Before moving to find the five rational numbers between 2/3 and 4/5 it is important to understand the meaning of rational numbers. The definition of rational numbers can be stated as the numbers that are presentable in the form of p/q. In this form, q is not equal to 0 (zero).
There exist various properties that make a number rational. Some of them are,
- On the multiplication, subtraction or the addition of two rational numbers the number obtained will always be a rational number.
- If the division or multiplication of numerator and denominator takes place by the same factor then the rational number is going to remain the same.
- If the addition of any rational number happens to take place with zero then the rational number remains to be the same.
- Under addition, multiplication and subtraction the rational numbers remain to be closed.
To find five rational numbers between 2/3 and 4/5
Multiplication of 2/3 and 5/5
2/3 * 5/5 = 10/15
Multiplication of 4/5 and 3/3
4/5 * 3/3 = 12/15
Now multiplication of 2/3 and 4/5 by 6/6 to obtain the five rational numbers
10/15 * 6/6 = 60/90
11/15 * 6/6 = 72/90.
Therefore the five rational numbers are, 61/90, 62/90, 63/90, 64/90 and 65/90.