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 equation for this sequence is:

a_n = a_n-1 + 2

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
a₆ = 9 + 2
a₆ = 11

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

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

7\( \sqrt{125} \) + 9\( \sqrt{5} \)
7\( \sqrt{25 \times 5} \) + 9\( \sqrt{5} \)
7\( \sqrt{5^2 \times 5} \) + 9\( \sqrt{5} \)
(7)(5)\( \sqrt{5} \) + 9\( \sqrt{5} \)
35\( \sqrt{5} \) + 9\( \sqrt{5} \)

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

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.