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

\( \frac{16\sqrt{15}}{8\sqrt{5}} \)
\( \frac{16}{8} \) \( \sqrt{\frac{15}{5}} \)
2 \( \sqrt{3} \)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{16} \) = 2\(\frac{5}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 270 small cakes are needed for the party so \( \frac{270}{76} \) = 3\(\frac{21}{38}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 4 = 7 cooks.

The equation for this sequence is:

a_n = a_n-1 + 7

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 + 7
a₆ = 29 + 7
a₆ = 36