Three Rational Numbers Between 1/3 and 1/4

To find three rational numbers between 1/3 and 1/4, we can use the fact that rational numbers are numbers that can be expressed as a fraction of two integers. We need to find three fractions that lie between 1/3 and 1/4.

Finding the Midpoint
To find rational numbers between 1/3 and 1/4, we first find the midpoint between these two fractions. The midpoint can be calculated by adding the two fractions and dividing by 2.
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Midpoint = 7/12

Three Rational Numbers
Now, to find three rational numbers between 1/3 and 1/4, we can consider fractions that lie between 1/3 and the midpoint 7/12, and between the midpoint and 1/4.

- Rational Number 1: Between 1/3 and 7/12
To find a rational number between 1/3 and 7/12, we can take the average of these two fractions.
(1/3 + 7/12) / 2 = (4/12 + 7/12) / 2 = 11/24

- Rational Number 2: Between 7/12 and 1/4
Similarly, to find a rational number between 7/12 and 1/4, we can take the average of these two fractions.
(7/12 + 1/4) / 2 = (7/12 + 3/12) / 2 = 10/24 = 5/12

- Rational Number 3: Between 1/3 and 1/4
Lastly, we can find a rational number between 1/3 and 1/4 by taking the average of these two fractions.
(1/3 + 1/4) / 2 = (4/12 + 3/12) / 2 = 7/24

Therefore, the three rational numbers between 1/3 and 1/4 are 11/24, 5/12, and 7/24. These fractions lie in between the given range and are rational numbers.