Final answer:
Ken has given away 160 of his 300 marbles which is 8/15 of his marbles after simplifying the fraction 160/300.
Step-by-step explanation:
The subject of this question is Mathematics, and it involves the concept of fractions and probability. Ken has a total of 300 marbles and he gives away a certain number of them. To find the fraction of marbles Ken has given away, we need to add up the number of marbles given to Sofia, Paul, and Lucas, and then write that sum over the total number of marbles Ken started with.
Ken gave away 45 marbles to Sofia, 90 to Paul, and 25 to Lucas. This sums up to 45 + 90 + 25 marbles, which equals 160 marbles.
Now, to put this in the simplest form, we write the fraction of marbles given away as 160/300. To simplify this fraction, we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor, 20. So, 160 divided by 20 is 8, and 300 divided by 20 is 15, giving us the simplest form of the fraction, 8/15. Thus, Ken has given away 8/15 of his marbles.