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:

\( \frac{4 x 3}{4 x 3} \) - \( \frac{6 x 1}{12 x 1} \)

\( \frac{12}{12} \) - \( \frac{6}{12} \)

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

\( \frac{12 - 6}{12} \) = \( \frac{6}{12} \) = \(\frac{1}{2}\)

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

43,000 fans x \( \frac{4}{5} \) = \( \frac{172000}{5} \) = 34,400 fans.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-9z² - 4z²
(-9 - 4)z²
-13z²

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

If 33% of the town's 19,000 voters cast ballots the number of votes cast is:

(\( \frac{33}{100} \)) x 19,000 = \( \frac{627,000}{100} \) = 6,270

The mayor got 83% of the votes cast which is:

(\( \frac{83}{100} \)) x 6,270 = \( \frac{520,410}{100} \) = 5,204 votes.