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

\( \frac{21\sqrt{10}}{3\sqrt{5}} \)
\( \frac{21}{3} \) \( \sqrt{\frac{10}{5}} \)
7 \( \sqrt{2} \)

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.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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 simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 6 factors [1, 2, 4, 7, 14, 28] making 28 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{56} \) = \( \frac{\frac{28}{28}}{\frac{56}{28}} \) = \( \frac{1}{2} \)