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.

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 $1,500
i = 0.03 x $1,500

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

The number of students taking German or Spanish is 15 + 13 = 28. Of that group of 28, 9 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 28 - 9 = 19 who are taking at least one language. 25 - 19 = 6 students who are not taking either language.

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:

\( \frac{3!}{6!} \)
\( \frac{3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4} \)
\( \frac{1}{120} \)

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

\( \frac{3}{7} \) ÷ \( \frac{1}{9} \) = \( \frac{3}{7} \) x \( \frac{9}{1} \)

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

\( \frac{3}{7} \) x \( \frac{9}{1} \) = \( \frac{3 x 9}{7 x 1} \) = \( \frac{27}{7} \) = 3\(\frac{6}{7}\)