To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{56\sqrt{49}}{8\sqrt{7}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{49}{7}} \)
7 \( \sqrt{7} \)

There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 9 people needing transportation leaving 9 - 8 = 1 who will have to find other transportation.

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{81}} \)
\( \frac{\sqrt{36}}{\sqrt{81}} \)
\( \frac{\sqrt{6^2}}{\sqrt{9^2}} \)
\(\frac{2}{3}\)