To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{4}{8} \) = \( \frac{3}{7} \) x \( \frac{8}{4} \)

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

\( \frac{3}{7} \) x \( \frac{8}{4} \) = \( \frac{3 x 8}{7 x 4} \) = \( \frac{24}{28} \) = \(\frac{6}{7}\)

If the tiger has consumed 36 pounds of food in 4 days that's \( \frac{36}{4} \) = 9 pounds of food per day. The tiger needs to consume 81 - 36 = 45 more pounds of food to reach 81 pounds total. At 9 pounds of food per day that's \( \frac{45}{9} \) = 5 more days.

The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 have in common.

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

vans = \( \frac{39}{8} \) = 4\(\frac{7}{8}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

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.