Rational Numbers ICSE Class-8th Concise Selina Solutions Chapter-1

Rational Numbers ICSE Class-8th Concise Selina Solutions Chapter-1. We provide step by step Solutions of Exercise / lesson-1 Rational Numbers for ICSE Class-8 Concise Selina Mathematics. Our Solutions contain all type Questions with Exe-1 A, Exe-1 B, Exe-1 C , Exe-1 D and Exe-1 E to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8.

Rational Numbers ICSE Class-8th Concise Selina Solutions Chapter-1

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Exercise – 1 A Rational Numbers ICSE Class-8th

Question -1.

Add, each pair of rational numbers, given below, and show that their addition (sum) is also a rational number:

(i) 5/8 and 3/8

(ii) 8/13 and 4/13

(iii) 6/11 and 9/11

(iv) 5/26 and 8/39

(v) 5/6 and 2/3

(vi) 2 and 2/5

(vii) 9/4 and 3/8

(viii) 7/18 and 8/27

(i) 5/8 and 3/8

= -58 + 38

(Denominators are same, LCM = 8)

Which is rational number

(LCM of 13 and 13 = 13)

Which is rational number

Which is a rational number

Question-2

(i) 59 + -76

 2 9, 6 3 9, 3 3 3, 1 1, 1

(ii) 4 + 3-5

(iii)

 2 15, 12 2 15, 6 3 15, 3 5 5, 1 1, 1

LCM of 15 and 12 = 2 x 2 x 3 x 5 = 60

(iv)

 2 9, 4 2 9, 2 3 9, 1 3 3, 1 1,1

(LCM of 9 and 4 = 2 x 2 x 3 x 3 = 36)

(LCM of 9 and 4 = 36)

= -736

(v)   -89 -512

 2 9, 12 2 9, 6 3 9, 3 3 3, 1 1, 1

LCM of 9, 12 = 2 x 2 x 3 x 3 = 36

(vi) 0 + -27

( LCM of 1 and 7 = 7 )

(vii)   5-11 +0

(LCM of 1 and 11 = 11)

-5 + 011

= -511

(viii) 2 + -35

(ix) 4-9 + 1

Question -3.

Evaluate:
(i) 37  + -4+ -117 + 7

(ii) 23 + -45+ 13+ 25

(iii) 47 +0 +-89 + -13/7 + 179

(iv) 38 + -512 + 37 + 312 + -58 + -27

(i) 3 -49  -117

 3 7, 3 7 7,1 1,1

LCM of 3 and 2 = 3 x 7 = 21

(ii) 2-451325

 3 3, 5 5 1, 5 1, 1

LCM of 3 and 5 = 3 x 5 = 15

(iii) 4++-8+ -13/179

(iv) 3-512 3312 -58 -27

 2 4, 6, 7 2 2, 3, 7 3 1, 3, 7 7 1, 1, 7 1, 1, 1

(LCM of 4, 6 and 7 = 2 x 2 x 3 x 7 = 84)

Question -4.

For each pair of rational numbers, verify commutative property of addition of rational numbers:

(i) -87 and 514

(ii) 59 and 5-12

(iii) –45 and -13-15

(iv) 2-5 and 11-15

(v) 3 and -27

(vi) 2 and 3-5

(i) -87 and 514

LCM of  7, 14 is 14

 2 7, 14 7 7, 7 1, 1

This verifies that commutative property for the addition of rational numbers.

(ii) 59 and 5-12

LCM of  9, 12 is 36

 2 9, 12 2 9, 6 3 9, 3 3 3, 1 1, 1

This verifies that commutative property for the addition of rational numbers.

(iii) –45 and -13-15

LCM of  5, 15 is 15

 5 5, 15 3 1, 3 1, 1

This verifies that commutative property for the addition of rational numbers.

(iv) 2-5 and 11-15

To prove: 2-5+11-15 =11-15 +2-5

LHS 2-5+11-15

Taking LCM
3 5,15
5 5,5
1,1
∴LCM of 5 and 15=15

Hence, the commutative property for the addition of rational numbers is verified.

(v) 3 and -27

To prove   31-27    =   ..-27..+.. 31 .

LCM of 1 and 7=7)

RHS = LHS

Hence, the commutative property for the addition of rational numbers is verified.

(vi) 2 and 3-5

To prove: -21+ 3-5= 3-5+21

∵(LCM of 1 and 5=5)

Hence, the commutative property for the addition of rational numbers is verified

Question -5.

For each set of rational numbers, given below, verify the associative property of addition of rational numbers:

(i)  12and -1

(ii) -25 415 and -710

(iii) -79 2and -518

(iv) -1 56 and -2

(i)  12 , 23 and -1

To prove:

… 1+ (2+ -16.)..= (.1+ 23 )+ -1….

LHS

1+ (2-16.)..

Taking LCM
2 3,6
3 3,3
1,1
∴LCM of 3 and 6=6

RHS = (.123 )-1 Taking LCM
2 2,3
3 1,3
1,1
∴ LCM of 2 and 3=6

Hence, the associative property for the addition of rational numbers is verified.

(ii) -2415 and -710

 2 15 ,10 3 15 ,5 5 5 ,5 1 ,1

∴ LCM of 5, 15, 10 =2 x 3 x 5 = 30

 3 5, 15 5 5 ,5 1, 1

∴ LCM  of 5 and 15 = 3 x 5 = 15

This verifies associative property of the addition of rational numbers.

(iii) -72and -518

 2 3, 18 3 3, 9 5 3, 3 1, 1

∴ LCM of 3 and 18 = 2 x 3 x 3 = 18

 3 3, 9 3 3, 3 1, 1

∴ LCM of 3 and 9 = 3

This verifies associative property of the addition of rational numbers.

(iv) -1 5and -2

Show that :

This verifies associative  property  of the addition of rational numbers

….-1 + (5+ -23 )..=….(-1 + 56 )+  -2….

 2 6, 3 3 3, 3 1, 1

LCM of 6 and 3 = 6

Hence LHS= RHS
Question- 6.

Write the additive inverse (negative) of:

(i)  -38

(ii) 4-9

(iii) -7

(iv) -4-13

(v)  0

(vi)-2

(vii) 1

(viii) -13

(ix) -31

we know that sum of number and its additive inverse=0

(i)  -3

The additive inverse of ….-3..= …38 …………

(ii) 4-9

The additive inverse of …-49 ..= …49  …………

(iii) -7

(iv) -4-13

The additive inverse of -4-13 , =4-13 ,

(v)  0

(vi)-2

(vii) 1

(viii) -13

The additive inverse of -13  , =13  ,

(ix) -31

Question- 7.

Fill in the blanks:

(ii)  -5-12+ its additive inverse =__________.

(iii) If  ab is additive inverse of  -cd then -cd is additive inverse of __________.

(ii)  -5-12+ its additive inverse =__0________.

(iii) If  ais additive inverse of  -cthen -cis additive inverse of _ab_

Question -8.

State, true or false:

(i) 79= 7+59+5

(ii) 797-59-5

(iii) 797×59×5

(iv797/59/5

(v) -5-12 is a negative rational number

(vi) -1325 smaller than -25-13

(i) 797+59+5

False

(ii) 797-59-5

False

(iii) 797×59×5

True

(iv797/59/5

True

(v) -5-12 is a negative rational number

False

(vi) -1325 smaller than -25-13

False

Exercise- 1 B Selina Concise Solutions Rational Numbers ICSE Class-8th

Evaluate:

(i) 2/34/5

(ii) 4/923

(iii) 149

(iv) 27314

(v) 51829

(vi) 5211342

Subtract:

Question- 3.

The sum of two rational numbers is 9/20. If one of them is 2/5, find the other.

Question -4.

The sum of the two rational numbers is -2/3. If one of them is -8/5, find the other.

Question- 5.

The sum of the two rational numbers is -6. If one of them is -8/5, find the other.

Question -6.

Which rational number should be added to -7/8 to get -5/9 ?

Question -7.

Which rational number should be added to -5/9 to get -2/3 ?

Question- 8.

Which rational number should be subtracted from -5/6 to get 4/9 ?

Question -9.

(i) What should be subtracted from -2 to get 3/8
(ii) What should be added to -2 to get 3/8

Evaluate:

Exercise – 1 C Rational Numbers ICSE Class-8th Concise Selina Solutions

Evaluate:

Multiply:

Evaluate:

Question -4.

Multiply each rational number, given below, by one (1):

Question- 5.

For each pair of rational numbers, given below, verify that the multiplication is commutative:

Question -6.

Write the reciprocal (multiplicative inverse) of each rational number, given below :

Question -7.

Find the reciprocal (multiplicative inverse) of:

Question- 10.

Name the multiplication property of rational numbers shown below :

Question -11.

Fill in the blanks:
(i) The product of two positive rational numbers is always ……………
(ii) The product of two negative rational numbers is always ……………
(iii) If two rational numbers have opposite signs then their product is always …………..
(iv) The reciprocal of a positive rational number is ………. and the reciprocal of a negative rational number is ……………
(v) Rational number 0 has ………….. reciprocal.
(vi) The product of a rational number and its reciprocal is ………..
(vii) The numbers ……….. and ……….. are their own reciprocals.
(viii) If m is reciprocal of n, then the reciprocal of n is ………….

Exercise – 1 D Rational Numbers ICSE Class-8th

Evaluate:

Divide:

Question -3.

The product of two rational numbers is -2. If one of them is $\frac { 4 }{ 7 }$, find the other.

Question -4.

The product of two numbers is $\frac { -4 }{ 9 }$. If one of them is $\frac { -2 }{ 27 }$, find the other.

Question -5.

m and n are two rational numbers such that

Question -6.

By what number must $\frac { -3 }{ 4 }$ be multiplied so that the product is $\frac { -9 }{ 16 }$ ?

Question -7.

By what number should $\frac { -8 }{ 13 }$ be multiplied to get 16?

Question 8.

If 3  1/2 litres of milk costs ₹49, find the cost of one litre of milk?

Question -9.

Cost of 3$\frac { 2 }{ 5 }$ metre of cloth is ₹88$\frac { 1 }{ 2 }$. What is the cost of 1 metre of cloth?

Question -10.

Divide the sum of $\frac { 3 }{ 7 }$ and $\frac { -5 }{ 14 }$ by $\frac { -1 }{ 2 }$.

Question 12.

The product of two rational numbers is -5. If one of these numbers is $\frac { -7 }{ 15 }$, find the other.

Question 13.
Divide the sum of $\frac{5}{8}$ and $\frac{-11}{12}$ by the difference of $\frac{3}{7}$ and $\frac{5}{14}$

Rational Numbers Exercise 1 E – Selina Concise Mathematics Class 8 ICSE Solutions

Question -2.

Question -3.

Insert one rational number between (0 7 and 8 (ii) 3.5 and 5
(i) 2 and 3.2
(ii) 3.5 and 5
(iii) 2 and 3.2
(iv) 4.2 and 3.6
(v) $\frac { 1 }{ 2 }$ and 2

Question- 4.

Insert two rational numbers between
(i) 6 and 7
(ii) 4.8 and 6
(iii) 2.7 and 6.3

Question -5.

Insert three rational numbers between
(i) 3 and 4
(ii) 10 and 12

Question -6.

Insert five rational numbers between $\frac { 3 }{ 5 }$ and $\frac { 2 }{ 5 }$

Question -7.

Insert six rational numbers between $\frac { 5 }{ 6 }$ and $\frac { 8 }{ 9 }$

Question -8.

Insert seven rational numbers between 2 and 3.