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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The number of students taking German or Spanish is 13 + 10 = 23. Of that group of 23, 6 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 23 - 6 = 17 who are taking at least one language. 23 - 17 = 6 students who are not taking either language.

If the tiger has consumed 70 pounds of food in 5 days that's \( \frac{70}{5} \) = 14 pounds of food per day. The tiger needs to consume 140 - 70 = 70 more pounds of food to reach 140 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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 $1,400
i = 0.03 x $1,400

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