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Reduce to simplest form. -(1)/(4)-(-(3)/(5))=

Reduce to simplest form.\newline−14−(−35)= -\frac{1}{4}-\left(-\frac{3}{5}\right)=

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Full solution

Q. Reduce to simplest form.\newline−14−(−35)= -\frac{1}{4}-\left(-\frac{3}{5}\right)=
  1. Apply Rule and Concept: Apply the subtraction of fractions rule and the concept of subtracting a negative number, which is the same as adding its positive counterpart.\newline−14−(−35)=−14+35-\frac{1}{4} - (-\frac{3}{5}) = -\frac{1}{4} + \frac{3}{5}
  2. Find Common Denominator: Find a common denominator for the fractions 14\frac{1}{4} and 35\frac{3}{5}. The least common denominator (LCD) for 44 and 55 is 2020.
  3. Convert to Equivalent Fractions: Convert each fraction to an equivalent fraction with the denominator of 2020.
    -14\frac{1}{4} becomes -520\frac{5}{20} because 1×5=51 \times 5 = 5 and 4×5=204 \times 5 = 20.
    35\frac{3}{5} becomes 1220\frac{12}{20} because 3×4=123 \times 4 = 12 and 5×4=205 \times 4 = 20.
  4. Add Fractions: Now add the two fractions with the common denominator.\newline−(520)+(1220)=(1220)−(520)-(\frac{5}{20}) + (\frac{12}{20}) = (\frac{12}{20}) - (\frac{5}{20})
  5. Perform Subtraction: Perform the subtraction.\newline(1220)−(520)=12−520=720(\frac{12}{20}) - (\frac{5}{20}) = \frac{12 - 5}{20} = \frac{7}{20}

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