CBSE Class 6 Mathematics The Other Side of Zero Practice Paper Worksheet Set 03 with Answers

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

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Here is Class 6 Maths Ganita Prakash Chapter 10 The Other Side of Zero Practice Paper 24 (CBSE): 20 questions worth 40 marks in Sections A to E, each followed by a worked answer. This paper asks you to follow a chain of moves on the number line, find the integer that balances −7 + □ = +5, choose the integer with the least distance from zero, spot the sign error in a student's sum, and use integers for a scientific probe, Arctic ice thickness and warehouse stock levels.

Section A: Multiple Choice Questions (1 Mark Each)

Question 1: Start at −9. If you add 12 and then subtract 5, the final integer is:
(a) −2
(b) +2
(c) −4
(d) +4
Show Answer & Explanation

Answer: (a) −2

Explanation:
1. −9 + 12 = +3.
2. +3 − 5 = −2.
3. The final integer is −2.

Teacher's Note:
1. Do the operations in the order they are given.
2. Overall change is +12 − 5 = +7, and −9 + 7 = −2.

Question 2: Which integer x satisfies: −4 < x < +2?
(a) −6
(b) −3
(c) +2
(d) +4
Show Answer & Explanation

Answer: (b) −3

Explanation:
1. x must be greater than −4 and less than +2: x can be −3, −2, −1, 0 or +1.
2. −6 is less than −4, +4 is more than +2, and +2 itself is not allowed (the sign is <, not ≤).
3. So x = −3.

Teacher's Note:
1. The sign < leaves out the end numbers.
2. Draw the number line from −4 to +2 and pick an integer strictly inside.

Question 3: Which option balances the equation? −7 + □ = +5
(a) +10
(b) +12
(c) +11
(d) +13
Show Answer & Explanation

Answer: (b) +12

Explanation:
1. □ = (+5) − (−7) = 5 + 7.
2. 5 + 7 = 12.
3. Check: −7 + 12 = +5. The answer is +12.

Teacher's Note:
1. 7 steps take −7 to 0, and 5 more reach +5.
2. Always check the balance by putting the answer in the box.

Question 4: Which statement explains why −1 > −8?
(a) −1 is positive
(b) −1 is closer to zero
(c) −8 has no inverse
(d) −8 lies right of −1
Show Answer & Explanation

Answer: (b) −1 is closer to zero

Explanation:
1. The integer that lies further right on the number line is greater.
2. −1 is only 1 step from zero, while −8 is 8 steps away, so −1 lies to the right of −8.
3. So −1 > −8 because −1 is closer to zero.

Teacher's Note:
1. −1 is negative, so (a) is wrong; −8 lies to the left of −1, so (d) is wrong.
2. −1 is the greatest negative integer.

Question 5: Start at 0. Apply +15, −22, +6. Final position is:
(a) −1
(b) −7
(c) +1
(d) −3
Show Answer & Explanation

Answer: (a) −1

Explanation:
1. 0 + 15 = +15.
2. +15 + (−22) = −7.
3. −7 + 6 = −1.

Teacher's Note:
1. −7 is only the position after two moves; do not stop early.
2. Check: ups total 21, downs total 22, so the result is −1.

Question 6: Which integer has the least distance from zero?
(a) −11
(b) +7
(c) −3
(d) +5
Show Answer & Explanation

Answer: (c) −3

Explanation:
1. Distances from zero: −11 → 11, +7 → 7, −3 → 3, +5 → 5.
2. The smallest distance is 3.
3. So −3 is nearest to zero.

Teacher's Note:
1. Least distance from zero is not the same as the least integer (that would be −11).
2. Ignore the sign when measuring distance from zero.

Question 7: A student writes: −14 + 9 = +5
The error is in:
(a) Addition rule
(b) Sign of answer
(c) Value of −14
(d) Value of 9
Show Answer & Explanation

Answer: (b) Sign of answer

Explanation:
1. −14 + 9: the negative part is bigger, so the answer must be negative. Its size is 14 − 9 = 5.
2. So −14 + 9 = −5, not +5.
3. The size 5 is right but the sign is wrong, so the error is in the sign of the answer.

Teacher's Note:
1. When adding a negative and a positive number, the answer takes the sign of the one farther from zero.
2. From −14, nine steps up reach only −5.

Question 8: Which comparison is correct?
(a) −21 > −19
(b) −8 < −13
(c) −4 > −17
(d) −6 = −9
Show Answer & Explanation

Answer: (c) −4 > −17

Explanation:
1. −21 lies left of −19, so −21 < −19; (a) is false.
2. −8 lies right of −13, so −8 > −13; (b) is false. −6 ≠ −9; (d) is false.
3. −4 is nearer to zero than −17, so −4 > −17 is correct.

Teacher's Note:
1. For negative integers, the one nearer zero is greater.
2. Think of temperatures: −4°C is warmer than −17°C.

Question 9:
Assertion (A): Adding zero to an integer does not change its value.
Reason (R): Zero is the additive identity.
(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. For example, −12 + 0 = −12 and 9 + 0 = 9. A is true.
2. Zero is called the additive identity because adding it keeps every number the same. R is true.
3. R gives the property that makes A happen, so R is the correct explanation of A.

Teacher's Note:
1. Adding 0 on the number line means staying where you are.
2. Check A and R separately first; only then ask whether R gives the reason for A.

Question 10:
Assertion (A): (−6) − (+9) = −15
Reason (R): Subtracting a positive integer moves left on number line
(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. (−6) − (+9): start at −6 and move 9 steps left to −15. A is true.
2. Subtracting a positive integer always means moving left on the number line. R is true.
3. The result −15 comes from exactly that leftward move, so R explains A.

Teacher's Note:
1. Moving left makes numbers smaller, even on the negative side.
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 −72
(b) Find their sum
Answer:
(a) The additive inverse of −72 is +72 (same size, opposite sign).
(b) (−72) + (+72) = 0.
In simple words: Flip the sign; a number plus its inverse is always zero.

Teacher's Note:
1. 72 negative tokens and 72 positive tokens make 72 zero pairs.
2. −72 and +72 are equally far from 0.

 

Question 12. (a) Starting integer = −18, final integer = +7
(b) Find the total movement
Answer:
(a) Movement = final − start = (+7) − (−18).
(b) (+7) − (−18) = 7 + 18 = +25.
So we move 25 steps in the positive direction. Check: −18 + 25 = +7.
In simple words: 18 steps from −18 reach 0 and 7 more reach +7: 25 steps up.

Teacher's Note:
1. Subtracting −18 is the same as adding +18.
2. The sign of the movement shows its direction.

 

Question 13. (a) Which is greater: −56 or −49?
(b) Give one valid reason
Answer:
(a) −49 is greater.
(b) −49 is closer to zero, so it lies to the right of −56 on the number line.
In simple words: −49 is 49 steps below zero and −56 is 56 steps below, so −49 is higher.

Teacher's Note:
1. We write −56 < −49.
2. On the negative side, larger digits mean smaller integers.

 

Question 14. (a) Final result = −12, starting integer = +5
(b) Find the operation performed
Answer:
(a) Change = final − start = (−12) − (+5).
(b) (−12) − (+5) = −12 − 5 = −17.
So the operation performed is adding −17 (subtracting 17): +5 + (−17) = −12.
In simple words: From +5 it takes 5 steps down to 0 and 12 more to −12, which is 17 steps down.

Teacher's Note:
1. Change = final − start, never start − final.
2. Check: 5 − 17 = −12.

 

Section C: Short Answer Questions (3 Marks Each)

Question 15. (a) Evaluate: −48 + 26
(b) Explain using number-line movement
(c) State the sign of result
Answer:
(a) The negative part (48) is bigger than the positive part (26), so the answer is negative, with size 48 − 26 = 22. So −48 + 26 = −22.
(b) Start at −48 and move 26 steps to the right. We land on −22, which is still to the left of zero.
−50 −40 −30 −20 −10 0 +26 start −48 end −22
(c) The result is negative.
In simple words: From −48, 26 steps up are not enough to reach zero; we stop 22 below zero.

Teacher's Note:
1. Tokens: 48 negative and 26 positive leave 22 negative tokens after cancelling pairs.
2. Check: −22 − 26 = −48.

 

Question 16. (a) Rewrite as addition: +9 − (+34)
(b) Solve
(c) Interpret the result
Answer:
(a) +9 − (+34) = +9 + (−34) (subtracting a number = adding its inverse).
(b) 34 − 9 = 25 and the negative part is bigger, so the answer is −25.
(c) Starting at +9 and going 34 steps down takes us past zero to 25 steps below zero. The negative result shows a net downward movement (a net decrease).
In simple words: Taking 34 away from 9 overshoots zero by 25, so the answer is −25.

Teacher's Note:
1. Turn every subtraction into addition of the inverse before calculating.
2. Check: −25 + 34 = 9.

 

Question 17. (a) Arrange: −12, +31, −57 in increasing order
(b) Find the integer nearest to zero
(c) Find the integer farthest from zero
Answer:
(a) Increasing order: −57 < −12 < +31.
(b) Distances from zero: 12, 31 and 57. The nearest to zero is −12.
(c) The farthest from zero is −57.
In simple words: The leftmost integer is the smallest; distance from zero decides nearest and farthest.

Teacher's Note:
1. Negative integers always come before positive ones in increasing order.
2. Nearest to zero is not the same as smallest.

 

Section D: Long Answer Question (5 Marks)

Question 18. A scientific probe is initially 6 units above reference level. It descends 19 units, rises 12 units, descends 7 units, and finally rises 3 units.
(a) Write the integer expression
(b) Simplify stepwise
(c) Find the final position
(d) Find the net movement
(e) Find the position relative to reference level
Answer:
Reference level = 0; up is positive and down is negative.
(a) (+6) + (−19) + (+12) + (−7) + (+3), that is, 6 − 19 + 12 − 7 + 3.
(b) 6 − 19 = −13; −13 + 12 = −1; −1 − 7 = −8; −8 + 3 = −5.
(Grouping: (6 + 12 + 3) − (19 + 7) = 21 − 26 = −5.)
−14 −12 −10 −8 −6 −4 −2 0 +2 +4 +6 +8 reference level 0 −19 +12 −7 +3 +6 start −13 move 1 −1 move 2 −8 move 3 −5 move 4
(c) Final position = −5.
(d) Net movement = (−19) + 12 + (−7) + 3 = −11, i.e. 11 units down overall (check: 6 + (−11) = −5).
(e) The probe is 5 units below the reference level.
In simple words: The probe went down 26 units and up 15 units, a net drop of 11, ending 5 units below the reference level.

Teacher's Note:
1. Net movement counts only the moves; final position also includes the start.
2. Negative position = below the reference level.

 

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

Question 19. Case Study 1: Researchers record changes in Arctic ice thickness using integers, where zero represents the baseline thickness. During summer, the ice thins by 18 units. In winter, snowfall increases thickness by 26 units. In early spring, partial melting reduces thickness by 5 units. Positive integers represent increase, while negative integers represent decrease. Using integer operations, answer the following questions.
(a) Write the integer that represents the decrease in ice thickness by 18 units during summer.
(b) Find the ice thickness after it increases by 26 units in winter.
(c) Calculate the final ice thickness after it decreases by 5 units in early spring.
(d) State whether the final thickness is above, below, or equal to the baseline thickness.
Answer:
(a) A decrease is negative, so it is −18.
(b) (−18) + (+26) = +8, i.e. 8 units above the baseline.
(c) (+8) + (−5) = +3.
(d) +3 is positive, so the final thickness is above the baseline thickness (by 3 units).
In simple words: The ice lost 18, gained 26 and lost 5, ending 3 units thicker than the baseline.

Teacher's Note:
1. Thinning and melting are negative changes; snowfall is a positive change.
2. Check: −18 + 26 − 5 = +3.

 

Question 20. Case Study 2: A warehouse tracks inventory changes using integers. Zero represents the initial stock level. A shipment delay causes a reduction of 13 units. Later, a bulk delivery adds 22 units. Finally, urgent dispatch reduces stock by 6 units. Losses are shown as negative integers and additions as positive integers. Using integer operations, answer the following.
(a) Write the integer that represents the reduction of 13 units in stock due to shipment delay.
(b) Find the stock level after a bulk delivery increases the stock by 22 units.
(c) Calculate the final stock level after urgent dispatch reduces the stock by 6 units.
(d) State whether the final stock level represents a surplus, deficit, or zero stock.
Answer:
(a) A reduction is negative, so it is −13.
(b) (−13) + (+22) = +9.
(c) (+9) + (−6) = +3.
(d) +3 is positive, so the final stock is 3 units more than the initial level: a surplus.
In simple words: Stock fell 13, rose 22 and fell 6, ending 3 units above the starting level.

Teacher's Note:
1. Here 0 means the starting stock, not an empty warehouse.
2. Check: −13 + 22 − 6 = +3.

 

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Chapter 10 The Other Side of Zero Printable Worksheets and Exercises for Class 6 Mathematics

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