To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{8} \) ÷ \( \frac{4}{6} \) = \( \frac{1}{8} \) x \( \frac{6}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{8} \) x \( \frac{6}{4} \) = \( \frac{1 x 6}{8 x 4} \) = \( \frac{6}{32} \) = \(\frac{3}{16}\)

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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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 9 people needing transportation leaving 9 - 4 = 5 who will have to find other transportation.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 24 meters so the equation becomes: 2w + 2h = 24.

Putting these two equations together and solving for width (w):

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²