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

The greatest common factor (GCF) is the greatest factor that divides two integers.

To add these radicals together their radicands must be the same:

5\( \sqrt{63} \) + 3\( \sqrt{7} \)
5\( \sqrt{9 \times 7} \) + 3\( \sqrt{7} \)
5\( \sqrt{3^2 \times 7} \) + 3\( \sqrt{7} \)
(5)(3)\( \sqrt{7} \) + 3\( \sqrt{7} \)
15\( \sqrt{7} \) + 3\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

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 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:

\( \frac{5 x 5}{4 x 5} \) - \( \frac{7 x 2}{10 x 2} \)

\( \frac{25}{20} \) - \( \frac{14}{20} \)

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

\( \frac{25 - 14}{20} \) = \( \frac{11}{20} \) = \(\frac{5}{9}\)

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

45,000 fans x \( \frac{3}{4} \) = \( \frac{135000}{4} \) = 33,750 fans.