If the tiger has consumed 45 pounds of food in 5 days that's \( \frac{45}{5} \) = 9 pounds of food per day. The tiger needs to consume 108 - 45 = 63 more pounds of food to reach 108 pounds total. At 9 pounds of food per day that's \( \frac{63}{9} \) = 7 more days.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{4}} \)
\( \frac{\sqrt{16}}{\sqrt{4}} \)
\( \frac{\sqrt{4^2}}{\sqrt{2^2}} \)
\( \frac{4}{2} \)
2

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

\( \frac{1}{7} \) x \( \frac{1}{7} \) = \( \frac{1 x 1}{7 x 7} \) = \( \frac{1}{49} \) = \(\frac{1}{49}\)

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

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.