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

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.

Solution-length = 36*(3/5)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.

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
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 :–