Rational Numbers Class 8 RS Aggarwal Exe-1D Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-1. We provide step by step Solutions of ICSE mathematics of famous publications hence Our Solutions contain all type Questions 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-1D 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 | Inserting Rational Number between Two Rational Number |

Edition | 2024-2025 |

### Inserting Rational Number between Two Rational Number

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

**Page- 24**

**Exercise- 1D**

(Inserting Rational Number between Two Rational Number)

**Que-1: Find a rational number between each of the following pairs of rational numbers :**

**(i) 7/10 and 10/17 (ii) 1*(3/8) and 2 ****(iii) -3/5 and -4/7 (iv) -2 and -17/21**

**Solution- **(i) For the given pair of rational numbers 7/10 and 10/17, we can find their average as follows:

Average = [(7/10)+(10/17)]/2

= [(119/170)+(100/170)]/2

= (219/170)/2

= 219/340

(ii) For the given pair of rational numbers 1*(3/8) and 2, we can find their average as follows:

Average = [(11/8)+(2/1)]/2

= [(11/8)+(16/8)]/2

= (27/8)/2

= 27/16 = 1*(11/16)

(iii) For the given pair of rational numbers -3/5 and -4/7, we can find their average as follows:

Average = [(-3/5)+(-4/7)]/2

= [(-21/35)+(-20/35)]/2

= (-41/35)/2

= -41/70

(iv) For the given pair of rational numbers -2 and -17/21, we can find their average as follows:

Average = [(-2/1)+(-17/21)]/2

= [(-42/21)+(-17/21)]/2

= (-59/21)/2

= -59/42 = -1*(17/42)

**Que-2: Find three rational number between :**

**(i) 4 and 4*(2/3) (ii) -1/2 and -1/4 (iii) 2 and 3**

**Solution- **(i) The number is 4*(2/3) = 14/3

Now make the denominator of 14/3 and 4 same,

Multiply and divide 4 by 3,

i.e. 4 = (4×3)/3 = 12/3

The rational number between 12/3 and 14/3 is multiply numerator and denominator by 4,

12/3 = (12×4)/(3×4) = 38/12

14/3 = (14×4)/(3×4) = 56/12

The three rational number between the numbers are 49/12, 50/12, 51/12

(ii) Rational no. between 1/4 and 1/2

1/4 = (1×8)/(4×8) = 8/32

1/2 = (1×16)/(2×16) = 16/32

Rational no. between 8/32 and 16/32 are 9/32, 10/32, 11/32

(iii) 2 = 2 x (4/4) = 8/4

3 = 3 x (4/4) = 12/4

9/4, 10/4, 11/4 are three rational numbers between 2 and 3.

**Que-3: Find five rational number between :**

**(i) 3/5 and 2/3 (ii) -2 and -1*(1/2) (iii) -3 and -2**

**Solution- **(i) LCM of denominators 5 and 3 is 15

Make, denominator of each given rational number equal to 15 i.e ,

the LCM 3/5 = (3×3)/(5×3) = 9/15 and 2/3 = (2×5)/(3×5) = 10/15

Since, five rational numbers are required, multiply the numerator and denominator of each rational by 5+1 = +6

∴ 9/15 = (9×6)/(15×6) = 54/90 and 10/15 = (10×6)/(15×6) = 60/90

∴Required rational numbers between 3/5 and 2/3 are

55/90, 56/90, 57/90, 58/90 and 59/90

(ii) -2/1 and -3/2

The LCM of 1 and 2 is 2.

-2/1 = -4/2 and -3/2 = -3/2

Since, five rational numbers are required, multiply the numerator and denominator of each rational by 5+1 = +6

∴ -4/2 = (-4×6)/(2×6) = -24/12 and -3/2 = (-3×6)/(2×6) = -18/12

∴ Required rational numbers between 3/5 and 2/3 are

-23/12, -22/12, -21/12, -20/12 and -19/12

(iii) First of all convert both rational numbers into fractions by placing 1 in denominator that is :- -3/1 & -2/1

now, multiply the fractions with the successor of the no of required rational no that is :- 6

thus:- -3/1*6/6= -18/6

-2/1*6/6= -12/6

so, the rational numbers between -2 & -3 are -13/6, -14/6, -15/6, -16/6, -17/6

**Que-4: Find 10 rational number between -3/4 and 5/6.**

**Solution- **The LCM of the denominators 4 and 6 is 12

−3/4 = (−3×3)/(4×3) = −9/12

and 5/6 = (5×2)/(6×2) = 10/12

10 rational number can be between −3/4, 5/6

= −8/12, −7/12, −6/12, −5/12, −4/12, −3/12, −2/12, −11/2, 0 and 1/12

**Que-5: Find 12 rational number between -1 and 2.**

**Solution- **−1 = −5/5 and 2 = 10/5

∴ 12 rational number between -1 and 2 can be

−4/5, −3/5, −2/5, −1/5, 0, 1/5, 2/5, 3/5, 4/5, 5/5, 6/5, 7/5

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

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

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