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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

9\( \sqrt{18} \) + 7\( \sqrt{2} \)
9\( \sqrt{9 \times 2} \) + 7\( \sqrt{2} \)
9\( \sqrt{3^2 \times 2} \) + 7\( \sqrt{2} \)
(9)(3)\( \sqrt{2} \) + 7\( \sqrt{2} \)
27\( \sqrt{2} \) + 7\( \sqrt{2} \)

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

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{25\sqrt{35}}{5\sqrt{7}} \)
\( \frac{25}{5} \) \( \sqrt{\frac{35}{7}} \)
5 \( \sqrt{5} \)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{9} \) ÷ \( \frac{4}{5} \) = \( \frac{4}{9} \) x \( \frac{5}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{9} \) x \( \frac{5}{4} \) = \( \frac{4 x 5}{9 x 4} \) = \( \frac{20}{36} \) = \(\frac{5}{9}\)