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.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{150mi}{30mph} \)
5 hours

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{15 + 11 + 14 + 12}{4} \) = \( \frac{52}{4} \) = 13

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{64} \) = \( \frac{\frac{16}{16}}{\frac{64}{16}} \) = \( \frac{1}{4} \)