Basic Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.2.4.2

Add $4$ and $1$ .

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

Step 2

Convert $3 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Add $3$ and $\frac{1}{4}$ .

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $3$ by $4$ .

$\frac{- \frac{5}{2} - - \frac{12 + 1}{4}}{- 3}$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{- \frac{5}{2} - - \frac{13}{4}}{- 3}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Multiply $- - \frac{13}{4}$ .

Tap for more steps...

Step 3.1.1

Multiply $- 1$ by $- 1$ .

$\frac{- \frac{5}{2} + 1 (\frac{13}{4})}{- 3}$

Step 3.1.2

Multiply $\frac{13}{4}$ by $1$ .

$\frac{- \frac{5}{2} + \frac{13}{4}}{- 3}$

Step 3.2

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

$\frac{- \frac{5}{2} \cdot \frac{2}{2} + \frac{13}{4}}{- 3}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

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

$\frac{- \frac{5 \cdot 2}{2 \cdot 2} + \frac{13}{4}}{- 3}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{- \frac{5 \cdot 2}{4} + \frac{13}{4}}{- 3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{\frac{- 5 \cdot 2 + 13}{4}}{- 3}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $- 5$ by $2$ .

$\frac{\frac{- 10 + 13}{4}}{- 3}$

Step 3.5.2

Add $- 10$ and $13$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{4} \cdot \frac{1}{- 3}$

Step 5

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $- 3$ .

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

Step 5.2

Cancel the common factor.

$\frac{3}{4} \cdot \frac{1}{3 \cdot - 1}$

Step 5.3

Rewrite the expression.

$\frac{1}{4} \cdot \frac{1}{- 1}$

Step 6

Multiply $\frac{1}{4}$ by $\frac{1}{- 1}$ .

$\frac{1}{4 \cdot - 1}$

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Multiply $4$ by $- 1$ .

$\frac{1}{- 4}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$