Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $3$ by $4$ .

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

Step 1.2.4.2

Add $12$ and $1$ .

$\frac{13}{4} - \frac{1}{2}$

Step 2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{4} - \frac{1}{2} \cdot \frac{2}{2}$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{13}{4} - \frac{2}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $2$ from $13$ .

$\frac{11}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{4}$

Decimal Form:

$2.75$

Mixed Number Form:

$2 \frac{3}{4}$