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:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

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

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

5\( \sqrt{18} \) + 4\( \sqrt{2} \)
5\( \sqrt{9 \times 2} \) + 4\( \sqrt{2} \)
5\( \sqrt{3^2 \times 2} \) + 4\( \sqrt{2} \)
(5)(3)\( \sqrt{2} \) + 4\( \sqrt{2} \)
15\( \sqrt{2} \) + 4\( \sqrt{2} \)

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

If the tiger has consumed 32 pounds of food in 4 days that's \( \frac{32}{4} \) = 8 pounds of food per day. The tiger needs to consume 72 - 32 = 40 more pounds of food to reach 72 pounds total. At 8 pounds of food per day that's \( \frac{40}{8} \) = 5 more days.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.