To find three rational numbers between the fractions 3/7 and 2/7, we can start by observing the position of these fractions on a number line. Since 3/7 is greater than 2/7, we need to find numbers that lie between them.
One method to find numbers between two fractions is to convert them to decimal form. The fraction 3/7 is approximately 0.4286 and 2/7 is approximately 0.2857. We need to find three numbers that fall between these two decimal values.
Let’s consider the following three rational numbers:
- 1/2 (which is 0.5)
- 4/7 (which is approximately 0.5714)
- 5/12 (which is approximately 0.4167)
Now we can check if these numbers indeed lie between 2/7 and 3/7:
- 2/7 (approximately 0.2857) < 5/12 (approximately 0.4167) < 3/7 (approximately 0.4286)
- 3/7 (approximately 0.4286) < 4/7 (approximately 0.5714) < 2/7 (approximately 0.2857)
- 2/7 (approximately 0.2857) < 1/2 (approximately 0.5) < 3/7 (approximately 0.4286)
Thus, 5/12, 1/2, and 4/7 are three rational numbers that sit between 3/7 and 2/7.