Understanding Fractions Between 2/6 and 2/3

When working with fractions, one common task is to identify the fractions that lie between two given fractions. In this article, we will explore how to find fractions between 2/6 and 2/3.

Converting Fractions for Comparison

To find fractions between 2/6 and 2/3, it's essential to have a common denominator. This makes the comparison and calculation simpler. Let's first convert 2/6 and 2/3 to fractions with a common denominator.

First, let's convert 2/6 to an equivalent fraction with a denominator of 18:

2/6 can be written as 6/18 because:

6/18 (2 * 3) / (6 * 3) 2/6

NEXT, let's convert 2/3 to an equivalent fraction with a denominator of 18:

2/3 can be written as 12/18 because:

12/18 (2 * 6) / (3 * 6) 2/3

Now that both fractions have the same denominator, we can identify the fractions between 6/18 and 12/18.

Identifying Fractions Between 6/18 and 12/18

Since 6/18 is less than 12/18, we can list some fractions between them. These fractions can be:

7/18 8/18 or 4/9 9/18 or 1/2 10/18 or 5/9

These fractions lie between 2/6 and 2/3 because 6/18 7/18 8/18 9/18 10/18 12/18.

Another Method: The Common Denominator of 6

Another way to approach this is by considering a common denominator of 6. Let's convert 2/3 to an equivalent fraction with a denominator of 6:

2/3 is the same as 4/6 because:

4/6 (2 * 2) / (3 * 2) 4/6

So, the fraction between 2/6 and 4/6 is 3/6:

3/6 is exactly halfway between 2/6 and 4/6, and it can be simplified to 1/2.

Therefore, one fraction between 2/6 and 2/3 is 1/2:

1/2 is the same as 3/6 because:

3/6 (1 * 3) / (2 * 3) 3/6 (1/2 * 3) / (1 * 3) 3/6 1/2

Conclusion

In summary, there are several fractions between 2/6 and 2/3. Using common denominators and equivalent fractions makes this process straightforward. Some of the key fractions we identified are 7/18, 9/18 (or 1/2), and 10/18 (or 5/9).

Understanding these concepts can help in various mathematical problems and real-life scenarios where comparing and working with fractions is necessary.