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

\( \frac{14\sqrt{49}}{2\sqrt{7}} \)
\( \frac{14}{2} \) \( \sqrt{\frac{49}{7}} \)
7 \( \sqrt{7} \)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{20} \) = 1\(\frac{13}{20}\) 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 4 hours, a single cook can bake 18 x 4 = 72 small cakes during that time. 310 small cakes are needed for the party so \( \frac{310}{72} \) = 4\(\frac{11}{36}\) 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.

The greatest common factor (GCF) is the greatest factor that divides two integers.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{13 + 11 + 15 + 9}{4} \) = \( \frac{48}{4} \) = 12