To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{36}} \)
\( \frac{\sqrt{36}}{\sqrt{36}} \)
\( \frac{\sqrt{6^2}}{\sqrt{6^2}} \)
1

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

\( \frac{3}{6} \) ÷ \( \frac{4}{9} \) = \( \frac{3}{6} \) x \( \frac{9}{4} \)

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

\( \frac{3}{6} \) x \( \frac{9}{4} \) = \( \frac{3 x 9}{6 x 4} \) = \( \frac{27}{24} \) = 1\(\frac{1}{8}\)

First, solve for \( \left|y + 9\right| \):

\( \left|y + 9\right| \) + 9 = -2
\( \left|y + 9\right| \) = -2 - 9
\( \left|y + 9\right| \) = -11

The value inside the absolute value brackets can be either positive or negative so (y + 9) must equal - 11 or --11 for \( \left|y + 9\right| \) to equal -11:

So, y = 2 or y = -20.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).