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

Mathematics (Maths) Class 6

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

 Page 1


 
 
 
 
 
 
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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