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-(3)/(2)+(24)/(20)-1.75= Enter the answer as an exact decimal or simplified fraction.

−32+2420−1.75= -\frac{3}{2}+\frac{24}{20}-1.75= \newlineEnter the answer as an exact decimal or simplified fraction.

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Full solution

Q. −32+2420−1.75= -\frac{3}{2}+\frac{24}{20}-1.75= \newlineEnter the answer as an exact decimal or simplified fraction.
  1. Convert to Fractions: Convert all terms to fractions to simplify the calculation.\newline−32-\frac{3}{2} is already a fraction.\newline2420\frac{24}{20} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 44. So, 2420\frac{24}{20} simplifies to 65\frac{6}{5}.\newline1.751.75 can be written as a fraction by recognizing that 1.75=1+34=44+34=741.75 = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}.
  2. Rewrite with Simplified Fractions: Rewrite the expression with the simplified fractions.\newlineThe expression now is −32+65−74-\frac{3}{2} + \frac{6}{5} - \frac{7}{4}.
  3. Find Common Denominator: Find a common denominator for the fractions to combine them.\newlineThe least common multiple of 22, 55, and 44 is 2020. We will convert all fractions to have a denominator of 2020.\newline−32=−3×102×102=−3020-\frac{3}{2} = -3 \times \frac{10}{2} \times \frac{10}{2} = -\frac{30}{20}\newline65=6×45×45=2420\frac{6}{5} = 6 \times \frac{4}{5} \times \frac{4}{5} = \frac{24}{20}\newline−74=−7×54×54=−3520-\frac{7}{4} = -7 \times \frac{5}{4} \times \frac{5}{4} = -\frac{35}{20}
  4. Combine Fractions: Combine the fractions using the common denominator.\newlineNow we have −3020+2420−3520-\frac{30}{20} + \frac{24}{20} - \frac{35}{20}.\newlineAdding and subtracting the numerators, we get −30+24−3520\frac{-30 + 24 - 35}{20}.
  5. Perform Addition and Subtraction: Perform the addition and subtraction in the numerator.\newline−30+24−35=−41-30 + 24 - 35 = -41.\newlineSo the combined fraction is −4120-\frac{41}{20}.
  6. Check for Simplification: Check if the fraction can be simplified.\newlineSince −41-41 and 2020 have no common factors other than 11, the fraction −4120-\frac{41}{20} is already in its simplest form.

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