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

Rational Numbers Class 8 RS Aggarwal Exe-1A Goyal Brothers Prakashan ICSE Foundation Maths Solutions.  We provide step by step Solutions of lesson-1 Rational Numbers about Natural, Whole, Integers, Rational Numbers . Our Solutions contain all type Questions of Exe-1 A 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-1A Goyal Brothers ICSE Maths Solutions

Board	ICSE
Publications	Goyal Brothers Prakshan
Subject	Maths
Class	8th
writer	RS Aggarwal
Book Name	Foundation
Topics	Natural, Whole, Integers, Rational Numbers
Edition	2024-2025

Natural, Whole, Integers, Rational Numbers, Number Line Representaion, Comparison

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

Page- 12,13

Exercise- 1A

(Natural, Whole, Integers, Rational Numbers, Number Line Representaion, Comparison)

Que-1: Express -64/112 as a rational number with denominator 7.

Solution- We  can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 16.
So, -64/112 = -64 ÷ 16 / 112 ÷ 16
= -4/7.
Now, we have the simplified fraction -4/7, which already has a denominator of 7.

Que-2: Express -48/60 as a rational number with denominator 25.

Solution- The fraction −48/60​ by dividing both the numerator and the denominator by their greatest common divisor, which is 12:
−48/60 = (−48÷12)/(60÷12) = −4/5​

Now, to express this fraction with a denominator of 25, we need to multiply both the numerator and the denominator by a factor that will result in a denominator of 25. Since 5 times 5 equals 25, we can multiply both the numerator and the denominator by 5:

−4/5×5/5 = −20/25​ Ans.

Que-3: Express each of the following rational number in standard form :

(i) -12/30  (ii) -14/49   (iii) 24/-64   (iv) -36/-63

Solution- (i) The greatest common divisor of 12 and 30 is 6. So, we can simplify the fraction as follows:
−12/30 = (−12÷6)/(30÷6)
=−2/5

(ii) the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 7:
−14/49 = (−14÷7)/(49÷7)
=−2/7

(iii) let’s find the greatest common divisor (GCD) of 24 and -64, which is 8.
Now, divide both the numerator and denominator by the GCD:
24/−64 = (24÷8)/(−64÷8)
= 3/−8

(iv) ​let’s simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
−36/−63 = (−36÷9)/(−63÷9)
= 4/7

Que-4: Compare the following pairs of rational numbers :

(i) 15/32 and 17/24     (ii) 10/11 and 17/18
(iii) -5/12 and -3/4     (iv) -7/24 and 9/-20

Solution- (i) The least common multiple (LCM) of 32 and 24 is 96. Now, let’s convert each fraction so that they both have a denominator of 96:

15/32 becomes (15×3)/(32×3) =45/96
17/24​ becomes (17×4)(/24×4) =68/96​
Now, we can compare the numerators:
45<68
Since 45 is less than 68, 15/32<17/24.

So, 1532​ < 17/24.

(ii) Let’s use the second method (cross-multiplication):

For 10/11​ and 17/18 ​:
Cross-multiplying:
10×18 = 180
17×11=187
Since 187>180, we conclude that 17/18 > 10/11.

So, 17/18>10/11​.

(iii) The least common multiple (LCM) of 12 and 4 is 12.
Now, let’s convert both fractions so they have a common denominator of 12 :
−5/12 remains −5/12
−3/4​ becomes (−3×3)/(4×3) = −9/12​
Now that both fractions have the same denominator, we can compare their numerators.
The numerator of -5/12 is -5, and the numerator of -3/4 is -9.
Since -9 is less than -5, −3/4​ is less than −5/12.

So, −3/4<−5/12.

(iv) First, let’s rewrite the fractions with a common denominator, which is the least common multiple (LCM) of 24 and 20, which is 120:
(−7/24)×(5/5) = −35/120
(9/−20)×(6/6) = −54/120​
Now, we can see that both fractions have the same denominator, so we only need to compare their numerators:
For −7/24, the numerator is -35.
For 9/−20​, the numerator is -54.
Since -54 is less than -35, 9/−20 is smaller than −7/24​.
Therefore, −7/24>9/−20​.

Que-5: Arrange in ascending order :

(i) 5/6, 7/9, 11/12 and 13/18    (ii) 5/-7, -9/14, -5/6 and 7/-12 (iii) -2, 1/3, -13/6 and 8/-3    (iv) 13/-28, -23/42, -4/7 and -9/14

Solution- (i) 13/18, 7/9, 5/6, 11/12
(ii) -5/6, 5/-7, -9/14, 7/-12
(iii) 8/-3, -13/6, -2, 1/3
(iv) -9/14, -4/7, -23/42, 13/-28

Que-6: Represent each of the following numbers on the number line :

(i) 5/6     (ii) 14/3      (iii) -3/7 (iv) -17/5  (v) -2*(2/7)

Solution-  update soon

Que-7: State whether each of the following statements is true or false :

(i) Every whole number number is a rational number.
(ii) Every integers is a rational number.
(iii) 2/3 = (2 + 4)/(3 + 4)
(iv) -5/6 < -6/5
(v) -3/-4 is a negative rational number.
(vi) 0 is a whole number but it is not a rational number.

Solution- (i) True
(ii) True
(iii) False
(iv) False
(v) False
(vi) False

Que-8: Represent 13/5 and -13/5 on the number line.

Solution-  update soon

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

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