A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{6!}{5!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{6}{1} \)
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.

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.

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 11 people needing transportation leaving 11 - 6 = 5 who will have to find other transportation.

First, solve for \( \left|y + 7\right| \):

\( \left|y + 7\right| \) - 9 = -9
\( \left|y + 7\right| \) = -9 + 9
\( \left|y + 7\right| \) = 0

The value inside the absolute value brackets can be either positive or negative so (y + 7) must equal + 0 or -0 for \( \left|y + 7\right| \) to equal 0:

So, y = -7 or y = -7.