Reduce to simplest form. $\newline$ $-\frac{7}{8}-\left(-\frac{5}{6}\right)=$

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Algebra 2

Composition of linear functions: find an equation

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Q. Reduce to simplest form.

\newline

-\frac{7}{8}-\left(-\frac{5}{6}\right)=

Identify numbers and signs: Identify the numbers to be subtracted and their signs. $\newline$ We have two fractions, - $\frac{7}{8}$ and - $-\frac{5}{6}$ . The second fraction has a double negative, which means it will become positive when simplified.
Simplify double negative: Simplify the double negative in the second fraction. $\newline$ The expression - $-\frac{5}{6}$ becomes $\frac{5}{6}$ because a negative times a negative is a positive.
Find common denominator: Find a common denominator for the two fractions. $\newline$ The denominators are $8$ and $6$ . The least common multiple of $8$ and $6$ is $24$ , so we will use $24$ as the common denominator.
Convert to common denominator: Convert each fraction to an equivalent fraction with the common denominator of $24$ . $\newline$ For - $\frac{7}{8}$ , we multiply the numerator and denominator by $3$ to get - $\frac{21}{24}$ . $\newline$ For $\frac{5}{6}$ , we multiply the numerator and denominator by $4$ to get $\frac{20}{24}$ .
Subtract the fractions: Subtract the two fractions. $\newline$ Now we subtract - $\frac{21}{24}$ from $\frac{20}{24}$ to get $\frac{20}{24} - \frac{21}{24}$ .
Perform the subtraction: Perform the subtraction. $\newline$ $\frac{20}{24} - \frac{21}{24}$ equals $\frac{-1}{24}$ .
Check for further simplification: Check if the result can be simplified further. $\newline$ The fraction $\frac{-1}{24}$ is already in its simplest form because the numerator and denominator have no common factors other than $1$ .