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

\( \frac{4}{6} \) x \( \frac{2}{7} \) = \( \frac{4 x 2}{6 x 7} \) = \( \frac{8}{42} \) = \(\frac{4}{21}\)

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.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{14\sqrt{35}}{2\sqrt{7}} \)
\( \frac{14}{2} \) \( \sqrt{\frac{35}{7}} \)
7 \( \sqrt{5} \)

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