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Evaluate the expression shown below and write your answer as a fraction in simplest form. -(11)/(20)-(-(7)/(12)) Answer:

Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline−1120−(−712) -\frac{11}{20}-\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−1120−(−712) -\frac{11}{20}-\left(-\frac{7}{12}\right) \newlineAnswer:
  1. Understand Operations: Understand the expression and identify the operations to be performed. We need to subtract the second fraction from the first one, and also take into account the negative signs.
  2. Simplify Expression: Simplify the expression by removing the double negative.\newlineThe double negative in the expression −(1120)−(−(712)) -(\frac{11}{20}) - (-(\frac{7}{12})) turns the second term into a positive, so the expression becomes:\newline−(1120)+(712) -(\frac{11}{20}) + (\frac{7}{12})
  3. Find Common Denominator: Find a common denominator for the fractions.\newlineThe least common multiple (LCM) of 2020 and 1212 is 6060, so we will convert both fractions to have a denominator of 6060.
  4. Convert First Fraction: Convert the first fraction to have a denominator of 6060.\newlineTo convert 1120\frac{11}{20} to a fraction with a denominator of 6060, multiply both the numerator and the denominator by 33:\newline(11×3)/(20×3)=3360\left(11 \times 3\right) / \left(20 \times 3\right) = \frac{33}{60}
  5. Convert Second Fraction: Convert the second fraction to have a denominator of 6060. To convert 712\frac{7}{12} to a fraction with a denominator of 6060, multiply both the numerator and the denominator by 55: (7×5)/(12×5)=3560\left(7 \times 5\right) / \left(12 \times 5\right) = \frac{35}{60}
  6. Combine Fractions: Combine the fractions with the common denominator.\newlineNow that both fractions have the same denominator, we can combine them:\newline−3360+3560-\frac{33}{60} + \frac{35}{60}
  7. Perform Addition: Perform the addition of the fractions.\newlineSubtract the numerators and keep the common denominator:\newline−3360-\frac{33}{60} + 3560\frac{35}{60} = 3560\frac{35}{60} - 3360\frac{33}{60} = 35−3360\frac{35 - 33}{60} = 260\frac{2}{60}
  8. Simplify Resulting Fraction: Simplify the resulting fraction.\newlineThe fraction 260\frac{2}{60} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22:\newline(22)/(602)=130(\frac{2}{2}) / (\frac{60}{2}) = \frac{1}{30}

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