To add 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:

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

\( \frac{10}{10} \) + \( \frac{4}{10} \)

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

\( \frac{10 + 4}{10} \) = \( \frac{14}{10} \) = 1\(\frac{2}{5}\)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

You have 3 out of the total of 100 raffle tickets sold so you have a (\( \frac{3}{100} \)) x 100 = \( \frac{3 \times 100}{100} \) = \( \frac{300}{100} \) = 3% chance to win the raffle.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 9h \)
675 miles