To solve this problem, there are a couple things we need to do. First of all, we need to figure out how much more she's running every day. On day 1, she ran 3/16 of a mile. On day 2, she ran 3/8 of a mile. On day 3, she ran 9/16 of a mile.
How much are we adding each time? To find that out, we need all of our fractions to have the same denominator so we can compare. Let's give 3/8 a denominator of 16. 8*2=16. What you do on one side of the fraction bar, you MUST do to the other: 3*2=6. So, 3/8 = 6/16.
Day 1: 3/16. Day 2: 6/16. Day 3: 9/16. Now do you see the pattern? Every day, she runs 3/16 of a mile more. That's the answer to part 1: 3/16.
So, how long will it take her to get over 1 mile? Let's continue. Day 3: 9/16. Day 4: 9+3=12, so that's 12/16. Day 5: 15/16. Day 6: 18/16! Since the numerator is bigger than the denominator, guess what? That's more than one mile!! So on the 6th time she runs, she ran 18/16 miles. Keep in mind that 18/16 = 9/8 = 1 1/8 miles.
Answers: 3/16; 6th; 1 1/8 (or 9/8)