**Ten Rational Numbers Between 2/5 and 2/3**

To find ten rational numbers between 2/5 and 2/3, we first need to understand what rational numbers are. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers.

Given that the rational numbers lie between 2/5 and 2/3, we can start by finding their decimal equivalents. By dividing the numerator by the denominator, we can determine the decimal representation of each fraction.

**Decimal Equivalent of 2/5:**
Dividing 2 by 5, we get 0.4.

**Decimal Equivalent of 2/3:**
Dividing 2 by 3, we get 0.6666... (repeating).

Now that we have the decimal equivalents, we can find ten rational numbers between these two decimal values.

**Method 1: Incrementing by a Common Difference**
One approach is to increment the decimal values by a common difference to obtain the desired rational numbers. Let's choose a common difference of 0.02 and apply it to the decimal equivalent of 2/5:

- 0.4 + 0.02 = 0.42
- 0.42 + 0.02 = 0.44
- 0.44 + 0.02 = 0.46
- 0.46 + 0.02 = 0.48
- 0.48 + 0.02 = 0.5

Similarly, we can apply the same common difference to the decimal equivalent of 2/3:

- 0.66 + 0.02 = 0.68
- 0.68 + 0.02 = 0.7
- 0.7 + 0.02 = 0.72
- 0.72 + 0.02 = 0.74
- 0.74 + 0.02 = 0.76

Therefore, the ten rational numbers between 2/5 and 2/3 would be:
- 0.42
- 0.44
- 0.46
- 0.48
- 0.5
- 0.68
- 0.7
- 0.72
- 0.74
- 0.76

**Method 2: Fractional Conversion**
Another approach is to convert the decimal values back into fractions. Using this method, we can find ten rational numbers between 2/5 and 2/3:

- 0.4 can be written as 4/10 or simplified as 2/5.
- 0.42 can be written as 42/100, which simplifies to 21/50.
- 0.44 can be written as 44/100, which simplifies to 11/25.
- 0.46 can be written as 46/100, which simplifies to 23/50.
- 0.48 can be written as 48/100, which simplifies to 12/25.
- 0.5 remains the same as 2/4 or 1/2.
- 0.66 can be written as 66/100, which simplifies to 33/50.
- 0.68 can be written as

10 rational number between 2/5 and 2/3 are
6*3/15*3 and 10*3/15*3
18/45 and 30/45 = 19/45,20/45,21/45,22/45,23/45,24/45,25/45,26/45,27/45,28/45etc. are 10 rational numbers between 2/5 and 2/3.