To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{2 x 5}{8 x 5} \) + \( \frac{6 x 4}{10 x 4} \)

\( \frac{10}{40} \) + \( \frac{24}{40} \)

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

\( \frac{10 + 24}{40} \) = \( \frac{34}{40} \) = \(\frac{17}{20}\)

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

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

4x⁶ + 7x⁶
(4 + 7)x⁶
11x⁶

To simplify a radical, factor out the perfect squares:

\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)

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

9\( \sqrt{50} \) - 8\( \sqrt{2} \)
9\( \sqrt{25 \times 2} \) - 8\( \sqrt{2} \)
9\( \sqrt{5^2 \times 2} \) - 8\( \sqrt{2} \)
(9)(5)\( \sqrt{2} \) - 8\( \sqrt{2} \)
45\( \sqrt{2} \) - 8\( \sqrt{2} \)

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