The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

By buying two shirts, Bob will save $32 x \( \frac{15}{100} \) = \( \frac{$32 x 15}{100} \) = \( \frac{$480}{100} \) = $4.80 on the second shirt.

So, his total cost will be
$32.00 + ($32.00 - $4.80)
$32.00 + $27.20
$59.20

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

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

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

\( \frac{20}{20} \) + \( \frac{10}{20} \)

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

\( \frac{20 + 10}{20} \) = \( \frac{30}{20} \) = 1\(\frac{1}{2}\)

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

8,106,000 in scientific notation is 8.106 x 10⁶

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

30,000 fans x \( \frac{2}{3} \) = \( \frac{60000}{3} \) = 20,000 fans.