The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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

(\( \frac{30}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

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

\( \frac{7 x 5}{2 x 5} \) - \( \frac{4 x 1}{10 x 1} \)

\( \frac{35}{10} \) - \( \frac{4}{10} \)

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

\( \frac{35 - 4}{10} \) = \( \frac{31}{10} \) = 3\(\frac{1}{10}\)

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 3) ÷ 5 x 4 - 5²
P: 4 + (6) ÷ 5 x 4 - 5²
E: 4 + 6 ÷ 5 x 4 - 25
MD: 4 + \( \frac{6}{5} \) x 4 - 25
MD: 4 + \( \frac{24}{5} \) - 25
AS: \( \frac{20}{5} \) + \( \frac{24}{5} \) - 25
AS: \( \frac{44}{5} \) - 25
AS: \( \frac{44 - 125}{5} \)
\( \frac{-81}{5} \)
-16\(\frac{1}{5}\)