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

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