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 :–**

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

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