Which common denominator would be used to evaluate 2/3 + 4/5?

To find a common denominator for the fractions ( \frac{2}{3} ) and ( \frac{4}{5} ), you begin by determining the least common multiple (LCM) of the denominators, which are 3 and 5.

The multiples of 3 are:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

The multiples of 5 are:

5, 10, 15, 20, 25, 30...

The smallest multiple that both lists share is 15. Therefore, 15 is the least common denominator that can be used to add these two fractions together.

When the fractions are rewritten with 15 as the common denominator, ( \frac{2}{3} ) becomes ( \frac{10}{15} ) and ( \frac{4}{5} ) becomes ( \frac{12}{15} ). Adding these together gives ( \frac{10 + 12}{15} = \frac{22}{15} ).

This confirms that 15 is indeed the correct common denominator to evaluate ( \frac{2}{3} + \