The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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 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:

\( \sqrt{\frac{4}{9}} \)
\( \frac{\sqrt{4}}{\sqrt{9}} \)
\( \frac{\sqrt{2^2}}{\sqrt{3^2}} \)
\(\frac{2}{3}\)

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{98}{9} \) = 10\(\frac{8}{9}\)

So, it will take 10 full vans and one partially full van to transport the entire team making a total of 11 vans.

To subtract these radicals together their radicands must be the same:

3\( \sqrt{50} \) - 9\( \sqrt{2} \)
3\( \sqrt{25 \times 2} \) - 9\( \sqrt{2} \)
3\( \sqrt{5^2 \times 2} \) - 9\( \sqrt{2} \)
(3)(5)\( \sqrt{2} \) - 9\( \sqrt{2} \)
15\( \sqrt{2} \) - 9\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them: