Final answer:
The sum of the fractions 2/3 and 4/5 is found by creating equivalent fractions with a common denominator of 15, resulting in an answer of 22/15 or 1 7/15.
Step-by-step explanation:
To solve the addition of the fractions 2/3+4/5, we must find a common denominator to combine them. Intuition suggests that the common denominator of these two fractions is a product of the individual denominators, which leads us to 3 x 5 = 15.
To create equivalent fractions with this common denominator, we multiply both the numerator and denominator of the first fraction by 5, getting (2x5)/(3x5) = 10/15. For the second fraction, we multiply both the numerator and denominator by 3, getting (4x3)/(5x3) = 12/15. Now, we can add these two equivalent fractions since they have a common denominator:
10/15 + 12/15 = (10 + 12) / 15 = 22/15.
Thus, the sum of 2/3 and 4/5 is 22/15, which is an improper fraction that can also be represented as 1 7/15.