Final answer:
The fraction of oranges given away is 16 out of 40, which simplifies to 2/5 when reduced to the lowest terms.
Step-by-step explanation:
The student initially has 40 oranges and gives away 7 to Joy and 9 to Happiness, which totals 16 oranges given away. To find the fraction of oranges given away, we divide the number given away by the original number of oranges. Thus, the fraction is 16/40 oranges. To reduce this to its lowest terms, we divide both the numerator and the denominator by their greatest common divisor, which is 8. This gives us a simplified fraction of 2/5. Therefore, the fraction of oranges given away, reduced to the lowest term, is 2/5.