Rational Numbers Class 8 RS Aggarwal Exe-1C Goyal Brothers Prakashan ICSE Foundation Maths Solutions. We provide step by step Solutions of lesson-1 Rational Numbers about Multiplication of Rational Numbers . Our Solutions contain all type Questions of Exe-1C 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-1C Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-1

Board | ICSE |

Publications | Goyal Brothers Prakshan |

Subject | Maths |

Class | 8th |

writer | RS Aggarwal |

Book Name | Foundation |

Topics | Multiplication of Rational Numbers |

Edition | 2024-2025 |

### Multiplication of Rational Numbers

(Rational Numbers Class 8 RS Aggarwal Exe-1C Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-1)

**Page- 21,22**

**Exercise-1C**

(Multiplication of Rational Numbers)

**Que-1: Find the products :**

**(i) 4/9 x 7/12 (ii) -9 x 7/18 (iii) -3/16 x 8/-15****(iv) 6/7 x -21/12 (v) 5/-18 x (-9/20) (vi) -13/15 x (-25/26)**

**(vii) 7/24 x (-48) (viii) -13/5 x (-10)**

**Solution- **(i) (4×7)/(9×12)

= 28/108 = 7/27

(ii) (-9×7)/18

= -63/18 = -7/2

(iii) (-3×8)/(-15×16)

= -24/-240 = 1/10

(iv) (6x-21)/(7×12)

= -126/84 = -3/2

(v) (5x-9)/(-18×20)

= -45/-360 = 1/8

(vi) (-13x-25)/(15×26)

= 325/360 = 5/6

(vii) (7x-48)/24

= -14

(viii) (-13x-10)/5

= 26

**Que-2: Find the multiplicative inverse (or reciprocal) of :**

**(i) -17/12 (ii) -16 (iii) 0/2 ****(iv) -3/-5 (v) 2/-5**

**Solution-** (i)-12/17

(ii) -1/16

(iii) 0

(iv) 5/3

(v) -5/2

**Que-3: Find the quotient :**

**(i) 17/18 ÷ 51/4 (ii) -16/35 ÷ 15/14 ****(iii) -12/7 ÷ (-16) (iv) -9 ÷ (-5/18)**

**Solution- **(i) 17/18 x 4/51

= (17×4)/(18×51)

= 68/918 = 1/6

(ii) -16/35 x 14/15

= (-16×14)/(35×15)

= -224/ 525 = -32/75

(iii) -12/7 x 1/-16

= (-12×1)/(7x-16)

= -12/-112 = 3/28

(iv) -9 x -18/5

= (-9x-18)/5

= 162/5

**Que-4: Name the property of multiplication illustrated by each of the following statements :**

**(i) -8/9 x -13/7 = 13/7 x -8/9**

**(ii) (-3/4 x 5/7) x -9/11 = -3/4 x (5/7 x -9/11)**

**(iii) -2/3 x (-5/6 + 7/8) = (-2/3 x -5/6) + (-2/3 x 7/8)**

**(iv) -18/7 x 1 = 1 x -18/7 = -18/7**

**(v) -13/17 x 17/-13 = 17/-13 x -13/17 = 1**

**(vi) -9/7 x 0 = 0**

**Solution- **(i) Commutative property

(ii) Associative property

(iii) Distributive law

(iv) Multiplicative inverse

(v) Existence of multiplicative inverse

(vi) Multiplicative property of 0.

**Que-5: Verify whether the given statement is true or false :**

**(i) -8/9 ÷ -4/3 = -4/3 ÷ -8/9**

**(ii) -7/24 ÷ 3/-16 = 3/-16 ÷ -7/24**

**(iii) (-3/5 ÷ -12/35) ÷ 1/4 = -3/5 ÷ (-12/35 ÷ 1/4)**

**Solution- **(i) False

(ii) False

(iii) False

**Que-6: Fill in the blanks :**

**(i) ……….. is the rational number that does not have a multiplicative inverse.**

**(ii) ………… and ………….. are the rational numbers which are equal to their own reciprocals.**

**(iii) The product of a rational number is and its reciprocal is ……….. .**

**(iv) The reciprocal of a positive rational number is ………… .**

**(v) The reciprocal of a negative rational number is ………… .**

**(vi) ………….. is not the reciprocal of any number.**

**(vii) The multiplicative inverse of a rational number 1/a, a ≠ 0, is ………….. .**

**Solution- **(i) 0

(ii) 1,-1

(iii) 1

(iv) positive

(v) negative

(vi) 0

(vii) a

**Que-7: The product of two rational number is -7. If one of the number is -8/11, find the other.**

**Solution- **We are given that the product of two rational numbers is -7 and one of them is -8/11.

Let the other rational number be x.

Product of two rational numbers = -7

-8/11 X x = -7

-8x/11 = -7

x = (-7×11)/8

x = 77/8 = 9*(5/8) **Ans.**

**Que-8: ****The product of two rational number is -16/9. If one of the number is -4/3, find the other.**

**Solution- **Let other number is x,

According to the question,

-4/3 X x = -16/9

4/3 X x = 16/9

x = 16/9 ÷ 4/3

x = 16/9 X 3/4

x = 4/3**
**Other number is 4/3 Ans.

**Que-9: By what rational number must 1/26 be divided to get -8/39 ?**

**Solution- **Let the number be a.

a×(-8/39) = 1/26

So a = (1/26)/(-8/39)

= (1/26) ×(-39/8)

= -3/16. Ans.

**Que-10: Divide the sum of 13/5 and -12/7 by the product of -31/7 and 1/-2.**

**Solution- **First we have to find the sum 13/5 and -12/7

LCM of 5 and 7 is 35.

Then,

= 13/5 + (-12/7)

= 13/5 – 12/7

= (13×7)/(5×7) – (12×5)/(7×5)

= 91/35 – 60/35

= 31/35 ……(1)

Now, we have to find the product of -31/7 and 1/-2

= -31/7 x 1/-2

= (-31×1)/(-2×7)

= 31/14 ………(2)

Now divide the equations

= 31/35 ÷ 31/14

=31/35 x 14/31

= (31×14)/(35×31)

= 434/1085

= 2/5 Ans.

**Que-11: Divide the sum of 65/12 and 8/3 by their difference.**

**Solution- **First we have to find the sum (65/12)+(8/3)

LCM of 12 and 3 is 12

Then,

(65×1)/(12×1)=(65/12)

and (8×4)/(3×4)=(32/12)

Now,

= (65+32)/12

= (97/12)

Now find the difference of (65/12)−(8/3)

LCM of 12 and 3 is 12

Then,

(65×1)/(12×1) = (65/12)

(8×4)/(3×4) = (32/12)

Now,

= (65−32)/12

= (33/12)

Now divide (97/12)÷(33/12)

= (97×12)×(12/33)

= (97×12)/(12×33)

= (97×1)/(1×33)

= 97/33 Ans.

**Que-12: Find the cost of 3*(2/5) metres of cloth at Rs 63*(3/4) per metre.**

**Solution- **Given that,

Cost of 1 metre = 63*(3/4) = 255/4

Then,

Cost of 3*(2/5) metre = 3*(2/5) x cost of 1 metre

Substituting the given

Cost of 3*(2/5) metre = 3*(2/5) x 255/4

Cost of 3*(2/5) metre = 17/5 x 255/4

Cost of 3*(2/5) metre = (17×255)/(5×4)

Cost of 3*(2/5) metre = 4335/20

Cost of 3*(2/5) metre = 216*(3/4) Ans.

**Que-13: Find the area of a rectangular part which is 36*(3/5)m long and**

16*(2/5)m broad.

16*(2/5)m broad.

**Solution-**length = 36*(3/5)m

breadth = 16*(2/5)m

Area of rectangular park = length × breadth

= 36*(3/5)m ×16*(2/5)m

= 183/5m × 82/5m

= 15006/25 m² = 600*(6/25) m² Ans.

**Que-14: Find the area of a square plot of land whose each side measure**

8*(1/2) metres.

8*(1/2) metres.

**Solution- **We know that the given details are

One side measures = 8*(1/2)m

By using the formula,

Area of square = side x side

Area of square plot = 8*(1/2)m × 8*(1/2)m

= 17/2m × 17/2m

= 289/4m² = 72*(1/4)m²

∴ Area of square plot is 72*(1/4)m². Ans.

**Que-15: A cord of length 71*(1/2)m has been cut into 26 pieces of equal length. What is the length of each piece ?**

**Solution- **Total length of piece of chord = 71*(1/2) m

No. of pieces = 26

∴ Length of each piece = 71*(1/2) ÷ 26m

= 143/2÷26

= 143/2×1/26 m

= 143/52 m

= (143÷13)/(52÷13) m

= 11/4 m

= 2*(3/4) m Ans.

**Que-16: The area of a room is 65*(1/4)sq. metres. If its breadth is 5*(1/16) metres, what is its length ?**

**Solution- **Area = 65*(1/4)m²

breadth = 5*(1/16)

we know that length × breadth = area

let the length of room be x

5*(1/16) × x = 65*(1/4)

81/16 × x = 261/4

x = 261 ×16 /4×81

x = (29 × 4)/9 = 116/9

x = 12*(8/9)m Ans.

**— : End of Rational Numbers Class 8 RS Aggarwal Exe-1C Goyal Brothers Prakashan ICSE Foundation Maths Solutions :–**

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

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