CBSE Class 6 Maths Important Questions Chapter 10 - The Other Side of Zero

1. Determine whether the following statements are true or false: 

(a) The smallest natural number is zero.
(b) Zero is not considered an integer because it is neither positive nor negative.
(c) The sum of two negative integers is always less than both of the integers.
(d) Since 5 > 3, it follows that -5 > -3.

Ans:
(a) False. The smallest natural number is 1.
(b) False. Zero is an integer, as integers include all whole numbers and their negative counterparts.
(c) True. For example, (-1) + (-10) = (-11), and -11 is less than both -10 and -1.
(d) False. Since 5 > 3, then -5 < -3.

2. Complete the blanks in the following statements: 

(a) On the number line, -15 is positioned to the ____ of zero.
(b) On the number line, 10 is positioned to the ____ of zero.
(c) The additive inverse of -1 is ____.
(d) (-11) + (-2) + (-1) = ____.

Ans:
(a) On the number line, -15 is to the left of zero.
(b) On the number line, 10 is to the right of zero.
(c) The additive inverse of -1 is +1 or 1.
(d) (-11) + (-2) + (-1) = -14.

3. List five integers that are greater than -150 but less than -100.

Ans:
Since -100 is greater than -150, the difference between -100 and -150 is:
-100 – (-150) = -100 + 150 = 50.
This range includes (50 - 1) = 49 integers between -100 and -150.
Any five integers from this range are -101, -102, -103, …, -148, -149.

4. If profit is considered positive, state the following values as profit: 

(a) Profit of ₹80
(b) Loss of ₹66

Ans:
(a) Since profit is positive, a profit of ₹80 is denoted as +80.
(b) Since profit is positive but loss is negative, a loss of ₹66 is represented as -66.

5. If depth is considered positive, express the following as depth: 

(a) 25 metres deep
(b) 45 metres height

Ans:
(a) Given that depth is positive, 35 metres deep is expressed as +35 metres depth.
(b) Since depth is positive, height would be the opposite, so 95 metres height is represented as -95 metres depth.

6. Using a number line, place the appropriate symbol ‘>’ or ‘<’ in each of the following:

(i) -1 ___ 0
(ii) 0 ___ -2
(iii) -5 ___ -2
(iv) 4 ___ -5

Ans:

(i) Since -1 is positioned to the left of 0 on the number line, -1 is less than 0.
∴ -1 < 0.

(ii) Since -2 is located to the left of 0 on the number line, it indicates that 0 is greater than -2.
∴ 0 > -2.

(iii) Since -5 is found to the left of -2 on the number line, -5 is therefore less than -2.
∴ -5 < -2.

(iv) Since 4 is positioned to the right of -5 on the number line, it shows that 4 is greater than -5.
∴ 4 > -5.

7. Locate the integer on the number line that is: 

(i) 4 less than -1
(ii) 5 more than -2

Ans:
As we move leftward on the number line, numbers decrease.

(i) Moving 4 steps left from -1 (4 less than -1), we arrive at -5. This is represented on the number line in the diagram.

(ii) Moving 5 steps right from -2 (5 more than -2), we reach 3. This point is indicated on the number line.

(ii) To represent 5 more than -2, we begin at -2 on the number line and move five steps to the right, reaching 3.

8. Check whether the following are true.
(i) 3 + (0 + 9) = (3 + 0) + 9
(ii) 34 + {90 + (-11)} = (34 + 90) + (-11)
Ans:
(i) LHS = 3 +(0 + 9) = 3 + 9 = 12
RHS = (3 + 0)+ 9 = 3 + 9 = 12
∴ LHS = RHS

(ii) LHS = 34 + {90 + (-11)} = 34 + {90 – 11}
= 34 + 79 = 113
RHS = (34 + 90) + (-11) = 124 + (-11)
= 124 – 11 = 113
∴ LHS = RHS

9. Evaluate the following:
(i) 79 – 68 + 28 – (-32)
(ii) 153 + 218- {29 – (367)}
Ans:
(i) 79 – 68 + 28 – (-32) = 79-68 + 28 + 32
= (79 + 28 + 32) – 68
= 139 – 68
= 71
(ii) 153 + 218 – {29 – (367)} = 153 + 218 – {29 – 367}
= 153 + 218 – (-338)
= 153 + 218 + 338
= 709.

10. Fill in the blanks using <, = or >.
(a) (-11)+ (-15) ____ 11 + 15
(b) (-71) + (+9) ___ (-81) + (-9)
(c) (-101) ____ (-102)
(d) 1 + 2 + 3 ___ (-1) + (-2) + (-3)
Ans:
(a) (-11)+ (-15) = -26 and 11 + 15 = 26
Since, – 26 < 26, so (-11) + (-15) < 11 + 15
(b) (-71) + (+9) = – 62 and (-81) + (-9) = -90
Since, -62 > -90, so (-71) + (+9) > (-81) + (-9)
(c) Since, 101 < 102, so -101 > -102
(d) 1 + 2 + 3 = 6 and (-1) + (-2) + (-3) = -6
Since, 6 > -6, so 1 + 2 + 3 > (-1) + (-2) + (-3)

11. What is the smallest negative integer?
Ans: There is no smallest negative integer as they go infinitely in the negative direction.

12. Is zero a positive or a negative integer?
Ans: Zero is neither positive nor negative; it’s a neutral integer.

13. Where is -10 located on the number line relative to zero?
Ans: -10 is to the left of zero on the number line.

14. What is the additive inverse of -5?
Ans: The additive inverse of -5 is +5.

15. If profit is positive, how would you represent a profit of ₹50 and a loss of ₹30?
Ans: Profit of ₹50 would be +50, and loss of ₹30 would be -30.

16. Explain why the sum of two negative integers is also negative.
Ans: Adding two negative integers results in a larger negative value because both numbers contribute to moving further left on the number line. For example, -3 + (-4) = -7. This is because when adding negatives, we combine their absolute values in a negative direction.

17. On a number line, what does it mean if an integer is to the left of another integer?
Ans: On a number line, an integer to the left of another integer is always smaller. For instance, -5 is to the left of -2, meaning -5 is less than -2. This arrangement visually helps in comparing integer values easily.

18. How would you represent a depth of 20 metres below sea level and an elevation of 15 metres above sea level using integers?
Ans: Depth below sea level can be represented as a negative integer, so 20 metres below sea level would be -20. An elevation above sea level is positive, so 15 metres above would be +15.

19. Describe the process of adding a positive integer and a negative integer with examples.
Ans: When adding a positive and a negative integer, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. For example, for -8 + 5, we take the difference (8 - 5 = 3) and keep the negative sign, so the result is -3. In another example, if we add 10 and -6, we subtract (10 - 6 = 4) and keep the positive sign, making the result +4. This rule helps in combining numbers with different signs on a number line.

20. Explain how to use a number line to compare two integers, and provide examples with both positive and negative integers.
Ans: To compare integers on a number line, we look at their positions relative to each other. Numbers on the right are always greater than those on the left. For example, comparing -3 and 2, -3 is to the left of 2, so -3 < 2. Similarly, between -7 and -4, -7 is to the left of -4, meaning -7 < -4. Positive numbers are always to the right of negative numbers, which makes them larger. This method makes it easy to visually see which integer is greater or smaller by simply observing their positions on the line.

Extra Questions on Class 6 Maths Chapter 10 The Other Side of Zero

1. If Floor A = –12, Floor D = –1 and Floor E = +1 in the building shown on the right as a line, find the numbers of Floors B, C, F, G, and H.

Ans: 

2. Complete these expressions. 

a. (+40)+ ______ = +200 

b. (+40)+_______=–200 

c. (–50)+ ______ = +200 

d. (–50)+_______=–200 

e. (–200) – (–40) = _______ 

f. (+200)– (+40) = _______ 

g. (–200) –(+40) = _______ 

Ans:

a. (+40)+(+160) = +200 

b. (+40)+ (-240) =–200 

c. (–50)+ (+250) = +200 

d. (–50)+ (-150) =–200 

e. (–200) – (–40) = -160 

f. (+200)– (+40) = +160 

g. (–200) –(+40) = -240 

3. Write down the above 3 marked negative numbers in the following boxes: ___ ___ ___.

Ans: -7, -3. -2

4. Complete the additions using tokens.

a. (+6)+(+4) 

Ans:

For (+6), we use 6 positive tokens 

And for (+4), we use 4 positive tokens

Therefore, by combining we will get 

(+6) + ( +4) = (+10)

Hence, Counting all the positive tokens we get (+10)

b. (−3)+(−2)

Ans: For (-3) we use 3 negative tokens

For (-2) we use 2 negative tokens

Token

Now combining them we will get 

(-3) + (-2) = -5

Hence, counting all the negative tokens we get (-5)

5. Suppose you start with ₹ 0 in your bank account, and then you have credits of ₹ 30, ₹ 40, and ₹ 50, and debits of ₹ 40, ₹ 50, and ₹ 60. What is your bank account balance now? 

Ans: Given 

Credits = ₹ 30 + ₹ 40 + ₹ 50 = ₹ 120

Debits = ₹ 40 + ₹ 50 + ₹ 60 = ₹ 150

Therefore balance = Credits - Debits 

= ₹ 120 - ₹ 150

= - ₹ 30

Hence, your bank account balance is - ₹30.

6. Suppose you start with `0 in your bank account, and then you have debits of ₹ 1, 2, 4, 8, 16, 32, 64, and 128, and then a single credit of ₹ 256. What is your bank account balance now? 

Ans: Given

Debits = ₹ 1 + ₹ 2 + ₹ 4 + ₹ 8 + ₹ 16 + ₹ 32 + ₹ 64 + ₹ 128 = ₹ 255

Credit = ₹ 256

Therefore, Balance = Credits - Debits 

= ₹ 256 - ₹ 255 

= ₹ 1

Hence, your bank account balance is ₹ 1.

This page offers important questions on CBSE Class 6 Matha Chapter 10 - The Other Side Of Zero for extra practice. Solving these will help students to prepare well for exams. Also, these extra questions follow the same pattern as your test papers.

With these short question answers, students can improve their problem-solving skills. Start practising today to improve your confidence and score better!

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