RD Sharma Solutions: Negative Numbers and Integers (Exercise 5.1)

# Negative Numbers and Integers (Exercise 5.1) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

``` 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
```

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

## FAQs on Negative Numbers and Integers (Exercise 5.1) RD Sharma Solutions - Mathematics (Maths) Class 6

 1. What are negative numbers and integers?
Ans. Negative numbers are numbers less than zero, represented by a minus sign (-) before the number. Integers, on the other hand, include both positive and negative whole numbers, including zero.
 2. How are negative numbers and integers represented on a number line?
Ans. On a number line, negative numbers are represented to the left of zero, with increasing negative values as we move further left. Integers are represented by points on the number line, including both positive and negative numbers.
 3. How do we perform addition and subtraction with negative numbers and integers?
Ans. To add or subtract negative numbers or integers, we follow the rules of sign. If both numbers have the same sign, we add their absolute values and keep the common sign. If the signs are different, we subtract their absolute values and keep the sign of the number with the larger absolute value.
 4. Can negative numbers and integers be multiplied or divided?
Ans. Yes, negative numbers and integers can be multiplied or divided. When multiplying or dividing numbers with the same sign, the result is positive. When multiplying or dividing numbers with different signs, the result is negative.
 5. How are negative numbers and integers used in real-life situations?
Ans. Negative numbers and integers are used in various real-life situations, such as measuring temperatures below freezing, representing debts or losses in financial transactions, calculating elevations above and below sea level, and determining positions in a coordinate system.

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

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