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 add these radicals together their radicands must be the same:

7\( \sqrt{12} \) + 8\( \sqrt{3} \)
7\( \sqrt{4 \times 3} \) + 8\( \sqrt{3} \)
7\( \sqrt{2^2 \times 3} \) + 8\( \sqrt{3} \)
(7)(2)\( \sqrt{3} \) + 8\( \sqrt{3} \)
14\( \sqrt{3} \) + 8\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

1

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

\( \frac{4}{9} \) x \( \frac{3}{7} \) = \( \frac{4 x 3}{9 x 7} \) = \( \frac{12}{63} \) = \(\frac{4}{21}\)

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31