Algebra Examples

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

Step 1

Convert $2 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{3}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$- \frac{10 + 3}{5} - (- 1 \frac{2}{5}) - \frac{4}{5}$

Step 1.2.4.2

Add $10$ and $3$ .

$- \frac{13}{5} - (- 1 \frac{2}{5}) - \frac{4}{5}$

Step 2

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

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Step 2.1

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

$- \frac{13}{5} - - (1 + \frac{2}{5}) - \frac{4}{5}$

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$- \frac{13}{5} - - (\frac{5}{5} + \frac{2}{5}) - \frac{4}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

$- \frac{13}{5} - - \frac{5 + 2}{5} - \frac{4}{5}$

Step 2.2.3

Add $5$ and $2$ .

$- \frac{13}{5} - - \frac{7}{5} - \frac{4}{5}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$- - \frac{7}{5} + \frac{- 13 - 4}{5}$

Step 3.2

Subtract $4$ from $- 13$ .

$- - \frac{7}{5} + \frac{- 17}{5}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- - \frac{7}{5}$ .

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{7}{5}) + \frac{- 17}{5}$

Step 4.1.2

Multiply $\frac{7}{5}$ by $1$ .

$\frac{7}{5} + \frac{- 17}{5}$

Step 4.2

Move the negative in front of the fraction.

$\frac{7}{5} - \frac{17}{5}$

Step 5

Combine fractions.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{7 - 17}{5}$

Step 5.2

Simplify the expression.

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Step 5.2.1

Subtract $17$ from $7$ .

$\frac{- 10}{5}$

Step 5.2.2

Divide $- 10$ by $5$ .

$- 2$