Full solution

Q. Reduce to simplest form.

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-\frac{5}{8}-\left(-\frac{4}{3}\right)=

Remove double negative: First, we need to rewrite the expression by removing the double negative. The double negative turns into a positive, so the expression becomes - $\frac{5}{8}$ + $\frac{4}{3}$ .
Find common denominator: Next, we need to find a common denominator for the two fractions. The least common multiple of $8$ and $3$ is $24$ , so we will convert both fractions to have a denominator of $24$ .
Convert $-5$ / $8$ to $24$ : To convert - $\frac{5}{8}$ to a denominator of $24$ , we multiply both the numerator and the denominator by $3$ . This gives us - $\frac{5 \times 3}{8 \times 3}$ = - $\frac{15}{24}$ .
Convert $4$ / $3$ to $24$ : To convert $\frac{4}{3}$ to a denominator of $24$ , we multiply both the numerator and the denominator by $8$ . This gives us $\frac{4 \times 8}{3 \times 8}$ = $\frac{32}{24}$ .
Add fractions with $24$ : Now we can add the two fractions with the common denominator. - $\frac{15}{24}$ + $\frac{32}{24}$ = $\frac{32}{24} - \frac{15}{24}$ .
Subtract numerators: Subtracting the numerators, we get $\frac{32 - 15}{24}$ = $\frac{17}{24}$ .
Simplify fraction: The fraction $\frac{17}{24}$ is already in its simplest form because $17$ and $24$ have no common factors other than $1$ .