To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{7 x 5}{6 x 5} \) - \( \frac{7 x 3}{10 x 3} \)

\( \frac{35}{30} \) - \( \frac{21}{30} \)

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

\( \frac{35 - 21}{30} \) = \( \frac{14}{30} \) = \(\frac{7}{15}\)

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 have in common.

The amount of flour you need is (2\(\frac{1}{4}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups

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

8\( \sqrt{175} \) + 3\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) + 3\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) + 3\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) + 3\( \sqrt{7} \)
40\( \sqrt{7} \) + 3\( \sqrt{7} \)

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