RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS

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.