from x we reach −9.
2. So x is 5 more than −9: x = −9 + 5 = −4.
3. Check: −4 − 5 = −9. So x = −4.

Teacher's Note:
1. Undo the subtraction by adding the same number.
2. Always put your answer back into the equation to check.

Question 3: Complete: □ + (−18) = −7
(a) +11
(b) +10
(c) +9
(d) +8
Show Answer & Explanation

Answer: (a) +11

Explanation:
1. The missing number is −7 − (−18) = −7 + 18.
2. −7 + 18 = +11.
3. Check: +11 + (−18) = 11 − 18 = −7. The answer is +11.

Teacher's Note:
1. Adding −18 is the same as moving 18 steps down.
2. Start at 11 and go down 18 steps: you land on −7.

Question 4: Why is −5 greater than −22?
(a) −5 is positive
(b) −5 lies closer to zero
(c) −22 has no inverse
(d) −22 lies right of −5
Show Answer & Explanation

Answer: (b) −5 lies closer to zero

Explanation:
1. On the number line, a number further to the right is greater.
2. For negative integers, the one closer to zero lies further to the right.
3. −5 is only 5 steps from zero, −22 is 22 steps away, so −5 is greater because it lies closer to zero.

Teacher's Note:
1. −5 is negative, so (a) is wrong; every integer has an inverse, so (c) is wrong.
2. −22 lies to the left of −5, not to the right, so (d) is wrong.

Question 5: Start at 0. Apply −14, +9, +6. Final integer is:
(a) −1
(b) +1
(c) −3
(d) +3
Show Answer & Explanation

Answer: (b) +1

Explanation:
1. 0 + (−14) = −14.
2. −14 + 9 = −5.
3. −5 + 6 = +1.

Teacher's Note:
1. Do the moves one at a time, in order.
2. Quick check: the positive moves add to 15 and the negative move is 14, so the result is +1.

Question 6: Which integer is farthest from zero?
(a) −16
(b) +12
(c) −9
(d) +14
Show Answer & Explanation

Answer: (a) −16

Explanation:
1. Distance from zero ignores the sign: −16 is 16 steps away, +12 is 12, −9 is 9 and +14 is 14.
2. The largest distance is 16.
3. So −16 is farthest from zero.

Teacher's Note:
1. Farthest from zero does not mean greatest; −16 is actually the smallest of the four.
2. Count steps from 0 on either side.

Question 7: Which expression equals +6?
(a) −4 + 10
(b) +8 − 3
(c) −12 + 6
(d) +9 − 1
Show Answer & Explanation

Answer: (a) −4 + 10

Explanation:
1. −4 + 10 = +6.
2. +8 − 3 = +5, −12 + 6 = −6 and +9 − 1 = +8.
3. Only −4 + 10 equals +6.

Teacher's Note:
1. Work out every option; (c) gives −6, which is a common trap.
2. From −4, ten steps up reaches +6.

Question 8: Which statement is correct?
(a) −25 > −19
(b) −7 < −15
(c) −6 > −21
(d) −10 = −12
Show Answer & Explanation

Answer: (c) −6 > −21

Explanation:
1. −25 is further left than −19, so −25 < −19; (a) is false.
2. −7 is to the right of −15, so −7 > −15; (b) is false. −10 and −12 are different, so (d) is false.
3. −6 is closer to zero than −21, so −6 > −21 is correct.

Teacher's Note:
1. For negative integers, the bigger the number after the minus sign, the smaller the integer.
2. Picture a lift: floor −6 is above floor −21.

Question 9:
Assertion (A): The sum of an integer and its additive inverse is zero.
Reason (R): Every integer has exactly one additive inverse.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The additive inverse of a number is the number that adds to it to give 0 (for example 7 + (−7) = 0). So A is true.
2. Each integer has just one such partner (the inverse of 7 is only −7), so R is also true.
3. R only tells us how many inverses there are; it does not explain why the sum is zero. That comes from the meaning of additive inverse. So both are true, but R is not the correct explanation of A.

Teacher's Note:
1. The answer key of the source paper gives (a); we have used (b) because R talks about uniqueness, not about the sum.
2. Check A and R separately first; only then ask whether R gives the reason for A.

Question 10:
Assertion (A): (−3) − (+7) = −10
Reason (R): Subtracting a positive integer decreases the value.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. (−3) − (+7) means start at −3 and go 7 steps down: −3 − 7 = −10. A is true.
2. Taking away a positive number always gives a smaller result, so R is true.
3. A works exactly because subtracting +7 lowers −3 by 7, so R explains A.

Teacher's Note:
1. Subtracting a positive number = moving left on the number line.
2. Check A and R separately first; only then ask whether R gives the reason for A.

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Write the additive inverse of −108
(b) Find their sum
Answer:
(a) The additive inverse has the same size and the opposite sign. So the additive inverse of −108 is +108.
(b) (−108) + (+108) = 0.
In simple words: Flip the sign to get the inverse; a number and its inverse always add to zero.

Teacher's Note:
1. −108 and +108 are the same distance from zero, on opposite sides.
2. Think of 108 negative tokens and 108 positive tokens: they make 108 zero pairs.

 

Question 12. (a) Starting integer = −19, final integer = +4
(b) Find the total movement
Answer:
(a) The movement is the change from the start to the end: movement = final − start = (+4) − (−19).
(b) (+4) − (−19) = 4 + 19 = +23.
So we move 23 steps in the positive direction (up). Check: −19 + 23 = +4.
In simple words: From −19 it is 19 steps to 0 and 4 more to +4, so 23 steps up.

Teacher's Note:
1. Subtracting a negative is the same as adding its inverse.
2. A positive answer means the movement is upward or to the right.

 

Question 13. (a) Which is greater: −73 or −61?
(b) Give one valid reason
Answer:
(a) −61 is greater.
(b) −61 is closer to zero than −73, so it lies to the right of −73 on the number line. Any integer to the right is greater.
In simple words: −61 is only 61 steps below zero, while −73 is 73 steps below, so −61 is higher.

Teacher's Note:
1. Do not compare 73 and 61 directly; the minus sign reverses the order.
2. We can write −73 < −61.

 

Question 14. (a) Final integer = −6, starting integer = +9
(b) Find the operation performed
Answer:
(a) Change = final − start = (−6) − (+9).
(b) (−6) − (+9) = −6 − 9 = −15.
So the operation performed is adding −15 (subtracting 15): +9 + (−15) = −6.
In simple words: To go from +9 down to −6 we go 9 steps to 0 and 6 more, which is 15 steps down.

Teacher's Note:
1. A negative change means the value went down.
2. Always check by applying the operation to the starting number.

 

Section C: Short Answer Questions (3 Marks Each)

Question 15. (a) Evaluate: −57 + 34
(b) Explain using number-line movement
(c) State the sign of the result
Answer:
(a) −57 + 34: the negative part is bigger, so the answer is negative and its size is 57 − 34 = 23. So −57 + 34 = −23.
(b) Start at −57 on the number line. Adding +34 means moving 34 steps to the right. After 34 steps we land on −23 (still left of zero, because 34 steps are not enough to reach 0 from −57).
−60 −50 −40 −30 −20 −10 0 +34 start −57 end −23
(c) The result is negative.
In simple words: From −57 we climb 34 steps but need 57 to reach zero, so we stop 23 steps below zero.

Teacher's Note:
1. With tokens: 57 negative and 34 positive make 34 zero pairs, leaving 23 negative tokens.
2. The sign of the answer is the sign of the number farther from zero.

 

Question 16. (a) Rewrite as addition: +16 − (+41)
(b) Solve
(c) Interpret the result
Answer:
(a) Subtracting +41 is the same as adding its inverse −41: +16 − (+41) = +16 + (−41).
(b) +16 + (−41): the negative part is larger, 41 − 16 = 25, so the answer is −25.
(c) The result is negative: starting at +16 and going 41 steps down takes us past zero to 25 steps below zero. The overall movement is downward (a net decrease).
In simple words: Going 41 steps down from 16 crosses zero and ends at −25.

Teacher's Note:
1. Subtracting a number = adding its additive inverse.
2. Check: −25 + 41 = 16.

 

Question 17. (a) Arrange: −21, +38, −64 in increasing order
(b) Find the integer nearest to zero
(c) Find the integer farthest from zero
Answer:
(a) Negative integers are smaller than positive ones, and −64 is further left than −21. Increasing order: −64 < −21 < +38.
(b) Distances from zero: −21 → 21, +38 → 38, −64 → 64. The nearest to zero is −21.
(c) The farthest from zero is −64.
In simple words: Smallest is the one furthest left (−64); nearest to zero has the smallest distance (21).

Teacher's Note:
1. Increasing order means smallest first.
2. Distance from zero never has a sign.

 

Section D: Long Answer Question (5 Marks)

Question 18. A survey drone is 12 units above reference level. It descends 27 units, rises 14 units, descends 6 units, and rises 5 units.
(a) Write the integer expression
(b) Simplify stepwise
(c) Find the final position
(d) Find the net vertical movement
(e) Find the position relative to reference level
Answer:
Take the reference level as 0, upward as positive and downward as negative.
(a) Expression: (+12) + (−27) + (+14) + (−6) + (+5), that is, 12 − 27 + 14 − 6 + 5.
(b) Step by step: 12 − 27 = −15; −15 + 14 = −1; −1 − 6 = −7; −7 + 5 = −2.
(Or group them: rises and start (12 + 14 + 5) = 31, descents (27 + 6) = 33, and 31 − 33 = −2.)
−16 −12 −8 −4 0 +4 +8 +12 reference level 0 −27 +14 −6 +5 +12 start −15 move 1 −1 move 2 −7 move 3 −2 move 4
(c) Final position = −2.
(d) Net vertical movement = (−27) + 14 + (−6) + 5 = −14, i.e. 14 units down overall (check: 12 + (−14) = −2).
(e) −2 means the drone is 2 units below the reference level.
In simple words: The drone went down 33 units and up 19 units in all, so it ended 14 units lower than its start, at 2 units below the reference level.

Teacher's Note:
1. The net movement uses only the moves, not the starting height.
2. A negative final position means below the reference level.

 

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: A research submarine is exploring the deep sea. At the beginning of the day, it is at a depth of 35 metres below sea level. During the first exploration, it descends 18 metres. Later, it rises 22 metres to study marine life. After that, it again dives 15 metres to reach a deeper trench. Finally, the submarine rises 10 metres before ending its mission. The crew wants to calculate the final position of the submarine relative to sea level and understand how its depth changed after each movement. Use integer operations to find the correct answers to the following questions.
(a) Write the integer expression for the submarine's movement.
(b) Find the depth after the first two movements.
(c) Find the depth after the third movement.
(d) Find the final depth of the submarine.
Answer:
Take sea level as 0; below sea level is negative, so the start is −35 m.
(a) (−35) + (−18) + (+22) + (−15) + (+10)
(b) First movement: −35 + (−18) = −53. Second movement: −53 + 22 = −31, i.e. 31 m below sea level.
(c) Third movement: −31 + (−15) = −46, i.e. 46 m below sea level.
(d) Fourth movement: −46 + 10 = −36. Final depth = 36 metres below sea level (−36 m).
In simple words: The submarine went 33 m further down and 32 m up, so it ended 1 m deeper than it started: 36 m below sea level.

Teacher's Note:
1. Depth below sea level is written as a negative integer.
2. Check: total change = −18 + 22 − 15 + 10 = −1, and −35 − 1 = −36.

 

Question 20. Case Study 2: In a hill station town, the temperature early morning was 12°C below zero. By noon, the temperature increased by 15°C due to sunshine. In the afternoon, cold winds caused the temperature to fall by 9°C. Later in the evening, the temperature rose by 6°C as the clouds cleared. At night, the temperature again dropped by 8°C. The weather department wants to calculate the temperature at different times of the day and finally determine the temperature at night using integer operations.
(a) Write the integer expression representing the temperature changes.
(b) Find the temperature by noon.
(c) Find the temperature in the evening.
(d) Find the final temperature at night.
Answer:
12°C below zero is −12°C; a rise is positive and a fall is negative.
(a) (−12) + (+15) + (−9) + (+6) + (−8)
(b) Noon: −12 + 15 = +3°C.
(c) Afternoon: 3 + (−9) = −6°C. Evening: −6 + 6 = 0°C.
(d) Night: 0 + (−8) = −8°C, i.e. 8°C below zero.
−14 −12 −10 −8 −6 −4 −2 0 +2 +4 +6 0°C °C +15 −9 +6 −8 −12 morning +3 noon −6 afternoon 0 evening −8 night
In simple words: The temperature went −12, 3, −6, 0 and finally −8 degrees Celsius.

Teacher's Note:
1. Write the starting temperature with its sign before adding the changes.
2. Check: total change = 15 − 9 + 6 − 8 = +4, and −12 + 4 = −8.

 

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CBSE Class 6 Mathematics Worksheets for Chapter 10 The Other Side of Zero

Mastering Chapter 10 The Other Side of Zero with Printable Worksheets

Review targeted practice exercises for Class 6 Mathematics Chapter 10 The Other Side of Zero. Curated to match official CBSE guidelines, these printable problem sets support daily revision and improve overall test readiness.

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