Basic Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

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

Step 2.2

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

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

Step 2.3

Multiply $\frac{- 1}{- 2}$ by $\frac{- 5}{- 5}$ .

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

Step 2.4

Multiply $\frac{- 1}{- 2}$ by $\frac{- 5}{- 5}$ .

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

Step 2.5

Multiply $\frac{- 3}{5}$ by $\frac{2}{2}$ .

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

Step 2.6

Multiply $\frac{- 3}{5}$ by $\frac{2}{2}$ .

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

Step 2.7

Multiply $2$ by $5$ .

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

Step 2.8

Reorder the factors of $- 2 \cdot - 5$ .

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

Step 2.9

Multiply $- 5$ by $- 2$ .

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

Step 2.10

Reorder the factors of $5 \cdot 2$ .

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

Step 2.11

Multiply $2$ by $5$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $- 3$ by $5$ .

$\frac{- 15 - - 5 + 3 \cdot 2}{10}$

Step 4.2

Multiply $- 1$ by $- 5$ .

$\frac{- 15 + 5 + 3 \cdot 2}{10}$

Step 4.3

Multiply $3$ by $2$ .

$\frac{- 15 + 5 + 6}{10}$

Step 5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1

Add $- 15$ and $5$ .

$\frac{- 10 + 6}{10}$

Step 5.2

Add $- 10$ and $6$ .

$\frac{- 4}{10}$

Step 5.3

Cancel the common factor of $- 4$ and $10$ .

Tap for more steps...

Step 5.3.1

Factor $2$ out of $- 4$ .

$\frac{2 (- 2)}{10}$

Step 5.3.2

Cancel the common factors.

Tap for more steps...

Step 5.3.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot - 2}{2 \cdot 5}$

Step 5.3.2.2

Cancel the common factor.

$\frac{2 \cdot - 2}{2 \cdot 5}$

Step 5.3.2.3

Rewrite the expression.

$\frac{- 2}{5}$

Step 5.4

Move the negative in front of the fraction.

$- \frac{2}{5}$