The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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.

The amount of flour you need is (2\(\frac{1}{4}\) - 1\(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{14}{8} \)) cups
\( \frac{4}{8} \) cups
\(\frac{1}{2}\) cups

First, solve for \( \left|c - 4\right| \):

\( \left|c - 4\right| \) + 5 = 1
\( \left|c - 4\right| \) = 1 - 5
\( \left|c - 4\right| \) = -4

The value inside the absolute value brackets can be either positive or negative so (c - 4) must equal - 4 or --4 for \( \left|c - 4\right| \) to equal -4:

So, c = 8 or c = 0.

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

vans = \( \frac{34}{16} \) = 2\(\frac{1}{8}\)

So, it will take 2 full vans and one partially full van to transport the entire team making a total of 3 vans.