If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{15} \) = 1\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 240 small cakes are needed for the party so \( \frac{240}{54} \) = 4\(\frac{4}{9}\) 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 2 + 5 = 7 cooks.

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 amount of flour you need is (2\(\frac{3}{8}\) - 1) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{19}{8} \) - \( \frac{8}{8} \)) cups
\( \frac{11}{8} \) cups
1\(\frac{3}{8}\) cups

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

\( \frac{4}{7} \) x \( \frac{1}{6} \) = \( \frac{4 x 1}{7 x 6} \) = \( \frac{4}{42} \) = \(\frac{2}{21}\)

The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 20 and 44 have in common.