To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{52} \) = \( \frac{\frac{28}{4}}{\frac{52}{4}} \) = \( \frac{7}{13} \)

The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 3

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $800
i = 0.08 x $800

No payments were made so the total amount due is the original amount + the accumulated interest:

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 9}{5 x 9} \) - \( \frac{9 x 5}{9 x 5} \)

\( \frac{18}{45} \) - \( \frac{45}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{18 - 45}{45} \) = \( \frac{-27}{45} \) = -\(\frac{3}{5}\)