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 factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-y^6}{6y^4} \)
\( \frac{-1}{6} \) y^{(6 - 4)}
-\(\frac{1}{6}\)y²

The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 20 are [1, 2, 4, 5, 10, 20]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 20 have in common.

To subtract these radicals together their radicands must be the same:

7\( \sqrt{63} \) - 3\( \sqrt{7} \)
7\( \sqrt{9 \times 7} \) - 3\( \sqrt{7} \)
7\( \sqrt{3^2 \times 7} \) - 3\( \sqrt{7} \)
(7)(3)\( \sqrt{7} \) - 3\( \sqrt{7} \)
21\( \sqrt{7} \) - 3\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them: