To find rational numbers between the given rational numbers, we have two different ways.
Find three rational numbers between 2/3 and 3/4.
Method 1 :
To find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2.
a = 2/3 and b = 3/4
Method 2 :
By creating equivalent fraction :
In between 32/48 and 36/48, we have
33/48, 34/48, 35/48
Problem 1 :
Find out a rational numbers lying between 1/4 and 1/3.
Solution :
Let a = 1/4 and b = 1/3
Let a and b be two rational numbers between the given rational numbers. By making the denominators same.
L.C.M of the denominator (4, 3) is 12.
a = (1/4) × (3/3) = 3/12
b = (1/3) × (4/4) = 4/12
The next value of 3/12 is 4/12, so to get more values let us create equivalent fractions.
(3/12) × (2/2) = 6/24
(4/12) × (2/2) = 8/24
In between 6/24 and 8/24, we have 7/24.
Rational numbers lying between 1/4 < 7/24 < 1/3.
Problem 2 :
Find out a rational numbers lying between 2 and 3.
Solution :
Let a = 2 and b = 3, to get one rational number between them, we may use halfway method.
c = (a + b)/2
c = (2 + 3)/2
c = 5/2
So, one rational number between 2 and 3 is 5/2.
Problem 3 :
Find out a rational numbers lying between -1/3 and 1/2.
Solution :
Let a = -1/3 and b = 1/2
LCM (3, 2) = 6
(-1/3) x (2/2) = -2/6
(1/2) x (3/3) = 3/6
-2/6 < -1/6 < 0/6 < 1/6 < 2/6 < 3/6
Problem 4 :
Find out two rational numbers lying between -3 and -2.
Solution :
Let a = -3 and b = -2
Let c and d be two rational numbers.
c = 1/2 × (a + b)
= 1/2 × (-3 - 2)
= 1/2 × (-5)
= -5/2
d = 1/2 × (-2 - 5/2)
= 1/2 × (-4 - 5)/2
= 1/2 × (-9)/2
= -9/4
Rational numbers lying between -3 < -5/2 < -9/4 < -2
So, two rational numbers -5/2, -9/4.
Problem 5 :
Find out six rational numbers lying between -4/8 and 3/8.
Solution :
Rational
numbers lying between
-4/8 < -3/8 < -2/8 < -1/8 < 0 < 1/8 < 2/8 < 3/8
So, six rational numbers is -3/8, -2/8, -1/8, 0, 1/8, 2/8.
Problem 6 :
Find out ten rational numbers lying between -4/13 and 7/13.
Solution :
In between -4/13 and 7/13.
-4/13 < -3/13 < -2/13 < -1/13 < 0/13 < 1/13 < 2/13 < 3/13 <4/13 < 5/13 < 6/13 < 7/13
So, ten rational numbers is -3/13 < -2/13 < -1/13 < 0/13 < 1/13 < 2/13 < 3/13 <4/13 < 5/13 < 6/13
Problem 7 :
Find out three rational numbers lying between 4 and 5.
Solution :
Let a = 4 and b = 5
Since we find more than one rational numbers, let us create equivalent fractions.
Let us
create another equivalent fraction 4/1 and 5/1.
4/1 × 3/3 = 12/3
5/1 × 3/3 = 15/3
Since, we find two rational numbers in between 12/3 and 15/3.
Let us create another equivalent fraction 4/1 and 5/1.
4/1 × 4/4 = 16/4
5/1 × 4/4 = 20/4
Since, we find three rational numbers in between 16/4 and 20/4.
Rational numbers lying between
16/4 < 17/4 < 18/4 < 19/4 < 5
So, three rational numbers 17/4, 18/4, 19/4.
Problem 8 :
Find out three rational numbers lying between 2/3 and 3/4.
Solution :
Let a = 2/3 and b = 3/4
L.C.M of the denominator (3, 4) is 12.
So, we can write ‘a’ and ‘b’ as given below.
a = (2/3) × (4/4) = 8/12
b = (3/4) × (3/3) = 9/12
Let us
create equivalent fraction 8/12 and 9/12.
8/12 × 3/3 = 24/36
9/12 × 3/3 = 27/36
Since, we find two rational numbers in between 24/36 and 27/36.
Let us create another equivalent fraction 8/12 and 9/12.
8/12 × 4/4 = 32/48
9/12 × 4/4 = 36/48
Since, we find three rational numbers in between 32/48 and 36/48.
Rational numbers lying between
32/48 < 33/48 < 34/48 < 35/48 < 36/48
So, three rational numbers 33/48, 34/48, 35/48.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM