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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.\newline118+(−516) \frac{11}{8}+\left(-\frac{5}{16}\right) \newlineAnswer:

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Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline118+(−516) \frac{11}{8}+\left(-\frac{5}{16}\right) \newlineAnswer:
  1. Identify LCD: Identify the Least Common Denominator (LCD) The fractions (118)(\frac{11}{8}) and (−516)(\frac{-5}{16}) have denominators of 88 and 1616, respectively. The LCD of 88 and 1616 is 1616.
  2. Convert first fraction: Convert the first fraction to have the LCD as its denominator\newlineThe first fraction (11/8)(11/8) needs to be converted to have a denominator of 1616. To do this, multiply both the numerator and the denominator by 22.\newline(11/8)×(2/2)=(22/16)(11/8) \times (2/2) = (22/16)
  3. Add fractions: Add the converted first fraction to the second fraction\newlineNow that both fractions have the same denominator, they can be added together.\newline(2216)+(−(516))=(22−516)(\frac{22}{16}) + (-(\frac{5}{16})) = (\frac{22 - 5}{16})
  4. Perform subtraction: Perform the subtraction in the numerator\newlineSubtract 55 from 2222 to get the new numerator.\newline22−5=1722 - 5 = 17
  5. Write result: Write the result as a fraction\newlineThe result of the addition is the new numerator over the common denominator.\newline(1716)(\frac{17}{16})
  6. Simplify fraction: Simplify the fraction if possible\newlineThe fraction (17/16)(17/16) is already in its simplest form because 1717 and 1616 have no common factors other than 11.

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