Identify common denominator: Identify the common denominator for the fractions (-5/6) and (3/4). The denominators are 6 and 4. The least common multiple of 6 and 4 is 12, which will be the common denominator.Convert to equivalent fractions: Convert each fraction to an equivalent fraction with the common denominator of 12. For (-5/6), multiply both the numerator and the denominator by 2 to get (-5*2)/(6*2) = (-10/12). For (3/4), multiply both the numerator and the denominator by 3 to get (3*3)/(4*3) = (9/12).Add fractions with common denominator: Add the two fractions with the common denominator. (-10/12) + (9/12) = (-10 + 9)/12 = (-1/12).

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(i) $\frac{-5}{6}+\frac{3}{4}$

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Algebra 2

Evaluate rational exponents

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Q. (i)

\frac{-5}{6}+\frac{3}{4}

Identify common denominator: Identify the common denominator for the fractions $(-\frac{5}{6})$ and $(\frac{3}{4})$ . $\newline$ The denominators are $6$ and $4$ . The least common multiple of $6$ and $4$ is $12$ , which will be the common denominator.
Convert to equivalent fractions: Convert each fraction to an equivalent fraction with the common denominator of $12$ . $\newline$ For $(-\frac{5}{6})$ , multiply both the numerator and the denominator by $2$ to get $(-5\times2)/(6\times2) = (-\frac{10}{12})$ . $\newline$ For $(\frac{3}{4})$ , multiply both the numerator and the denominator by $3$ to get $(3\times3)/(4\times3) = (\frac{9}{12})$ .
Add fractions with common denominator: Add the two fractions with the common denominator. $\newline$ $(-\frac{10}{12}) + (\frac{9}{12}) = (\frac{-10 + 9}{12}) = (\frac{-1}{12})$ .