The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 have in common.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

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

\( \frac{3 x 5}{9 x 5} \) + \( \frac{3 x 3}{15 x 3} \)

\( \frac{15}{45} \) + \( \frac{9}{45} \)

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

\( \frac{15 + 9}{45} \) = \( \frac{24}{45} \) = \(\frac{8}{15}\)

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

If 35% of the town's 20,000 voters cast ballots the number of votes cast is:

(\( \frac{35}{100} \)) x 20,000 = \( \frac{700,000}{100} \) = 7,000

The mayor got 68% of the votes cast which is:

(\( \frac{68}{100} \)) x 7,000 = \( \frac{476,000}{100} \) = 4,760 votes.

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.