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.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{78}{6} \) = 13

The equation for this sequence is:

a_n = a_n-1 + 8

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 + 8
a₆ = 33 + 8
a₆ = 41

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2c³ + 7c³
(2 + 7)c³
9c³

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 36 large cakes are needed for the party so \( \frac{36}{10} \) = 3\(\frac{3}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 270 small cakes are needed for the party so \( \frac{270}{28} \) = 9\(\frac{9}{14}\) 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 4 + 10 = 14 cooks.