To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{76} \) = \( \frac{\frac{24}{4}}{\frac{76}{4}} \) = \( \frac{6}{19} \)

The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.

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

7\( \sqrt{80} \) - 9\( \sqrt{5} \)
7\( \sqrt{16 \times 5} \) - 9\( \sqrt{5} \)
7\( \sqrt{4^2 \times 5} \) - 9\( \sqrt{5} \)
(7)(4)\( \sqrt{5} \) - 9\( \sqrt{5} \)
28\( \sqrt{5} \) - 9\( \sqrt{5} \)

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

There are 3 4-passenger taxis available so that's 3 x 4 = 12 total seats. There are 15 people needing transportation leaving 15 - 12 = 3 who will have to find other transportation.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.