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.

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The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

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

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

6\( \sqrt{5} \) x 3\( \sqrt{5} \)
(6 x 3)\( \sqrt{5 \times 5} \)
18\( \sqrt{25} \)

Now we need to simplify the radical:

18\( \sqrt{25} \)
18\( \sqrt{5^2} \)
(18)(5)
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