Pre-Algebra Examples

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

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $5$ .

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

Step 2.2.4.2

Add $10$ and $2$ .

$- \frac{12}{5} - 1 \frac{3}{5}$

Step 3

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 3.1

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

$- \frac{12}{5} - (1 + \frac{3}{5})$

Step 3.2

Add $1$ and $\frac{3}{5}$ .

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Step 3.2.1

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

$- \frac{12}{5} - (\frac{5}{5} + \frac{3}{5})$

Step 3.2.2

Combine the numerators over the common denominator.

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

Step 3.2.3

Add $5$ and $3$ .

$- \frac{12}{5} - \frac{8}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 12 - 8}{5}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $8$ from $- 12$ .

$\frac{- 20}{5}$

Step 5.2

Divide $- 20$ by $5$ .

$- 4$