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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(7)/(4)-(8)/(5) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{7}{4}-\frac{8}{5}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

\newline

-\frac{7}{4}-\frac{8}{5}

\newline

Answer:

Find common denominator: Find a common denominator for the fractions $(\frac{7}{4})$ and $(\frac{8}{5})$ . The least common denominator (LCD) for $4$ and $5$ is $20$ because it is the smallest number that both $4$ and $5$ can divide into without leaving a remainder.
Convert to equivalent fractions: Convert each fraction to an equivalent fraction with the common denominator of $20$ . For $(\frac{7}{4})$ , multiply both the numerator and the denominator by $5$ to get $(\frac{7\times 5}{4\times 5}) = \frac{35}{20}$ . For $(\frac{8}{5})$ , multiply both the numerator and the denominator by $4$ to get $(\frac{8\times 4}{5\times 4}) = \frac{32}{20}$ .
Rewrite with equivalent fractions: Rewrite the original expression with the equivalent fractions. $\newline$ The expression becomes $-\frac{35}{20}$ - $\frac{32}{20}$ .
Subtract fractions: Subtract the fractions by subtracting their numerators while keeping the common denominator. $\newline$ The subtraction is $-\frac{35}{20} - \frac{32}{20} = -\frac{35 + 32}{20} = -\frac{67}{20}$ .
Simplify final fraction: Simplify the fraction, if possible. $\newline$ The fraction $-\frac{67}{20}$ is already in its simplest form because $67$ and $20$ have no common factors other than $1$ .

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