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.

There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 10 people needing transportation leaving 10 - 8 = 2 who will have to find other transportation.

The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 2}{2 x 2} \) - \( \frac{6 x 1}{4 x 1} \)

\( \frac{6}{4} \) - \( \frac{6}{4} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{6 - 6}{4} \) = \( \frac{0}{4} \) =