RBSE Solutions for Class 7 Maths Chapter 1 Integers In Text Exercise is part of RBSE Solutions for Class 7 Maths. Here we have given Rajasthan Board RBSE Class 7 Maths Chapter 1 Integers In Text Exercise .

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 7 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Integers |

Exercise |
In Text Exercise |

Number of Questions |
24 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 7 Maths Chapter 1 Integers In Text Exercise

**(Page 2)**

Question

Check if integers are also (RBSESolutions.com) closed for addition.

S.No |
Integers |
Integer |
Addition |
As the Sum integer yes/no |

1. | +2 | +5 | +7 | yes |

2. | -3 | +7 | ||

3. | -4 | +4 | ||

4. | 3 | -5 |

Take various integers and check if (RBSESolutions.com) this is true only for positive integers or it is true for negative integers also.

Solution:

S.No |
Integers |
Integer |
Addition |
As the Sum integer yes/no |

1. | +2 | +5 | +7 | yes |

2. | -3 | +7 | +4 | yes |

3. | -4 | +4 | 0 | yes |

4. | 3 | -5 | -2 | yes |

From above table it is clear that all integers whether they are negative or positive are closed for addition.

**(Page 3)**

Question

Can you tell such integers (RBSESolutions.com) whose sum is not an integer?

Solution:

Such integers are impossible because sum of an two integers is always an integer.

Question

What happens when we subtract one integer from another? Does their difference is also an integer? Complete the following table by observation:

Solution:

S.No |
Statement |
Observation |

1. | 7 – 5 = 2 | Result is an integer |

2. | 4 – 9 = -5 | …………. |

3. | (-4) – (-5) = …. | Result is an integer |

4. | (-18) – (-18) = .. | ……….. |

5. | 17 – 0 = …. | …………. |

Solution:

S.No |
Statement |
Observation |

1. | 7 – 5 = 2 | Result is an integer |

2. | 4 – 9 = -5 | Result is an integer |

3. | (-4) – (-5) = 1 | Result is an integer |

4. | (-18) – (-18) = 0 | Result is an integer |

5. | 17 – 0 = 17 | Result is an integer |

From table it ¡s clear that when we subtract one integer from another integer then remainder is also an integer. Therefore difference of two integers, is also an integer.

Question

Can we find such pair of integers (RBSESolutions.com) whose difference is not an Integer?

Solution:

Such pair is impossible because difference of two integers is also an integer.

Question

Check weather the following statements are same?

(-8) + (-4) and (-4) + (-8)

(-2) + 5 and 5 + (-2)

12 + 0 and 0 + 12

does integers also follow (RBSESolutions.com) commutative property of addition ? Find some other additions also.

Solution:

MathematicalStatement |
Result |
MathematicalStatement |
Result |

(-8) + (-4) | -12 | (-4) + (-8) | -12 |

(-2) + 5 | +3 | 5 + (-2) | +3 |

12 + 0 | 12 | 0 + 12 | 12 |

17 + (-2) | 15 | (-2) + 17 | 15 |

2 + (-3) | -1 | (-3) + 2 | -1 |

(-3) + 6 | 3 | 6 + (-3) | 3 |

From table it is clear that integers also follow the commutative property of addition.

Question

Is there any such pair of integers (RBSESolutions.com) where result changes on. After changing the order of integers?

Solution:

No, such pair is impossible where result changes on interchanging their order.

**(Page 4)**

Question

Observe the following and fill in the blanks :

(i)(-4) + 0 = -4,

(ii) 7 + 0 = 7,

(iii) 0+ (-14) = ….,

(iv) -8 + …. = – 8

(v) …. + 0 = 15,

(vi) – 23 + …. =- 23

Solution:

(iii) 0 + (-14) = – 14,

(iv) (-8) + 0 = -8

(v) 15 +0 = 15,

(vi) (-23) + 1 = -23

Question

From some other examples, (RBSESolutions.com) confirm that 0 is an additive identity for integers.

Solution:

From above examples, it is clear that on adding 0 with any other integer, same integer is found. Therefore 0 is additive identity for integers. It can be understand by following examples

(i) 5 + 0 = 5,

(ii) (- 10) + 0 = – 10,

(iii) (- 9) + 0 = – 9,

(iv) 23 + 0 = 23

(v) 0 + 20 = 20,

(vi) 0 + (-2) = -2

**(Page 6)**

Question

What happens when we multiply (RBSESolutions.com) a negative integer with a positive integer?

Solution:

When a negative integer is multiplied with a positive integer then negative integer is found, it can be verified from following examples –

(i) – 1 x 4 = – 4 = 0 – 4

(ii) – 2 x 4 = – 8 = – 4 – 4

(iii) -3 x 4 = – 12 = – 4 – 4 – 4

(iv) – 5 x 2 = -10 = – 5 – 5

(v) – 6 x 3 = -18 = – 6 – 6 – 6

**(Page 7)**

Question

Observe the (RBSESolutions.com) following :

-3 x 4 = -12

-3 x 3 = -9 = -12 – (-3)

-3 x 2 =-6 = -9 – (-3)

-3 x 1 = -3 = -6 – (-3)

-3 x 0 = 0 = -3 – (-3)

-3 x (-1) = 3 = 0 – (-3)

-3 x (-2) = 6 = 3-(-3)

Similarly, complete the following :

(i) -3 x (-3) = …….

(ii) – 3 x (-4) = …….

Solution:

(i) (-3) x (-3) = 9 = 6 – (-3)

(ii) (-3) x (-4) = 12 = 9 – (-3)

Question

Fill in the blanks in (RBSESolutions.com) similar manner:

-5 x 3 = -15

-5 x 2 = -10 = -15-(-5)

-5 x 1 =- = -10-(-5)

-5 x (-1) = ……. =

-5 x (-2) = ………. =

-5 x (-3) = ……… =

Solution:

-5 x 0 = 0 = – 5 -(-5)

-5 x (-1) = 5 = (0 -(-5)

(-5) x (-2) = 10 = 5-(-5)

(-5) x (-3) = 15 = 10 – (-5)

**(Page 9)**

Question

Observe the division statements in the (RBSESolutions.com) table and accordingly check the following statements and put the sign ( ✓ or ✘) :

Multiplication Statement |
Corresponding Division Statement |

3 x (-5) = (-15) | (-15) ÷ (3) = – 5, (15) ÷ (-5) = 3 |

(-3) x 4= (-12) |
(-12) ÷ (-3) = 4,(-12) ÷ 4=-3 |

(-2) x (-7) = (14)…. | 14 ÷ (-7)= -2, …….. |

(-4) x 5 = (- 20) | (-20) ÷ (-4) = 5, …….. |

5 x (-9) = – 45…. | ……………….. |

(- 6) x 5 = …. | ………………… |

(+ 5) x (+ 2) = …. | ……………….. |

(i) Negative integer ÷ Positive (RBSESolutions.com) integer = Negative integer ( )

(ii) Positive integer ÷ Negative integer = Negative integer ( )

(iii) Positive integer ÷ Positive integer = Positive integer ( )

(iv) Negative integer ÷ Negative integer = Positive integer ( )

Solution:

Multiplication Statement |
Corresponding Division Statement |

(-2) x (-7) = (14) | 14 ÷ (-7)=-2, 14 ÷ (-2) = -7 |

(-4) x 5 = (- 20) | (-20) ÷ (-4) = 5, (-20) ÷ 5 = -4 |

5 x (-9) = – 45 | (-45) ÷ 5 = -9 (-45) ÷ (-9) = 5 |

(- 6) x 5 = (-30) | (-30) ÷ (-6) = 5, (-30) ÷ 5 = -6 |

(+ 5) x (+ 2) = 10 | (+10) ÷ (+5) = +2, (+10) ÷ (+2) = +5 |

(i) Negative integer ÷ Positive (RBSESolutions.com) integer = Negative integer (✓)

(ii) Positive integer ÷ Negative integer = Negative integer (✓)

(iii) Positive integer ÷ Positive integer = Positive integer (✓)

(iv) Negative integer ÷ Negative integer = Positive integer (✓)

**(Page 10)**

Question

Complete the following table:

Integer-1 |
Integer-2 |
Product |
Product is an integer Yes/No |

2 | -3 | -6 | Integer |

-3 | 4 | -12 | Integer |

-2 | -3 | …… | ……. |

5 | 4 | ….. | ……. |

-5 | 3 | ….. | …… |

Solution:

Integer-1 |
Integer-2 |
Product |
Product is an integer Yes/No |

-2 | -3 | 6 | Integer |

5 | 4 | 20 | Integer |

-5 | 3 | -15 | Integer |

Conclusion: Product of two (RBSESolutions.com) integers is also an integer.

**(Page 11)**

Question

Observe and complete the following table

Solution:

Outcome: Product of integers does not depend on their order.

Question

Check for the (RBSESolutions.com) integers

(-3) x 1 =-3 1 x 5=5

(-4) x 1 = 1 x 8 =

1 x (-5) = 3 x 1 =

1 x (-6) = 7 x 1 =

Solution:

(-4) x 1 =-4 1 x 8 = 8

1 x (5) =-5 3 x 1 = 3

1 x (-6) = – 6 7 x 1 = 7

Outcome : Multiplicative identity for integers is 1.

**(Page 12)**

Question

Observe and complete (RBSESolutions.com) the following table

Statement |
Conclusion |

(- 8) ÷ (-2) = 4 | is an integer |

(-8 ) ÷ 4 | …………. |

(-2) ÷ (-8) = [latex]\frac { -2 }{ -8 }[/latex] | is not an integer |

(3) ÷ (-8) = [latex]\frac { 3 }{ -8 }[/latex] | ……………. |

Solution:

Statement |
Conclusion |

(-8 ) ÷ 4 = -2 | is an integer |

(3) ÷ (-8) = [latex]\frac { 3 }{ -8 }[/latex] | is not an integer |

**Do and Learn**

Question 1

In which direction one should (RBSESolutions.com) move on the number line to add – 5?

Solution:

On number line, left side will be used to add – 5.

Question 2

In which direction one will move on the number line to subtract – 5 from 3 and will reach on what number ? 3 – (- 5) = ……

Solution:

On number line, right side will be used and will reach at, 3 – (- 5) = 3 + 5 = 8.

Question 3

In which direction we will (RBSESolutions.com) move and on which number will we reach by adding 5 to 3?

Solution:

On number line, right side will be used and will reach at, 3 + 5 = 8.

Question 4

In which direction we will move and on which number will we teach by subtracting + 5 from – 3?

Solution:

On number line, left side will be (RBSESolutions.com) used and will reach at – 3 – (+ 5) = – 3 – 5 = -8.

**(Page 6)**

Question

Solve:

(i) 4 x (8) = …. = ….

(ii) 3 x (-3) = …. = ……

(iii) 5 x (-9) = …. = …..

Solution:

(i) 4 x (8) = (- 8) + (-8) + (-8) + (-8) = -32

(ii) 3 x (-3) = (-3) + (-3) + (-3) = -9

(iii) 5 x (-9) = (-9) + (-9) + (- 9) + (-9) + (-9) = -45

**(Page 7)**

Question

Find:

(i) 15 x (-5)

(ii) 27 x (- 10)

(iii) – 12 x 12

(iv) -7 x 4

Solution:

(i) 15 x (-5) = – 75

(ii) 27 x (- 10) = – 270

(iii) – 12 x 12 = – 144

(iv) – 7 x 4 = – 28

Question

Find the following (RBSESolutions.com) products:

(i) (-12) x (-15)

(ii) (-25) x (-4)

(iii) (-17) x (-11)

Solution:

(i) (-12) x (-15) = 180

(ii) (-25) x (-4) = 100

(iii) (-17) x (-11) = 187

**(Page 8)**

Question

Find the following (RBSESolutions.com) product

(i) (-1) x (-1) x (-1) = ……..

(ii) (-1) x (-1) x (-1) x (-1) = ……..

Solution:

(i) (-1) x (-1) x (-1) = [(-1) x (-1)] x (-1) = (+1) x (-1) = -1

(ii) (-1) x (-1) x (-1) x (-1) = [(-1) x (-1)] x [(-1) x (-1)] = 1 x 1 = 1

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