The value of $\frac{9}{-16} + \frac{-5}{-12}$ is:

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Examoogle · Accepted Answer

The correct answer is Option D: $\frac{-7}{48}$. Simplify signs first: $9/-16 = -9/16$ and $-5/-12 = 5/12$. Find the LCM of 16 and 12, which is 48. Then calculate $(-27 + 20) / 48 = -7/48$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Simplify signs first: $9/-16 = -9/16$ and $-5/-12 = 5/12$. Find the LCM of 16 and 12, which is 48. Then calculate $(-27 + 20) / 48 = -7/48$.

Formula Used: $$\frac{a}{-b} + \frac{-c}{-d} = -\frac{a}{b} + \frac{c}{d}$$

Given: Two fractions: 9/-16 and -5/-12

Steps: Simplify fractions: Convert the fractions to standard form by adjusting the negative signs. $\frac{9}{-16} = -\frac{9}{16}$ and $\frac{-5}{-12} = \frac{5}{12}$.. Find common denominator: The Least Common Multiple (LCM) of 16 and 12 is 48.. Calculate equivalent fractions: Rewrite the fractions with 48 as the denominator: $-\frac{9 	imes 3}{16 	imes 3} = -\frac{27}{48}$ and $\frac{5 	imes 4}{12 	imes 4} = \frac{20}{48}$.. Final addition: Add the numerators while keeping the denominator: $(-27 + 20) / 48 = -7/48$.

Answer: D is correct because the sum of the simplified fractions $-\frac{9}{16} + \frac{5}{12}$ results in $-\frac{7}{48}$.

Exam Tip: This concept of simplifying signs is fundamental in algebraic expressions and probability where signs often cancel out or change the polarity of the result.

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