A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

33,000 fans x \( \frac{2}{3} \) = \( \frac{66000}{3} \) = 22,000 fans.

You have 17 out of the total of 250 raffle tickets sold so you have a (\( \frac{17}{250} \)) x 100 = \( \frac{17 \times 100}{250} \) = \( \frac{1700}{250} \) = 7% chance to win the raffle.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{7} \) x \( \frac{3}{8} \) = \( \frac{4 x 3}{7 x 8} \) = \( \frac{12}{56} \) = \(\frac{3}{14}\)