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# Negative Numbers and Integers - Exercise 5.1 Class 6 Notes | EduRev

## Class 6 : Negative Numbers and Integers - Exercise 5.1 Class 6 Notes | EduRev

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Exercise 5.1                                                                         PAGE: 5.5
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:

(i) The opposite of Increase in population is Decrease in population.

(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.

(iii) The opposite of earning money is Spending money.

(iv) The opposite of Going North is Going South.

(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.

(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.

(vii) The opposite of 25 is – 25.

(viii) The opposite of – 15 is 15.

2. Indicate the following by using integers:
(i) 25
o
above zero
(ii) 5
o
below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:

(i) 25
o
above zero is + 25
o
.

(ii) 5
o
below zero is - 5
o
.

(iii) A profit of Rs 800 is + 800.

(iv) A deposit of Rs 2500 is + 2500.

(v) 3km above sea level is + 3.

(vi) 2km below level is – 2.

Page 2

Exercise 5.1                                                                         PAGE: 5.5
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:

(i) The opposite of Increase in population is Decrease in population.

(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.

(iii) The opposite of earning money is Spending money.

(iv) The opposite of Going North is Going South.

(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.

(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.

(vii) The opposite of 25 is – 25.

(viii) The opposite of – 15 is 15.

2. Indicate the following by using integers:
(i) 25
o
above zero
(ii) 5
o
below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:

(i) 25
o
above zero is + 25
o
.

(ii) 5
o
below zero is - 5
o
.

(iii) A profit of Rs 800 is + 800.

(iv) A deposit of Rs 2500 is + 2500.

(v) 3km above sea level is + 3.

(vi) 2km below level is – 2.

3. Mark the following integers on a number line:
(i) 7
(ii) -4
(iii) 0
Solution:

The following integers are marked on a number line as given below:

4. Which number in each of the following pairs is smaller?
(i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Solution:

(i) 0 is greater than the negative integers
So we get – 4 < 0
Therefore, - 4 is smaller.

(ii) 12 is greater than -3 on a number line
So we get
-3 < 12
Therefore, - 3 is smaller.

(iii) 13 is greater than 8 on a number line
So we get 8 < 13
Therefore, 8 is smaller.

(iv) – 15 is greater than – 27 on a number line
So we get – 27 < - 15
Therefore, - 27 is smaller.

5. Which number in each of the following pairs is larger?
(i) 3, -4
(ii) – 12, - 8
(iii) 0, 7
(iv) 12, - 18
Solution:

(i) We know that 3 is larger than – 4 on a number line
So we get 3 > - 4
Therefore, 3 is larger.

(ii) We know that – 8 is larger than – 12 on a number line
So we get – 8 > - 12
Page 3

Exercise 5.1                                                                         PAGE: 5.5
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:

(i) The opposite of Increase in population is Decrease in population.

(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.

(iii) The opposite of earning money is Spending money.

(iv) The opposite of Going North is Going South.

(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.

(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.

(vii) The opposite of 25 is – 25.

(viii) The opposite of – 15 is 15.

2. Indicate the following by using integers:
(i) 25
o
above zero
(ii) 5
o
below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:

(i) 25
o
above zero is + 25
o
.

(ii) 5
o
below zero is - 5
o
.

(iii) A profit of Rs 800 is + 800.

(iv) A deposit of Rs 2500 is + 2500.

(v) 3km above sea level is + 3.

(vi) 2km below level is – 2.

3. Mark the following integers on a number line:
(i) 7
(ii) -4
(iii) 0
Solution:

The following integers are marked on a number line as given below:

4. Which number in each of the following pairs is smaller?
(i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Solution:

(i) 0 is greater than the negative integers
So we get – 4 < 0
Therefore, - 4 is smaller.

(ii) 12 is greater than -3 on a number line
So we get
-3 < 12
Therefore, - 3 is smaller.

(iii) 13 is greater than 8 on a number line
So we get 8 < 13
Therefore, 8 is smaller.

(iv) – 15 is greater than – 27 on a number line
So we get – 27 < - 15
Therefore, - 27 is smaller.

5. Which number in each of the following pairs is larger?
(i) 3, -4
(ii) – 12, - 8
(iii) 0, 7
(iv) 12, - 18
Solution:

(i) We know that 3 is larger than – 4 on a number line
So we get 3 > - 4
Therefore, 3 is larger.

(ii) We know that – 8 is larger than – 12 on a number line
So we get – 8 > - 12

Therefore, - 8 is larger.

(iii) We know that 7 is larger than 0 on a number line
So we get 7 > 0
Therefore, 7 is larger.

(iv) We know that 12 is larger than – 18 on a number line
So we get 12 > - 18
Therefore, 12 is larger.

6. Write all integers between:
(i) – 7 and 3
(ii) – 2 and 2
(iii) – 4 and 0
(iv) 0 and 3
Solution:

(i) The integers between – 7 and 3 are
- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2

(ii) The integers between – 2 and 2 are
-1, 0, 1.

(iii) The integers between – 4 and 0 are
-3, -2, -1

(iv) The integers between 0 and 3 are
1, 2.

7. How many integers are between?
(i) – 4 and 3
(ii) 5 and 12
(iii) – 9 and – 2
(iv) 0 and 5
Solution:

(i) The integers between – 4 and 3 are
-3, -2, -1, 0, 1, 2
Therefore, number of integers between – 4 and 3 are 6.

(ii) The integers between 5 and 12 are
6, 7, 8, 9, 10, 11
Therefore, number of integers between 5 and 12 are 6.

(iii) The integers between – 9 and – 2 are
-8, -7, -6, -5, -4, -3
Therefore, number of integers between -9 and -2 are 6.

(iv) The integers between 0 and 5 are
1, 2, 3, 4
Page 4

Exercise 5.1                                                                         PAGE: 5.5
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:

(i) The opposite of Increase in population is Decrease in population.

(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.

(iii) The opposite of earning money is Spending money.

(iv) The opposite of Going North is Going South.

(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.

(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.

(vii) The opposite of 25 is – 25.

(viii) The opposite of – 15 is 15.

2. Indicate the following by using integers:
(i) 25
o
above zero
(ii) 5
o
below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:

(i) 25
o
above zero is + 25
o
.

(ii) 5
o
below zero is - 5
o
.

(iii) A profit of Rs 800 is + 800.

(iv) A deposit of Rs 2500 is + 2500.

(v) 3km above sea level is + 3.

(vi) 2km below level is – 2.

3. Mark the following integers on a number line:
(i) 7
(ii) -4
(iii) 0
Solution:

The following integers are marked on a number line as given below:

4. Which number in each of the following pairs is smaller?
(i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Solution:

(i) 0 is greater than the negative integers
So we get – 4 < 0
Therefore, - 4 is smaller.

(ii) 12 is greater than -3 on a number line
So we get
-3 < 12
Therefore, - 3 is smaller.

(iii) 13 is greater than 8 on a number line
So we get 8 < 13
Therefore, 8 is smaller.

(iv) – 15 is greater than – 27 on a number line
So we get – 27 < - 15
Therefore, - 27 is smaller.

5. Which number in each of the following pairs is larger?
(i) 3, -4
(ii) – 12, - 8
(iii) 0, 7
(iv) 12, - 18
Solution:

(i) We know that 3 is larger than – 4 on a number line
So we get 3 > - 4
Therefore, 3 is larger.

(ii) We know that – 8 is larger than – 12 on a number line
So we get – 8 > - 12

Therefore, - 8 is larger.

(iii) We know that 7 is larger than 0 on a number line
So we get 7 > 0
Therefore, 7 is larger.

(iv) We know that 12 is larger than – 18 on a number line
So we get 12 > - 18
Therefore, 12 is larger.

6. Write all integers between:
(i) – 7 and 3
(ii) – 2 and 2
(iii) – 4 and 0
(iv) 0 and 3
Solution:

(i) The integers between – 7 and 3 are
- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2

(ii) The integers between – 2 and 2 are
-1, 0, 1.

(iii) The integers between – 4 and 0 are
-3, -2, -1

(iv) The integers between 0 and 3 are
1, 2.

7. How many integers are between?
(i) – 4 and 3
(ii) 5 and 12
(iii) – 9 and – 2
(iv) 0 and 5
Solution:

(i) The integers between – 4 and 3 are
-3, -2, -1, 0, 1, 2
Therefore, number of integers between – 4 and 3 are 6.

(ii) The integers between 5 and 12 are
6, 7, 8, 9, 10, 11
Therefore, number of integers between 5 and 12 are 6.

(iii) The integers between – 9 and – 2 are
-8, -7, -6, -5, -4, -3
Therefore, number of integers between -9 and -2 are 6.

(iv) The integers between 0 and 5 are
1, 2, 3, 4

Therefore, number of integers between 0 and 5 are 4.

8. Replace * in each of the following by < or > so that the statement is true:
(i) 2 * 5
(ii) 0 * 3
(iii) 0 * - 7
(iv) – 18 * 15
(v) – 235 * - 532
(vi) – 20 * 20
Solution:

(i) 2 < 5

(ii) 0 < 3

(iii) 0 > - 7

(iv) – 18 < 15

(v) – 235 > - 532

(vi) – 20 < 20

9. Write the following integers in increasing order:
(i) – 8, 5, 0, -12, 1, -9, 15
(ii) – 106, 107, - 320, - 7, 185
Solution:

(i) – 8, 5, 0, -12, 1, -9, 15 can be written in increasing order as
- 12, - 9, - 8, 0, 1, 5, 15

(ii) – 106, 107, - 320, - 7, 185 can be written in increasing order as
-320, - 106, - 7, 107, 185.

10. Write the following integers in decreasing order:
(i) – 15, 0, -2, -9, 7, 6, -5, 8
(ii) -154, 123, -205, -89, -74
Solution:

(i) – 15, 0, -2, -9, 7, 6, -5, 8 can be written in decreasing order as
8, 7, 6, 0, -2, -5, -9, -15

(ii) -154, 123, -205, -89, -74 can be written in decreasing order as
123, - 74, - 89, - 154, - 205

11. Using the number line, write the integer which is:
(i) 2 more than 3
(ii) 5 less than 3
(iii) 4 more than – 9
Solution:
Page 5

Exercise 5.1                                                                         PAGE: 5.5
1. Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4kg
(vi) A loss of Rs 1000
(vii) 25
(viii) – 15
Solution:

(i) The opposite of Increase in population is Decrease in population.

(ii) The opposite of Depositing money in a bank is Withdrawing money from a bank.

(iii) The opposite of earning money is Spending money.

(iv) The opposite of Going North is Going South.

(v) The opposite of gaining a weight of 4kg is losing a weight of 4kg.

(vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000.

(vii) The opposite of 25 is – 25.

(viii) The opposite of – 15 is 15.

2. Indicate the following by using integers:
(i) 25
o
above zero
(ii) 5
o
below zero
(iii) A profit of Rs 800
(iv) A deposit of Rs 2500
(v) 3km above sea level
(vi) 2km below level
Solution:

(i) 25
o
above zero is + 25
o
.

(ii) 5
o
below zero is - 5
o
.

(iii) A profit of Rs 800 is + 800.

(iv) A deposit of Rs 2500 is + 2500.

(v) 3km above sea level is + 3.

(vi) 2km below level is – 2.

3. Mark the following integers on a number line:
(i) 7
(ii) -4
(iii) 0
Solution:

The following integers are marked on a number line as given below:

4. Which number in each of the following pairs is smaller?
(i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Solution:

(i) 0 is greater than the negative integers
So we get – 4 < 0
Therefore, - 4 is smaller.

(ii) 12 is greater than -3 on a number line
So we get
-3 < 12
Therefore, - 3 is smaller.

(iii) 13 is greater than 8 on a number line
So we get 8 < 13
Therefore, 8 is smaller.

(iv) – 15 is greater than – 27 on a number line
So we get – 27 < - 15
Therefore, - 27 is smaller.

5. Which number in each of the following pairs is larger?
(i) 3, -4
(ii) – 12, - 8
(iii) 0, 7
(iv) 12, - 18
Solution:

(i) We know that 3 is larger than – 4 on a number line
So we get 3 > - 4
Therefore, 3 is larger.

(ii) We know that – 8 is larger than – 12 on a number line
So we get – 8 > - 12

Therefore, - 8 is larger.

(iii) We know that 7 is larger than 0 on a number line
So we get 7 > 0
Therefore, 7 is larger.

(iv) We know that 12 is larger than – 18 on a number line
So we get 12 > - 18
Therefore, 12 is larger.

6. Write all integers between:
(i) – 7 and 3
(ii) – 2 and 2
(iii) – 4 and 0
(iv) 0 and 3
Solution:

(i) The integers between – 7 and 3 are
- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2

(ii) The integers between – 2 and 2 are
-1, 0, 1.

(iii) The integers between – 4 and 0 are
-3, -2, -1

(iv) The integers between 0 and 3 are
1, 2.

7. How many integers are between?
(i) – 4 and 3
(ii) 5 and 12
(iii) – 9 and – 2
(iv) 0 and 5
Solution:

(i) The integers between – 4 and 3 are
-3, -2, -1, 0, 1, 2
Therefore, number of integers between – 4 and 3 are 6.

(ii) The integers between 5 and 12 are
6, 7, 8, 9, 10, 11
Therefore, number of integers between 5 and 12 are 6.

(iii) The integers between – 9 and – 2 are
-8, -7, -6, -5, -4, -3
Therefore, number of integers between -9 and -2 are 6.

(iv) The integers between 0 and 5 are
1, 2, 3, 4

Therefore, number of integers between 0 and 5 are 4.

8. Replace * in each of the following by < or > so that the statement is true:
(i) 2 * 5
(ii) 0 * 3
(iii) 0 * - 7
(iv) – 18 * 15
(v) – 235 * - 532
(vi) – 20 * 20
Solution:

(i) 2 < 5

(ii) 0 < 3

(iii) 0 > - 7

(iv) – 18 < 15

(v) – 235 > - 532

(vi) – 20 < 20

9. Write the following integers in increasing order:
(i) – 8, 5, 0, -12, 1, -9, 15
(ii) – 106, 107, - 320, - 7, 185
Solution:

(i) – 8, 5, 0, -12, 1, -9, 15 can be written in increasing order as
- 12, - 9, - 8, 0, 1, 5, 15

(ii) – 106, 107, - 320, - 7, 185 can be written in increasing order as
-320, - 106, - 7, 107, 185.

10. Write the following integers in decreasing order:
(i) – 15, 0, -2, -9, 7, 6, -5, 8
(ii) -154, 123, -205, -89, -74
Solution:

(i) – 15, 0, -2, -9, 7, 6, -5, 8 can be written in decreasing order as
8, 7, 6, 0, -2, -5, -9, -15

(ii) -154, 123, -205, -89, -74 can be written in decreasing order as
123, - 74, - 89, - 154, - 205

11. Using the number line, write the integer which is:
(i) 2 more than 3
(ii) 5 less than 3
(iii) 4 more than – 9
Solution:

(i) 2 more than 3
In order to get the integer 2 more than 3
We draw a number line from 2 and proceed 3 units to the right to obtain 5

Therefore, 2 more than 3 is 5.

(ii) 5 less than 3
In order to get the integer 5 less than 3
We draw a number line from 3 and proceed 5 units to the left to obtain – 2

Therefore, 5 less than 3 is – 2.

(iii) 4 more than – 9
In order to get the integer 4 more than – 9
We draw a number line from – 9 and proceed 4 units to the right to obtain -5

Therefore, 4 more than – 9 is – 5.

12. Write the absolute value of each of the following:
(i) 14
(ii) – 25
(iii) 0
(iv) – 125
(v) – 248
(vi) a – 7, if a is greater than 7
(vii) a – 7, if a - 2 is less than 7
(viii) a + 4, if a is greater than -4
(ix) a + 4 if a is less than – 4
(x) |-3|
(xi) -|-5|
(xii) |12 – 5|
Solution:

(i) The absolute value of 14 is
|14| = 14
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## Mathematics (Maths) Class 6

191 videos|224 docs|43 tests

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