To subtract 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:

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

\( \frac{10}{40} \) - \( \frac{20}{40} \)

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

\( \frac{10 - 20}{40} \) = \( \frac{-10}{40} \) = -\(\frac{1}{4}\)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.

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

3\( \sqrt{175} \) - 8\( \sqrt{7} \)
3\( \sqrt{25 \times 7} \) - 8\( \sqrt{7} \)
3\( \sqrt{5^2 \times 7} \) - 8\( \sqrt{7} \)
(3)(5)\( \sqrt{7} \) - 8\( \sqrt{7} \)
15\( \sqrt{7} \) - 8\( \sqrt{7} \)

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

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.