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.

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:

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

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $200
i = 0.08 x $200

No payments were made so the total amount due is the original amount + the accumulated interest:

If the tiger has consumed 80 pounds of food in 8 days that's \( \frac{80}{8} \) = 10 pounds of food per day. The tiger needs to consume 140 - 80 = 60 more pounds of food to reach 140 pounds total. At 10 pounds of food per day that's \( \frac{60}{10} \) = 6 more days.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 3}{2 x 3} \) + \( \frac{6 x 1}{6 x 1} \)

\( \frac{24}{6} \) + \( \frac{6}{6} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{24 + 6}{6} \) = \( \frac{30}{6} \) = 5