Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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.

Monica scored 97% on the test meaning she earned 97% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.97 = 261 points. Each question is worth 3 points so she got \( \frac{261}{3} \) = 87 questions right.

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 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{64} \) = \( \frac{\frac{24}{8}}{\frac{64}{8}} \) = \( \frac{3}{8} \)

The amount of flour you need is (3\(\frac{1}{2}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{28}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{22}{8} \) cups
2\(\frac{3}{4}\) cups