A farmer had 75 apples. Every day, the farmer kept a fraction of the apples. gave the rest away , and then ate one. The fractions he decided to keep are listed below:1/2 1/4 3/4 3/5 5/6 11/15

In which order did he use the fractions so he was left with just one apple at the end ?

11\15,5\6,3\5,3\4,1\4,1\2

To find the order in which the fractions were used so that the farmer was left with just one apple at the end, we need to go through each fraction and keep track of the number of apples remaining.

Let's start with 75 apples:

1. The farmer kept 1/2 of the apples, which is (1/2) * 75 = 37.5 apples. Since we cannot have a fraction of an apple, we'll consider it as 37 apples (rounded down to the nearest whole number). The farmer gave away the remaining apples, which is 75 - 37 = 38 apples. The farmer ate one apple.

2. Now the farmer has 37 - 1 = 36 apples. The farmer kept 1/4 of the apples, which is (1/4) * 36 = 9 apples. The farmer gave away the remaining apples, which is 36 - 9 = 27 apples. The farmer ate one apple.

3. Now the farmer has 27 - 1 = 26 apples. The farmer kept 3/4 of the apples, which is (3/4) * 26 = 19.5 apples. Considering it as 19 apples, the farmer gave away the remaining apples, which is 26 - 19 = 7 apples. The farmer ate one apple.

4. Now the farmer has 7 - 1 = 6 apples. The farmer kept 3/5 of the apples, which is (3/5) * 6 = 3.6 apples. Again, considering it as 3 apples, the farmer gave away the remaining apples, which is 6 - 3 = 3 apples. The farmer ate one apple.

5. Now the farmer has 3 - 1 = 2 apples. The farmer kept 5/6 of the apples, which is (5/6) * 2 = 1.6667 apples. Considering it as 1 apple, the farmer gave away the remaining apples, which is 2 - 1 = 1 apple. The farmer ate one apple.

6. Now the farmer has 1 - 1 = 0 apples. The farmer kept 11/15 of the apples, which is (11/15) * 0 = 0 apples. The farmer gave away the remaining apples, which is 0 - 0 = 0 apples. The farmer ate one apple.

Based on the above calculations, the order in which the fractions were used is:
1/2, 1/4, 3/4, 3/5, 5/6, 11/15.