Evaluate -2 1/5-3 3/4

$- 2 \frac{1}{5} - 3 \frac{3}{4}$

Convert $2 \frac{1}{5}$ to an improper fraction.

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A mixed number is an addition of its whole and fractional parts.

$- (2 + \frac{1}{5}) - 3 \frac{3}{4}$

Add $2$ and $\frac{1}{5}$ .

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To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- (2 \cdot \frac{5}{5} + \frac{1}{5}) - 3 \frac{3}{4}$

Combine $2$ and $\frac{5}{5}$ .

$- (\frac{2 \cdot 5}{5} + \frac{1}{5}) - 3 \frac{3}{4}$

Combine the numerators over the common denominator.

$- \frac{2 \cdot 5 + 1}{5} - 3 \frac{3}{4}$

Simplify the numerator.

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Multiply $2$ by $5$ .

$- \frac{10 + 1}{5} - 3 \frac{3}{4}$

Add $10$ and $1$ .

$- \frac{11}{5} - 3 \frac{3}{4}$

Convert $3 \frac{3}{4}$ to an improper fraction.

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A mixed number is an addition of its whole and fractional parts.

$- \frac{11}{5} - (3 + \frac{3}{4})$

Add $3$ and $\frac{3}{4}$ .

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To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{11}{5} - (3 \cdot \frac{4}{4} + \frac{3}{4})$

Combine $3$ and $\frac{4}{4}$ .

$- \frac{11}{5} - (\frac{3 \cdot 4}{4} + \frac{3}{4})$

Combine the numerators over the common denominator.

$- \frac{11}{5} - \frac{3 \cdot 4 + 3}{4}$

Simplify the numerator.

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Multiply $3$ by $4$ .

$- \frac{11}{5} - \frac{12 + 3}{4}$

Add $12$ and $3$ .

$- \frac{11}{5} - \frac{15}{4}$

To write $- \frac{11}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{11}{5} \cdot \frac{4}{4} - \frac{15}{4}$

To write $- \frac{15}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{11}{5} \cdot \frac{4}{4} - \frac{15}{4} \cdot \frac{5}{5}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{11}{5}$ and $\frac{4}{4}$ .

$- \frac{11 \cdot 4}{5 \cdot 4} - \frac{15}{4} \cdot \frac{5}{5}$

Multiply $5$ by $4$ .

$- \frac{11 \cdot 4}{20} - \frac{15}{4} \cdot \frac{5}{5}$

Multiply $\frac{15}{4}$ and $\frac{5}{5}$ .

$- \frac{11 \cdot 4}{20} - \frac{15 \cdot 5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$- \frac{11 \cdot 4}{20} - \frac{15 \cdot 5}{20}$

Combine the numerators over the common denominator.

$\frac{- 11 \cdot 4 - 15 \cdot 5}{20}$

Simplify the numerator.

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Multiply $- 11$ by $4$ .

$\frac{- 44 - 15 \cdot 5}{20}$

Multiply $- 15$ by $5$ .

$\frac{- 44 - 75}{20}$

Subtract $75$ from $- 44$ .

$\frac{- 119}{20}$

Move the negative in front of the fraction.

$- \frac{119}{20}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{119}{20}$

Decimal Form:

$- 5.95$

Mixed Number Form:

$- 5 \frac{19}{20}$