Which is greater: 2/3 or 3/5?

To determine which fraction is greater, it's helpful to compare the two fractions by converting them to a common denominator. The fractions 2/3 and 3/5 need to be expressed with a denominator that both can share.

The least common multiple (LCM) of the denominators 3 and 5 is 15. We can convert both fractions:

For 2/3:

Multiply both the numerator and denominator by 5:

2/3 = (2 * 5) / (3 * 5) = 10/15.

For 3/5:

Multiply both the numerator and denominator by 3:

3/5 = (3 * 3) / (5 * 3) = 9/15.

Now, comparing 10/15 and 9/15, it is evident that 10/15 is greater than 9/15. Therefore, 2/3 is indeed greater than 3/5.

This method clearly shows why the comparison yields the result that 2/3 is the larger fraction, allowing for an informed decision based on equivalent forms of the fractions. This approach illustrates the fundamental principle of fraction comparison through a common denominator, reinforcing understanding in fraction manipulation and comparison.