Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers Prakashan ICSE Foundation Maths Solutions. We provide step by step Solutions of lesson-1 Rational Numbers about Addition and subtraction on rational numbers . Our Solutions contain all type Questions of Exe-1B to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

## Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers ICSE Maths Solutions

Board | ICSE |

Publications | Goyal Brothers Prakshan |

Subject | Maths |

Class | 8th |

writer | RS Aggarwal |

Book Name | Foundation |

Topics | addition subtraction on rational numbers |

Edition | 2024-2025 |

### Addition and Subtraction on Rational Numbers

Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers Prakashan ICSE Foundation Maths Solutions

**.Page- 16**

**Exercise- 1B**

(Addition and Subtraction on Rational Numbers)

**Que-1: Find the additive inverse of :**

**(i) 9/13 (ii) 16/7 (iii) -3/23 ****(iv) 8/-11 (v) -22/15 (vi) -11/-9**

**Solution- ** we know that Additive inverse is a number which on getting added to the original number results in zero

(i) -9/13

(ii) -16/7

(iii) 3/23

(iv) 8/11

(v) 22/15

(vi) -11/9

**Que-2: Find the sum :**

**(i) -7/17 + 6/17 (ii) -5/12 + 7/-12 (iii) 8/15 + 5/12 ****(iv) -11/18 + 5/-12 (v) -11/6 + -3/4 + 5/8 + -7/3 ****(vi) 4/7 + 2/-3 + 5/21 + -8/9**

**Solution- **(i) -7/17 + 6/17

= (-7 + 6)/17

= -1/17

(ii) -5/12 + 7/-12

= (-5 + (-7))/12

= -12/12 = -1

(iii) 8/15 + 5/12

take lcm of 15 and 12 is 60.

[(8×4)+(5×5)]/60

(32+25)/60

57/60

(iv) on taking LCM of 12 and 18 is 36.

= [(-11×2)-(5×3)]/36

= -22-15/36

= -37/36 = -1*(1/36)

(v) LCM of 6,4,8 and 3 is 24.

−11/6×4/4 = −44/24

−3/4×6/6 = −18/24

5/8×3/3 = 15/24

−7/3×8/8 = −56/24

Now, we can add them together:

(−44/24) + (−18/24) + (15/24) + (−56/24)

=[(−44)+(−18)+15+(−56)]/24

= (−44−18+15−56)/24

= -103/24 = -4*(7/24) Ans.

(vi) The common denominator for 7, -3, 21, and 9 is 63

Then, rewrite each fraction with the common denominator:

= 4/7×9/9 = 36/63

= 2/−3×21/21 = −42/63

= 5/21×3/3 = 15/63

= −8/9×7/7 = −56/63

Now, add these fractions together:

36/63+(−42/63)+(15/63)+(−56/63)

= (36−42+15−56)/63

= −47/63

**Que-3: Subtract :**

**(i) 2/3 from 5/6 (ii) -2/5 from -5/7 ****(iii) 4/9 from -7/8 (iv) -11/6 from 8/3**

**Solution- **(i) 5/6 – 2/3

Taking LCM of 3 and 6 is 6

5/6 x 1/1 = 5/6

2/3 x 2/2 = 4/6

= 5/6 – 4/6

= 1/6

(ii) -5/7 – (-2/5)

Taking LCM of 5 and 7 is 35.

-5/7 x 5/5 = -25/35

-2/5 x 7/7 = -14/35

= -25/35 – (-14/35)

= -25/35 + 14/35

= -11/35

(iii) -7/8 – 4/9

Taking LCM of 8 and 9 is 72.

-7/8 x 9/9 = -63/72

4/9 x 8/8 = 32/72

= -63/72 – 32/72

= -95/72 = -1*(23/72)

(iv) 8/3 – (-11/6)

Taking LCM of 3 and 6 is 6.

8/3 x 2/2 = 16/6

-11/6 x 1/1 = -11/6

= 16/6 – (-11/6)

= 16/6 + 11/6

= 27/6 = 9/2 = 4*(1/2)

**Que-4: The sum of two rational numbers is -4/9. If one of them is 13/6, then find the other.**

**Solution- **According to the problem, the sum of two rational numbers is −4/9. So, we can write the equation:

13/6+x = −4/9

To find x, let’s isolate it on one side of the equation.

x = −4/9−13/6

To add these fractions, we need to find a common denominator, which is 18.

x = (−4×2)/(9×2)−(13×3(/(6×3)

x = −8/18−39/18

x = (−8−39)/18

x = −47/18 Ans.

**Que-5: What number should be added to -2/3 to get -1/7 ?**

**Solution- **According to the question:

let other number be x

sum of – 2 / 3 and a number = – 1 / 7

x + ( – 2 / 3 ) = – 1 / 7

x – 2 / 3 = – 1 / 7

x = ( – 1 / 7 ) + ( 2 / 3 )

x = { – ( 1 x 3 ) / ( 7 x 3 ) } + { ( 2 x 7 ) / ( 3 x 7 ) }

x = ( – 3 / 21 ) + ( 14 / 21 )

x = ( – 3 + 14 ) / 21

x = 11 / 21

**Que-6: What number should be subtracted from -2 to get 7/11 ?**

**Solution- **Let x be the number that needs to be subtracted from -2.

Then, the equation becomes:

−2−x = 7/11

Now, let’s solve for x:

x = −2−7/11

To subtract fractions, we need a common denominator, which is 11:

x = −22/11−7/11

x = (−22+7)/11

x = −29/11 = -2*(7/11) Ans.

**Que-7: What number should be added to -1 so as to get 5/7 ?**

**Solution-**Let x be the number that needs to be added to -1.

Then, the equation becomes:

−1+x = 5/7

Now, let’s solve for x:

x = 5/7+1

To add fractions, we need a common denominator, which is 7:

x = 5/7+7/7

x = (5+7)7

x = 12/7 Ans.

**Que-8: What number should be subtracted from -2/3 to get -1/6 ?**

**Solution- **Let x be the number that needs to be subtracted from −2/3.

Then, the equation becomes:

−2/3−x = −1/6

Now, let’s solve for x:

x = −1/6+2/3

To subtract fractions, we need a common denominator, which is 6:

x = −1/6+4/6

x = (−1+4)/6

x = 3/6

x = 1/2 Ans.

**Que-9: State whether each of the following statements is true or false ?**

**(i) The difference of two rational numbers is always a rational number.**

**(ii) 2/3 – 3/5 = 3/5 – 2/3**

**(iii) 1 is the additive identity for rational numbers.**

**(iv) Subtraction is commutative on rational numbers.**

**(v) There exists a rational number which is its own additive inverse.**

**(vi) 19/-5 + -3/11 = 19/5 + 3/11**

**Solution- **(i) True

(ii) False

(iii) False

(iv) False

(v) True

(vi) False

**— : End of Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers Maths Solutions :–**

**Return to- ICSE Class -8 RS Aggarwal Goyal Brothers Math Solutions**

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