The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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

9\( \sqrt{5} \) x 4\( \sqrt{4} \)
(9 x 4)\( \sqrt{5 \times 4} \)
36\( \sqrt{20} \)

Now we need to simplify the radical:

36\( \sqrt{20} \)
36\( \sqrt{5 \times 4} \)
36\( \sqrt{5 \times 2^2} \)
(36)(2)\( \sqrt{5} \)
72\( \sqrt{5} \)

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 have in common.

The greatest common factor (GCF) is the greatest factor that divides two 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.