The number of students taking German or Spanish is 15 + 5 = 20. Of that group of 20, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 4 = 16 who are taking at least one language. 23 - 16 = 7 students who are not taking either language.

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] 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 [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 have in common.

If 33% of the town's 27,000 voters cast ballots the number of votes cast is:

(\( \frac{33}{100} \)) x 27,000 = \( \frac{891,000}{100} \) = 8,910

The mayor got 86% of the votes cast which is:

(\( \frac{86}{100} \)) x 8,910 = \( \frac{766,260}{100} \) = 7,663 votes.

To subtract 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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

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

\( \frac{4 x 3}{4 x 3} \) - \( \frac{8 x 1}{12 x 1} \)

\( \frac{12}{12} \) - \( \frac{8}{12} \)

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

\( \frac{12 - 8}{12} \) = \( \frac{4}{12} \) = \(\frac{1}{3}\)

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