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Evaluate the expression shown below and write your answer as a fraction in simplest form. -(5)/(8)-(-(7)/(12)) Answer:

Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline−58−(−712) -\frac{5}{8}-\left(-\frac{7}{12}\right) \newlineAnswer:

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Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline−58−(−712) -\frac{5}{8}-\left(-\frac{7}{12}\right) \newlineAnswer:
  1. Identify Operation: Identify the operation required to solve the problem.\newlineWe need to subtract the second fraction from the first fraction, taking into account the negative signs.
  2. Simplify Expression: Simplify the expression by removing the double negative.\newline−(58)−(−(712))-\left(\frac{5}{8}\right) - \left(-\left(\frac{7}{12}\right)\right) becomes −(58)+(712)-\left(\frac{5}{8}\right) + \left(\frac{7}{12}\right) because subtracting a negative is the same as adding a positive.
  3. Find Common Denominator: Find a common denominator for the fractions.\newlineThe least common multiple (LCM) of 88 and 1212 is 2424, so we will use 2424 as the common denominator.
  4. Convert to Common Denominator: Convert each fraction to an equivalent fraction with the common denominator.\newlineFor the first fraction: (58)×(33)=(1524)(\frac{5}{8}) \times (\frac{3}{3}) = (\frac{15}{24})\newlineFor the second fraction: (712)×(22)=(1424)(\frac{7}{12}) \times (\frac{2}{2}) = (\frac{14}{24})
  5. Perform Addition: Perform the addition with the new fractions.\newline−(1524)+(1424)=(−15+1424)=−124-(\frac{15}{24}) + (\frac{14}{24}) = (\frac{-15 + 14}{24}) = \frac{-1}{24}
  6. Simplify Result: Simplify the result, if possible.\newlineThe fraction −124-\frac{1}{24} is already in its simplest form.

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