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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{8 x 4}{2 x 4} \) + \( \frac{2 x 1}{8 x 1} \)

\( \frac{32}{8} \) + \( \frac{2}{8} \)

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

\( \frac{32 + 2}{8} \) = \( \frac{34}{8} \) = 4\(\frac{1}{4}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

Latoya scored 83% on the test meaning she earned 83% of the possible points on the test. There were 140 possible points on the test so she earned 140 x 0.83 = 116 points. Each question is worth 2 points so she got \( \frac{116}{2} \) = 58 questions right.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

If 86% of the town's 26,000 voters cast ballots the number of votes cast is:

(\( \frac{86}{100} \)) x 26,000 = \( \frac{2,236,000}{100} \) = 22,360

The mayor got 54% of the votes cast which is:

(\( \frac{54}{100} \)) x 22,360 = \( \frac{1,207,440}{100} \) = 12,074 votes.