Three Rational Numbers between 1/3 and 2/5

To find three rational numbers between 1/3 and 2/5, we need to look for fractions that lie between these two given fractions.

Understanding Rational Numbers:
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. These numbers can be positive, negative, or zero.

Finding Rational Numbers between 1/3 and 2/5:

To find rational numbers between 1/3 and 2/5, we can use the following approach:

Step 1: Convert the given fractions to have a common denominator.
The least common denominator for 3 and 5 is 15.

1/3 becomes 5/15 by multiplying the numerator and denominator by 5.
2/5 becomes 6/15 by multiplying the numerator and denominator by 3.

Step 2: Find rational numbers between 5/15 and 6/15.

Method 1: Using Addition
We can find rational numbers between 5/15 and 6/15 by adding a fraction with a numerator greater than 5 and a fraction with a numerator less than 6.

- Adding 1/15 to 5/15, we get 6/15.
- Adding 2/15 to 5/15, we get 7/15.

Therefore, the rational numbers 6/15 and 7/15 lie between 1/3 and 2/5.

Method 2: Using Averaging
Another way to find rational numbers between 5/15 and 6/15 is by averaging the two fractions.

- Average of 5/15 and 6/15 is (5/15 + 6/15) / 2 = 11/30.
- Average of 5/15 and 11/30 is (5/15 + 11/30) / 2 = 16/45.

Therefore, the rational numbers 11/30 and 16/45 are between 1/3 and 2/5.

Summary:
In summary, three rational numbers between 1/3 and 2/5 are:
- 6/15
- 7/15
- 11/30
- 16/45

These fractions were found by converting the given fractions to have a common denominator and then either adding a fraction or averaging the two fractions to find rational numbers that lie between them.

15/45'
16/45
17/45