Class 6 Maths Chapter 10 Extra Questions The Other Side of Zero
Class 6 Maths The Other Side of Zero Extra Questions
NCERT Class 6 Maths Chapter 10 The Other Side of Zero Extra Questions and Answers
Very Short Answer Type Questions
Question 1.
Which number is smaller in -9,-10 ?
Solution :
-10 is smaller then -9.
Question 2.
Which temperature is higher -3° C or -5° C ?
Solution :
-3° C is higher than -5° C.
Question 3.
Find the value of -8-(-15).
Solution :
-8 – (-15) = -8 +15 = 7
Short Answer Type Questions
Question 1.
Subtract the first integer from the second:
-16,-9
Solution :
-16 from -9
= -9-(-16)
= -9+16
= 7
Question 2.
Put >,< or = (-3)+(-7) □ (-3)-(-7)
Solution :
-3-7 □ -3+7
-10 <4
(-3)+(-7) <(-3)-(-7)
Question 3.
Add: -729,-7098,729,-2
Solution :
-729+(-7098)+729+(-2)
= -729 + 729 – 7098 – 2
= 0 – 7098-2
= -7100
Question 3.
Using number line, how do you compare
(a) two negative integers?
(b) two positive integers?
(c) one positive and one negative integer?
Answer :
Since, the integer lying on right is greater than the integer lying on left.
∴ In all of the given cases (a), (b) and (c), we can compare by usihg the number line by observing which one of the given integers lie on the right or left.
Question 4.
If we are at 8 on the number line, in which direction should we move to reach the integer
(a) -5
(b) 11
(c) 0 ?
Answer :
(a) If we are at 8 on the number line, then to reach the integer -5 , we must move towards the left on the number line.
(b) If we are at 8 on the number line, then to reach the integer 11, we must move towards the right on the number line.
(c) If we are at 8 on the number line, then to reach the integer 0 , we must move towards the left on the number line
Question 5.
Write two integers whose sum is 6 and difference is also 6 .
Answer :
We have, 6 + 0 = 6,
6 – 0 = 6
∴ The required two integers are 6 and 0
Long Answer Type Questions
Question 1.
Subtract the sum of -360 and 165 from -65 .
Sol.
Sum of – 360 + 165 = – 360 + 165
= -195
Subtract – 195 from -65 = – 65 – (-195)
= -65 + 195
= 130
Question 2.
The sum of two integers is 65. If one of them is -32, find the other.
Solution :
Sum of two integers =65
One integer = -32
Other integer = x
-32 + x = 65
x = 65 + 32
x = 97
The other integer is 97.
Passage Based Questions
Passage 1: A child was given 5 quiz tests and the scores of his were recorded as follows:
-3,+7,0,-2,6
Question 1.
What is the lowest score the child got?
(a) -3
(b) -2
(c) 0
(d) 6
Answer :
Option (a) is correct.
Explanation: -3 is the smallest integer in the given set of scores.
Question 2.
What is the difference between the highest and the lowest score?
(a) 4
(b) -4
(c) -10
(d) 10
Answer :
Option (d) is correct.
Explanation: The highest score is 7, the lowest score is -3.
Difference = 7 – (-3)
= 7 + 3 = 10
Question 3.
Which integer lies to the extreme left on the number line?
(a) -2
(b) 0
(c) -3
(d) 7
Answer :
Option (c) is correct.
Explanation:
-3 lies to the extreme left.
Question 4.
Find the sum of -3,+ 7, 0, -2, 6.
Solution :
-3 + 7 + 0 -2 -6
= -3 -2 -6 + 7
= -11 + 7 = -4
Question 5.
Write the predecessor of positive number and successor of negative number of -3,7,-2,6.
Solution :
Predecessor of 7 = 6
Predecessor of 6 = 5
Successor of -3 = -2
Successor of -2 = -1
Passage 2: The level of the surface of oceans or seas is called the sea level. Land and hills are raised and are at some height from the sea level.
City A is 10 m below sea level, City B is 28 m below sea level and City C is 14 m above sea level.
Question 1.
Which of the three cities is at the highest elevation from the sea level?
Solution :
City C
Question 2.
Aditi uses the following rules to represent the elevation of different locations.
The sea level is considered red to be zero elevation. Below sea level is shown using the ‘-‘sign.
Above sea level is shown using the ‘+’ sign.
For example, the elevation of City A is shown as -10.
What would be the elevation of City B?
Solution :
-28
Question 3.
The elevation of City D is 1 m above the elevation of City B. What is the elevation of City D?
Solution :
-27
Question 4.
A submarine at the depth of 45 m rises to 20 m below sea level. What is the depth of the submarine after rising?
Solution :
45 – 20 = 25 m
Question 5.
A diver at the depth of 60 m spotted a seaweed 23 m below him. What is the depth of the seaweed from the sea level?
Solution :
60 + 23 = 83 m
Passage 3: The figure shows the position of the satellite above earth.
PR is the line joining the satellite and the centre of earth. P is the position of the satellite, Q is a point on the surface of earth and R is the centre of earth.
The distance between P and Q is 1300 km and the distance between the centre of earth and the satellite is 7617 km.
Question 1.
What is the distance between the points Q and R ?
(a) 1300 km
(b) 6371 km
(c) 7671 km
(d) 8971 km
Answer :
Option (b) is correct.
Explanation: 6371 km (7671-1300)
Question 2.
Shobhit marks Q as zero and the direction from Q to P is positive. What is the distance of R with reference to P ?
Solution :
7671 km
Question 3.
What is the opposite of the sentence ‘Ascending to a height of 6000 km ‘?
Solution :
Its opposite is ‘descending to a height of 6000 km.’
Question 4.
If point Q is taken as zero, then write 1050 km inside the earth surface or towards P in form of integers?
Solution :
-1050 km
Question 5.
8-8=0 Which of the following is true for the numbers shown above?
(a) -8 is a multiplicative inverse of 8.
(b) -8 is a multiplicative identity of 8.
(c) -8 is the additive identity of 8.
(d) -8 is the additive inverse of 8.
Solution :
Option (d) is correct.
Explanation: 8 + (-8) = 0
NCERT Exemplar Questions
Multiple Choice Questions
In the following questions, out of the four options, only one is correct. Write the correct answer.
Question 1.
Every integer less than 0 has the sign
(a) +
(b) –
(c) ×
(d) ÷
Answer:
Option (b) is correct.
Explanation: We know that, every integer less than 0 has negative (-) sign.
Question 2.
The integer ‘ 5 units’ to the right of 0 on the number line’ is
(a) +5
(b) -5
(c) +4
(d) -4
Answer:
Option (a) is correct.
Explanation: The integer ‘5 units’ to the right of 0 is +5.
Question 3.
The greatest integer lying between -10 and -15 is
(a) -10
(b) -11
(c) -15
(d) -14
Answer:
Option (b) is correct.
Explanation: The greatest integer is -11.
Question 4.
In which of the following pairs of integers, the first integer is not on the left of the other integer on the number line?
(a) (-1,10)
(b) (-3,-5)
(c) (-5,-3)
(d) (-6,0)
Answer:
Option (b) is correct.
Explanation: (-3,-5) is the pair in which first integer is not on left of the other integer.
Question 5.
The integer with negative sign (-) is always less than
(a) 0
(b) -3
(c) -1
(d) -2
Answer:
Option (a) is correct.
Explanation: The integer with negative sign is always less than 0 .
Question 6.
An integer with positive sign (+) is always greater than
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
Option (a) is correct.
Explanation: An integer with positive sign is always greater than 0.
Question 7.
The additive inverse of a negative integer
(a) is always negative
(b) is always positive
(c) is the same integer
(d) zero
Answer:
Option (b) is correct.
Explanation: The additive inverse of a negative integer is always positive.
True/False
Question 1.
The smallest natural number is zero.
Answer:
False
Question 2.
The successor of the integer 1 is 0.
Answer:
False
Question 3.
Every positive integer is larger than every negative integer.
Answer:
True
Question 4.
The sum of any two negative integers is always greater than both the integers.
Answer:
False
Question 5.
The sum of any two negative integers is always smaller than both the integers.
Answer:
True
Fill in the Blanks
Question 1.
On the number line, -15 is to the ________ of zero.
Answer:
Left
Question 2.
On the number line, 10 is to the ________ of zero.
Answer:
Right
Question 3.
The additive inverse of 14 is ________.
Answer:
-14
Question 4.
The additive inverse of -1 is ________.
Answer:
1
Question 5.
The additive inverse of 0 is. ________.
Answer:
0
Match the items of Column I with that of Column II:
(I) Column I | Column II |
(i) The additive inverse of +2 | (a) 0 |
(ii) The greatest negative integer | (b) -2 |
(iii) The greatest negative even integer | (c) 2 |
(iv) The smallest integer greater than every negative integer | (d) 1 |
(v) Sum of predecessor and successor of -1 | (e) -1 |
Answer:
(I) Column I | Column II |
(i) The additive inverse of +2 | (b) -2 |
(ii) The greatest negative integer | (e) -1 |
(iii) The greatest negative even integer | (b) -2 |
(iv) The smallest integer greater than every negative integer | (a) 0 |
(v) Sum of predecessor and successor of -1 | (b) -2 |
Short Answer Type Questions
Question 1.
Write the opposite of each of the following :
(a) Decrease in size.
(b) Failure.
(c) Profit of ₹ 10.
(d) 1000 AD.
(e) Rise in water level.
(f) 60 km South
(g) 10 m above the danger mark of river Ganga.
(h) 20 m below the danger mark of river Brahmaputra.
(i) Winning by a margin of 2000 votes.
(j) Depositing ₹ 100 in the Bank Account.
(k) 20° C rise in temperature.
Solution :
(a) Increase in size.
(b) Success.
(c) Loss of ₹ 10.
(d) 1000 BC.
(e) Fall in water level.
(f) 60 km North.
(g) 10 m below the danger mark of river Ganga.
(h) 20 m above the danger mark of river Brahamputra.
(i) Losing by a margin of 2000 votes.
(j) Withdrawing ₹ 100 from the Bank account.
(k) 20° C fall in temperature.
Question 2.
Temperature of a place at 12: 00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1° C in the second hour. What was the temperature at 2:00 p.m.?
Solution :
Given, initial temperature at 12: 00 noon was +5°C. Since, the temperature increased by 3°C in first hour.
∴ Temp, at 1:00 p.m. = 5° C + 3°C = 8°C
Also, the temperature decreased by 1° C in the second hour
∴ Temp. at 2 : 00 p.m. = 8° C-1° C = 7°C
Hence, the temperature at 2 : 00 p.m. is 7°C.
Question 3.
Write the digits 0,1,2,3, ….. 9 in this order and insert ‘+’or ‘-‘ between them to get the result 3.
Solution :
Arrange the given digits in the given order, we have
0 – 1 – 2 – 3 – 4 – 5 – 6 + 7 + 8 + 9 = -21 + 24 = 3
Question 4.
Write six distinct integers whose sum is 7.
Solution :
Let the six integers be 1,2,-2,3,-3 and 6.
Now, sum of above integers = 1 + 2 + (-2) + 3 + (-3) + 6.
We can arrange the numbers so that + ve integers and -ve integers are grouped together we have, i.e.,
= 1 + 2 + 3 + 6 + (-2) + (-3)
= 12 – 2 – 3
= 12-5 = 7
Hence, required integers are 1,2,-2,-3,3 and 6.
[Note: There are infinite combination exist]
Question 5.
Write the integer which is 4 more than its additive inverse.
Solution :
Let the integer be x.
According to the given condition
x= -x + 4, where -x is the additive inverse of x
→ 2 x = 4
→ x = 2
Long Answer Type Questions
Question 1.
Using number line, how do you compare
(a) two negative integers?
(b) two positive integers ?
(c) one positive and one negative integer ?
Solution :
We know that on the number line points to the right of zero are positive integer and points to the left of zero are negative integers. Also, if we move from left to the right on the number line, then number increases and if we move from right to the left on the number line, the number decreases.
(a) If we compare two negative integers on the number line, then the number which is on right of the other number will be greater.
Here, we see that -2 is on the right of -3 , so -2 is greater and -3 is smaller.
(b) If we compare two positive integers on the number line, then the number which is on right of the other number will be greater
Here, we see that 3 is on right of the 1 , so 3 is greater and 1 is smaller.
(c) If we compare one-positive and one negative integers on the number line, the the number which is on right of the other number will be greater.
Here, we see that 2 is on right of the -1 , so 2 is greater and -1 is smaller.
Question 2.
Observe the following :
1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = -5
Change one ‘-‘ sign as ‘+’ to get the sum 9.
Solution :
Given, 1 + 2 – 3 + 4 – 4 + 5 – 6 – 7 + 8 – 9 = -5
Now, add 14 both sides, because we have to get the sum of 9.
Now we can arrange the integer so that the +ve integers and-ve integers are grouped together.
∴ 1+2+4+5+8+14+(-3)+(-6)+(-7)+(-9)
= 1+2+4+5+8+14-3-6-7-9
= 34-25
= 9
As, we add 14 on left hand side, we see that (-7+ 14) = +7, it means that we have to change the sign of 7.
Question 3.
Write four pairs of integers which are at the same distance from 2 on the number line.
Solution :
First pair : (1,3)
As shown in above figure, we see that (1,3) is the pair of integers, which is at the same distance (i.e.,1 unit) from 2 on the number line.
Second pair : (0,4)
As shown in the above figure, we see that (0,4) is the pair of integers, which is at the same distance (i.e., 2 units) from 2 on the number line.
Third pair: (-1,5)
As shown in the above figure, we see that (-1,5) is the pair of integers, which is at the same distance (i.e., 3 units) from 2 on the number line.
Fourth pair : (-2,6)
As shown in the above figure, we see that (-2,6) is the pair of integers, which is at the same distance (i.e., 4 units) from 2 on the number line.
Question 4.
Using the number line, write the integer which is
(a) 4 more than -5
(b) 3 less than 2
(c) 2 less than -2
Solution :
(a) We want to know an integer 4 more than -5.
So, we start from -5 and proceed 4 steps to the right, then we obtain -1 as shown below.
Hence, 4 more than -5 is -1 .
(b) We want to know an integer 3 less than 2.
So, we start from 2 and proceed 3 steps to the left, then we obtain-1 as shown below.
Hence, 3 less than 2 is -1.
(c) We want to know an integer 2 less than- 2 . So, we start from -2 and proceed 2 steps to the left, then we obtain -4 as shown below.
Hence, 2 less than -2 is -4.