Add and subtract fractions with the same denominator and denominators that are multiples of the same number 2 - Reasoning

The task at hand involves a common misconception in the process of adding fractions with different denominators. The example provided is an incorrect method of combining two fractions, 3/5 and 3/7, by simply adding the numerators and denominators separately to get 6/12, which is then simplified to 1/2. However, this method is flawed as it does not take into account the need for a common denominator when adding fractions.

The correct approach to adding these two fractions is to first find a common denominator, which in this case is 35, since it is the lowest common multiple of 5 and 7. To achieve this, the fraction 3/5 is converted to 21/35 by multiplying both the numerator and denominator by 7, and the fraction 3/7 is converted to 15/35 by multiplying both the numerator and denominator by 5. Once both fractions have the same denominator, their numerators can be added to give 21/35 + 15/35, resulting in a sum of 36/35. This fraction cannot be simplified further and is already in its simplest form, representing a value greater than 1. Therefore, the initial claim that the sum of 3/5 and 3/7 equals 1/2 is incorrect, and the correct sum is actually 36/35.