RBSE Solutions for Class 7 Maths Chapter 1 Integers In Text Exercise

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:

Mathematical Statement	Result	Mathematical Statement	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) = \(\frac { -2 }{ -8 }\)	is not an integer
(3) ÷ (-8) = \(\frac { 3 }{ -8 }\)	…………….

Solution:

Statement	Conclusion
(-8 ) ÷ 4 = -2	is an integer
(3) ÷ (-8) = \(\frac { 3 }{ -8 }\)	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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