To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] 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 [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 3}{3 x 3} \) + \( \frac{5 x 1}{9 x 1} \)

\( \frac{12}{9} \) + \( \frac{5}{9} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{12 + 5}{9} \) = \( \frac{17}{9} \) = 1\(\frac{8}{9}\)

The amount of flour you need is (2 - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{16}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{14}{8} \) cups
1\(\frac{3}{4}\) cups

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 $800
i = 0.07 x $800

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

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.

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{76} \) = \( \frac{\frac{24}{4}}{\frac{76}{4}} \) = \( \frac{6}{19} \)