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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (11)/(8)+(-(5)/(16)) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{11}{8}+\left(-\frac{5}{16}\right)$ $\newline$ 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{11}{8}+\left(-\frac{5}{16}\right)

\newline

Answer:

Identify LCD: Identify the Least Common Denominator (LCD) The fractions $(\frac{11}{8})$ and $(\frac{-5}{16})$ have denominators of $8$ and $16$ , respectively. The LCD of $8$ and $16$ is $16$ .
Convert first fraction: Convert the first fraction to have the LCD as its denominator $\newline$ The first fraction $(11/8)$ needs to be converted to have a denominator of $16$ . To do this, multiply both the numerator and the denominator by $2$ . $\newline$ $(11/8) \times (2/2) = (22/16)$
Add fractions: Add the converted first fraction to the second fraction $\newline$ Now that both fractions have the same denominator, they can be added together. $\newline$ $(\frac{22}{16}) + (-(\frac{5}{16})) = (\frac{22 - 5}{16})$
Perform subtraction: Perform the subtraction in the numerator $\newline$ Subtract $5$ from $22$ to get the new numerator. $\newline$ $22 - 5 = 17$
Write result: Write the result as a fraction $\newline$ The result of the addition is the new numerator over the common denominator. $\newline$ $(\frac{17}{16})$
Simplify fraction: Simplify the fraction if possible $\newline$ The fraction $(17/16)$ is already in its simplest form because $17$ and $16$ have no common factors other than $1$ .

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