Integers
Class 6th Mathematics CBSE Solution
- Write opposites of the following: (a) Increase in weight (b) 30 km north (c) 326…
- Represent the following numbers as integers with appropriate signs. (a) An…
- Represent the following numbers on a number line: (a) +5 (b) -10 (c) + 8 (d) -1…
- Adjacent figure is a vertical number line, representing integers. Observe it and…
- Following is the list of temperatures of five places in India on a particular…
- In each of the following pairs, which number is to the right of the other on the…
- Write all the integers between the given pairs (write them in the increasing…
- Write four negative integers greater than -20
- Write four negative integers less than -10.
- For the following statements write True (t) or False (F). If the statement is…
- Draw a number line and answer the following: (a) Which number will we reach, if…
- Using the number line write the integer which is:(a) 3 more than 5(b) 5 more…
- Use number line and add the following integers: (a) 9 + (-6) (b) 5 + (-11) (c)…
- Add without using number line:(a) 11 + (-7)(b) (-13) + (+18)(c) (-10) + (+19)(d)…
- Find the sum of: (a) 137 and - 354 (b) -52 and 52 (c) -312, 39 and 192 (d) -50,…
- Find the sum:(a) (-7) + (-9) + 4 + 16(b) (37) + (-2) + (-65) + (-8)…
- Find:(a) 35 - (20)(b) 72 - (90)(c) (-15) - (-18)(d) (-20) - (13)(e) 23 -…
- Fill in the blanks with , or = sign. (a) (-3) + (-6) ..(-3) (-6) (b) (-21) (-10)…
- Fill in the blanks:(a) (-8) + .. = 0(b) 13 + . = 0(c) 12 + (-12) = ..(d) (-4) +…
- Find: (a) (-7) - 8 - (-25) (b) (-13) + 32 - 8 -1 (c) (-7) + (-8) + (-90) (d) 50…
Exercise 6.1
Question 1.Write opposites of the following:
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of Rs 700
(e) 100 m above sea level
Answer:
(a) As we know that,
The opposite of the word Increase is Decrease
Hence,
According to the question,
The opposite of ‘Increase in weight’ would be ‘Decrease in weight’.
(b) As we know that,
The opposite of the direction North is South
Hence,
According to the question,
The opposite of ’30 km North’ would be ’30 km South’.
(c) As we know that,
The opposite of the word BC is AD
Hence,
According to the question,
The opposite of ‘326 BC’ would be ‘326 AD’
(d) As we know that,
The opposite of the word Loss is Profit
Hence,
According to the question,
The opposite of ‘Loss of 700’ would be ‘Profit of Rs 700’.
(e) As we know that,
The opposite of the word above is below.
Hence,
According to the question,
The opposite of ‘100 m above sea level’ would be ‘100 m below sea level’.
Question 2.
Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height of two thousand metres above the ground.
(b) A submarine is moving at a depth, eight hundred metres below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.
Answer:
(a) In the given question,
If we consider the level of the sea at neutral level,
Then the height above the sea level is considered as positive
And,
The height below the sea level is considered as negative.
Hence,
According to the question,
The integer with appropriate sign will be +2000.
(b) In the given question,
If we consider the level of the sea at neutral level,
Then the height above the sea level is considered as positive
And,
The height below the sea level is considered as negative.
Hence,
According to the question,
The integer with appropriate sign will be -800.
(c) We know that,
Deposit refers to the saving of money
And,
Withdrawal refers to the intake of money.
Hence,
According to the question,
The integer with appropriate sign will be +200.
(d) We know that,
Deposit refers to the saving of money
And,
Withdrawal refers to the intake of money.
Hence,
According to the question,
The integer with appropriate sign will be -700.
Question 3.
Represent the following numbers on a number line:
(a) +5
(b) -10
(c) + 8
(d) -1
(e) -6
Answer:
(a) We can observe that in +5,
The integer has a positive sign
Therefore,
It will lie on the Right-hand side of the zero in the number line
Hence,
We can represent the number on a number line as follows:
(b) We can observe that in -10,
The integer has a negative sign
Therefore,
It will lie on the left hand side of the zero in the number line
Hence,
We can represent the number on a number line as follows:
(c) We can observe that in +8,
The integer has a positive sign
Therefore,
It will lie on the right hand side of the zero in the number line
Hence,
We can represent the number on a number line as follows:
(d) We can observe that in -1,
The integer has a negative sign
Therefore,
It will lie on the left hand side of the zero in the number line
Hence,
We can represent the number on a number line as follows:
(e) We can observe that in -6,
The integer has a negative sign
Therefore,
It will lie on the left hand side of the zero in the number line
Hence,
We can represent the number on a number line as follows:
Question 4.
Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:
(a) If point D is +8, then which point is -8?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of their values.
Answer:
(a) We know that,
If D is +8 then,
-8 will be a mirror image of D from 0 on the number line.
Hence,
According to the given vertical line,
-8 will be the point F on the number line.
(b) We know that,
The numbers that lie on the line above 0 are positive numbers
And,
The numbers that lie on the line below 0 are negative numbers
Now,
Since,
G lie on the line below 0
Hence,
G (-6) is a negative number.
(c) We can observe that,
Point B lies above the point 0
And,
Is at a distance of 4 units from 0
Hence,
The integer for point B is 4
Now,
Point E lies below the point 0
And,
Is at a distance of 10 units from 0
Hence,
The integer for point E is -10
(d) From the given vertical line,
We can observe that,
E has the least value
Because it represents -10
(e) Viewing the given diagram,
We can conclude that,
The points can be arranged in the decreasing order as follows:
D > C > B > A > O > H > G > F > E
Question 5.
Following is the list of temperatures of five places in India on a particular day of the year.
(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperatures in degree Celsius.
Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above 10°C.
Answer:
(a) The temperature of these places can be written in the form of integers as follows:
(b) 
(c) We can see that,
The temperature of the place Siachin has the lowest temperature of -10° C
Hence,
It is the coolest place.
(d) We can see that,
There are two places who have temperatures more than 10°C.
These places are as follows:
Ahmedabad and Delhi
Question 6.
In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9
(b) -3, -8
(c) 0, -1
(d) -11, 10
(e) -6, 6
(f) 1, -100
Answer:
(a) As we know that,
9 > 2
Hence,
According to the question:
9 will be right to 2 on the number line.
(b) As we know that,
-3 > -8
Hence,
According to the question:
-3 will be right to -8 on the number line.
(c) As we know that,
0 > -1
Hence,
According to the question:
0 will be right to -1 on the number line.
(d) As we know that,
10 > -11
Hence,
According to the question:
10 will be right to -11 on the number line.
(e) As we know that,
6 > -6
Hence,
According to the question:
6 will be right to -6 on the number line.
(f) As we know that,
1 > -100
Hence,
According to the question:
1 will be right to -100 on the number line.
Question 7.
Write all the integers between the given pairs (write them in the increasing order)
(a) 0 and -7
(b) -4 and 4
(c) -8 and -15
(d) -30 and -23
Answer:
(a) The integers that lie between the pair are:
-1, -2, -3, -4, -5, -6
They can be arranged in the following way:
-6, -5, -4, -3, -2, -1
(b) The integers that lie between the pair are:
3, 2, 1, 0, -1, -2, -3
They can be arranged in the following way:
-3, -2, -1, 0, 1, 2, 3
(c) The integers that lie between the pair are:
-9, -10, -11, -12, -13, -14
They can be arranged in the following way:
-14, -13, -12, -11, -10, -9
(d) The integers that lie between the pair are:
-24, -25, -26, -27, -28, -29
They can be arranged in the following way:
-29, -28, -27, -26, -25, -24
Question 8.
Write four negative integers greater than -20
Answer:
Four negative integers greater than -20 are as follows:
-19, -18, -17, -16
Question 9.
Write four negative integers less than -10.
Answer:
Four negative integers less than -10 are as follows:
-11, -12, -13, -14
Question 10.
For the following statements write True (t) or False (F). If the statement is false, correct the statement
(a) -8 is to the right of -10 on a number line.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative integer is -1.
(d) -26 is larger than -25.
Answer:
(a) The given statement is true.
Since,
-8 > -10
(b) The given statement is false
Since,
-50 > -100 (-100 is to the left of -50 on a number line)
(c) The given statement is false
Since,
The greatest negative number is -1
(d) The given statement is false
Since,
-26 is smaller than -25
Question 11.
Draw a number line and answer the following:
(a) Which number will we reach, if we move 4 numbers to the right of -2?
(b) Which number will we reach, if we move 5 numbers to the left of 1?
(c) If we are at -8 on the number line, in which direction should we move to reach -13?
(d) If we are at -6 on the number line, in which direction should we move to reach -1?
Answer:
(a) The number line is as follows:
In case, if we move 4 numbers to the right of -2, then we’ll reach number 2
(b) the number line is as follows:
In case, if we move 5 numbers to the left of 1, then we’ll reach number -4
(c) The number line is as follows:
We can observe that,
-13 is to the left of -8
Hence,
We should move towards to the left direction.
(d) The number line is as follows:
We can observe that,
-1 is to the left of -6
Hence,
We should move towards to the right direction.
Exercise 6.2
Question 1.Using the number line write the integer which is:
(a) 3 more than 5
(b) 5 more than -5
(c) 6 less than 2
(d) 3 less than -2
Answer:
(a) By using the number line, it is clear that:
Number 3 more than 5 is 8
(b) By using the number line, it is clear that:
Number 5 more than – 5 is 0
(c) By using the number line, it is clear that:
Number 6 less than 2 is – 4
(d) By using the number line, it is clear that:
Number 3 less than – 2 is – 5
Question 2.
Use number line and add the following integers:
(a) 9 + (-6)
(b) 5 + (-11)
(c) (-1) + (- 7)
(d) (-5) + 10
(e) (-1) + (-2) + (-3)
(f) (-2) + 8 + (-4)
Answer:
(a) By using number line, it is clear that:
9 + (-6)
= 9 – 6
= 3
(b) By using number line, it is clear that:
5 + (- 11)
= 5 – 11
= - 6
(c) By using number line, it is clear that:
(-1) + (-7)
= - 1 – 7
= - 8
(d) By using number line, it is clear that:
(- 5) + 10
= 5
(e) By using number line, it is clear that:
(-1) + (-2) + (-3)
= - 1 – 2 – 3
= - 6
(f) By using number line, it is clear that:
(- 2) + 8 + (- 4)
= -2 + 8 – 4
= - 6 + 8
= 2
Question 3.
Add without using number line:
(a) 11 + (-7)
(b) (-13) + (+18)
(c) (-10) + (+19)
(d) (-250) + (+150)
(e) (-380) + (-270)
(f) (-217) + (-100)
Answer:
(a) 11 + (-7)
= 11 – 7
= 4
Therefore, sum is 4
(b)(-13) + 18
= -13 + 18
= 5
Therefore, sum is 5
(c) (-10) + 19
= -10 + 19
= 9
Therefore, sum is 9
(d) (-250) + 150
= -250 + 150
= - 100
Therefore, sum is – 100
(e) (-380) + (-270)
= - 380 – 270
= - 650
Therefore, sum is – 650
(f) (-217) + (-100)
= - 217 – 100
= - 317
Therefore, sum is -317
Question 4.
Find the sum of:
(a) 137 and – 354
(b) -52 and 52
(c) -312, 39 and 192
(d) -50, -200 and 300
Answer:
After adding two numbers with different signs,always put the sign of largest number in the answer
IF the signs are same in the digits given numbers will be added,
IF the signs are different in the digits given numbers will be subtracted,
(a) We have to find the sum of given numbers:
= 137 + (-354)
= 137 – 354
= - 217
Therefore, sum is – 217
(b) We have to find the sum of given numbers:
= - 52 + 52
= 0
Therefore, sum is 0
(c) We have to find the sum of given numbers:
= - 312 + 39 + 192
= -312 + 231
= - 81
Thereore, sum is – 81
(d) We have to find the sum of given numbers:
= - 50 + (- 200) + 300
= - 50 – 200 + 300
= - 250 + 300
= 50
Therefore, sum is 50
Question 5.
Find the sum:
(a) (-7) + (-9) + 4 + 16
(b) (37) + (-2) + (-65) + (-8)
Answer:
(a) We have to find the sum of given numbers:
= (- 7) + (- 9) + 4 + 16
= - 7 – 9 + 4 + 16
= - 16 + 20
= 4
Therefore, sum is 4.
(b) We have to find the sum of given numbers:
= 37 + (- 2) + (- 65) + (- 8)
= 37 – 2 – 65 – 8
= 37 – 67 – 8
= 37 – 75
= - 38
Therefore, sum is – 38.
Exercise 6.3
Question 1.Find:
(a) 35 – (20)
(b) 72 – (90)
(c) (-15) – (-18)
(d) (-20) – (13)
(e) 23 – (-12)
(f) (-32) – (-40)
Answer:
(a) 35 – (20)
= 35 – (20)
= 35 – 20
= 15
Hence, answer is 15
(b) 72 – (90)
= 72 – (90)
= 72 – 90
= - 18
Hence, answer is – 18
(c) (- 15) – (- 18)
= (- 15) – (- 18)
= - 15 + 18
= 3
Hence, answer is 3
(d) (- 20) – (13)
= (- 20) – (13)
= - 20 – 13
= - 33
Hence, answer is – 33
(e) 23 – (- 12)
= 23 – (- 12)
= 23 + 12
= 35
Hence, answer is 35
(f) (- 32) – (- 40)
= (- 32) – (- 40)
= (- 32) + 40
= 8
Hence, answer is 8
Question 2.
Fill in the blanks with >, < or = sign.
(a) (-3) + (-6) ……..(-3) – (-6)
(b) (-21) – (-10) ……. (-31) + (-11)
(c) 45 – (-11) ….. 57 + (-4)
(d) (-25) – (-42) ….. (-42) – (-25)
Answer:
(a) We have,
= (- 3) + (- 6)
= - 3 – 6
= - 9
Also,
= (- 3) – (- 6)
= - 3 + 6
= 3
Therefore,
-9 < 3
Hence,
(-3) + (-6) < (-3) – (-6)
(b) We have,
= (- 21) – (- 10)
= - 21 + 10
= - 11
Also,
= (- 31) + (- 11)
= - 31 – 11
= - 42
Therefore,
- 11 > - 42
Hence,
(- 21) – (- 10) > (- 31) + (- 11)
(c) We have,
= 45 – (- 11)
= 45 + 11
= 56
Also,
= 57 + (- 4)
= 57 – 4
= 53
Therefore,
56 > 53
Hence,
45 – (- 11) > 57 + (- 4)
(d) We have,
= (- 25) – (- 42)
= - 25 + 42
= 17
Also,
= (- 42) – (- 25)
= - 42 + 25
= - 17
Therefore,
17 > - 17
Hence,
(- 25) – (- 42) > (- 42) – (- 25)
Question 3.
Fill in the blanks:
(a) (-8) + ….. = 0
(b) 13 + ……. = 0
(c) 12 + (-12) = ……..
(d) (-4) + …… = -12
(e) …… - 15 = -10
Answer:
(a) We have,
= - 8 + 8
= 0
(b) We have,
= 13 + (- 13)
= 13 – 13
= 0
(c) We have,
= 12 + (-12)
= 12 – 12
= 0
(d) We have,
= (- 4) + (- 8)
= - 4 – 8
= - 12
(e) We have,
= 5 – 15
= - 10
Question 4.
Find:
(a) (-7) – 8 – (-25)
(b) (-13) + 32 – 8 -1
(c) (-7) + (-8) + (-90)
(d) 50 – (-40) – (-2)
Answer:
(a) We have,
= (- 7) – 8 – (- 25)
= - 7 – 8 + 25 [negative into negative makes positive]
= - 15 + 25
= 10
Therefore, answer is 10
(b) We have,
= (- 13) + 32 – 8 – 1
= - 13 + 32 – 8 – 1
= - 13 + 32 – 9
= - 22 + 32
= 10
Therefore, answer is 10
(c) We have,
= (- 7) + (- 8) + (- 90) [positive into negative is negative]
= - 7 – 8 – 90
= - 15 – 90
= - 105
Therefore, answer is – 105
(d) We have,
= 50 – (- 40) – (- 2) [Negative into negative is positive]
= 50 + 40 + 2
= 90 + 2
= 92
Therefore, answer is 92