In the example of 5/6 - 3/5, what is the common denominator used for subtraction?

To find the common denominator for the fractions 5/6 and 3/5 when performing the subtraction, first identify the denominators, which are 6 and 5. The common denominator is the least common multiple (LCM) of these two numbers.

The prime factors of 6 are 2 and 3, while the prime factor of 5 is simply 5. To find the LCM, take the highest power of each prime number that appears in the factorization of both denominators. Thus, you would take 2 (from 6), 3 (from 6), and 5 (from 5).

Now, multiplying these together gives:

2 × 3 × 5 = 30.

This makes 30 the least common denominator that is suitable for both fractions, allowing them to be expressed in terms of the same denominator for proper subtraction. So, when subtracting 5/6 - 3/5, both fractions should be converted to have 30 as their common denominator.