A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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 99 - 36 = 63 more pounds of food to reach 99 pounds total. At 9 pounds of food per day that's \( \frac{63}{9} \) = 7 more days.

If 45% of the town's 46,000 voters cast ballots the number of votes cast is:

(\( \frac{45}{100} \)) x 46,000 = \( \frac{2,070,000}{100} \) = 20,700

The mayor got 88% of the votes cast which is:

(\( \frac{88}{100} \)) x 20,700 = \( \frac{1,821,600}{100} \) = 18,216 votes.

The number of students taking German or Spanish is 12 + 6 = 18. Of that group of 18, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 18 - 4 = 14 who are taking at least one language. 25 - 14 = 11 students who are not taking either language.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).