To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] 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 [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{3 x 4}{2 x 4} \) + \( \frac{9 x 1}{8 x 1} \)

\( \frac{12}{8} \) + \( \frac{9}{8} \)

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

\( \frac{12 + 9}{8} \) = \( \frac{21}{8} \) = 2\(\frac{5}{8}\)

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

3\( \sqrt{125} \) - 8\( \sqrt{5} \)
3\( \sqrt{25 \times 5} \) - 8\( \sqrt{5} \)
3\( \sqrt{5^2 \times 5} \) - 8\( \sqrt{5} \)
(3)(5)\( \sqrt{5} \) - 8\( \sqrt{5} \)
15\( \sqrt{5} \) - 8\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

1

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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