NCERT MCQ Solutions for Class 6 Maths Chapter 10 The Other Side of Zero

Integers include zero, the positive counting numbers and their negatives.
Negative integers < 0 < Positive integers Zero separates the positive and negative integers on the number line, but belongs to neither of those two groups.

On a number line, the number farther to the right is greater.
−5 is two units to the left of −3.
Therefore, −5 < −3. Both numbers are also less than zero.

Target floor = Starting floor + Movement
= (+2) + (−3)
= −1
The lift moves down two floors to reach zero and then one more floor below zero. So it reaches Floor −1.

Total movement = (+4) + (−3) + (−2)
= 1 − 2
= −1
There are 4 upward moves and 5 downward moves. The extra downward move leaves the lift one floor below its starting floor.

A number and its additive inverse add up to zero.
−543 + 543 = 0
Therefore, the additive inverse of −543 is 543. It has the same distance from zero on the opposite side of the number line.

On a number line, -10 is farthest to the left.

The numbers less than zero are called Negative numbers.

Movement = Target floor − Starting floor
= (−1) − (−2)
= −1 + 2 = +1
Floor −1 is one floor above Floor −2, so the lift must move up one floor.

Movement = Target level − Starting level
= −200 − 40
= −240 m
The lift first travels 40 m down to ground level and then 200 m farther down. Its total downward movement is 240 m.

Both numbers are negative, so their sum is negative.
125 + 30 = 155
Therefore, −125 + (−30) = −155.
Starting at −125 and moving 30 units left also takes us to −155 on the number line.

Subtracting a negative number is the same as adding its positive inverse.
−99 − (−200) = −99 + 200
= 101
A check using addition gives 101 + (−200) = −99, which returns the starting number.

In increasing order, these numbers are:
−25 < −12 < −10 < −7 Among negative numbers, the one closest to zero is greatest. Therefore, −7 is the greatest of the four numbers.

The statements 3 is greater than -3 is true.

This is correct about negative numbers; they are always smaller than positive numbers.

Value of a positive token + Value of a negative token
= (+1) + (−1)
= 0
This is a zero pair. Adding or removing this pair does not change the total value of a collection of tokens.

Each positive token cancels one negative token. Five zero pairs can be removed.
Negative tokens left = 8 − 5 = 3
So, (+5) + (−8) = −3. No positive tokens remain.

Only one more positive token is needed. Adding one zero pair gives 6 positive tokens and 1 negative token without changing the value.
After removing 6 positive tokens, 1 negative token remains.
(+5) − (+6) = −1

There are no positive tokens to remove, so 5 zero pairs provide the needed 5 positive tokens.
Negative tokens then present = 3 + 5 = 8
After removing the 5 positives, the value is −8.
−3 − (+5) = −8

Subtracting −6 means adding +6.
+4 − (−6) = 4 + 6 = 10
In the token model, six zero pairs supply six negative tokens to remove. Removing them leaves ten positive tokens.

Number 0 is neither positive nor negative.

The inverse of +7 is -7. Because -7 +7 = 0.

Final balance = 100 + 60 − 30 − 150
= 160 − 30 − 150
= 130 − 150
= −₹20
The payments exceed the money available by ₹20, so the balance is negative.

Total credits = 30 + 40 + 50 = ₹120
Total debits = 40 + 50 + 60 = ₹150
Final balance = 120 − 150 = −₹30
The debits are ₹30 greater than the credits.

Total debits = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
= ₹255
Final balance = 0 − 255 + 256 = ₹1
The single credit is ₹1 more than all the debits together.

Height difference = 1500 − (−1200)
= 1500 + 1200
= 2700 m
The vertical gap includes 1500 m above sea level and 1200 m below it. These distances add because the points lie on opposite sides of sea level.

Rise in temperature = Final temperature − Initial temperature
= 14 − (−4)
= 18°C
The temperature rises 4°C to reach zero and another 14°C to reach 14°C. The total rise is 18°C.

In Bela’s Building of Fun, 0 floor represents the ground level.

If the temperature is -5°C and it drops by 3°C, the new temperature is -5°C – 3°C = -8°C

Border sum = Sum of the three numbers in the top row
= 5 + (−3) + (−5)
= 2 − 5 = −3
Each of the other three borders must also add up to −3.

Value of one five-token group = 1 + 1 + 1 − 1 − 1 = 1
Number of groups = 100 ÷ 5 = 20
Total value = 20 × 1 = 20.
Each group has one more positive token than negative tokens.

A sum of zero needs two additive inverses. The faces have no pair such as −1 and +1, or −2 and +2.
−5 + (−5) = −10; −1 + (−3) = −4; 6 + 6 = 12.
Therefore, only zero is impossible among these choices.

The integers strictly between −4 and 4 are:
−3, −2, −1, 0, 1, 2, 3
There are 7 integers. The endpoints −4 and 4 are not counted, but zero is included because it lies between them.

The difference between consecutive terms is +6.
−34 − (−40) = 6
Next term = −22 + 6 = −16
The numbers become greater at each step because the movement is six units to the right.

The terms in odd positions are 3, 2, 1, 0, −1, −2, … .
The terms in even positions are 4, 5, 6, 7, 8, … .
Continuing the alternating lists after 0, 7 gives −1, 8, −2.

As time moves forward within BCE, the year numbers decrease.
680 − 320 = 360
Therefore, the year is 360 BCE. The interval stays entirely within BCE, so it does not cross the change from BCE to CE.

(−2) + (−9) − (+18) − (+1)
= −2 − 9 − 18 − 1
= −(2 + 9 + 18 + 1)
= −30
Every contribution is negative after the subtraction signs are applied.

A positive result is possible: 5 + (−3) = 2.
A negative result is possible: 3 + (−5) = −2.
Zero is also possible: 5 + (−5) = 0.
The result depends on the sizes of the two integers.

Addition: 4 + (−5) = −1
First subtraction: 4 − (−5) = 9
Reverse subtraction: −5 − 4 = −9
Since −9 < −1 < 9, the greatest result is 9. It gives a movement of nine steps in the positive direction.

The sum of (-4) + (+6) is 2.

If we are at floor +3 and press the “–” button 5 times, then we will be at +3 -5 = -2.