Pre-Algebra Examples

$\frac{1}{8} + 2 \frac{3}{4} + \frac{1}{2}$

Step 1

Convert

$2 \frac{3}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$\frac{1}{8} + 2 + \frac{3}{4} + \frac{1}{2}$

Step 1.2

Add

$2$ and

$\frac{3}{4}$ .

Tap for more steps...

Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{1}{8} + 2 \cdot \frac{4}{4} + \frac{3}{4} + \frac{1}{2}$

Step 1.2.2

Combine

$2$ and

$\frac{4}{4}$ .

$\frac{1}{8} + \frac{2 \cdot 4}{4} + \frac{3}{4} + \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1}{8} + \frac{2 \cdot 4 + 3}{4} + \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

$2$ by

$4$ .

$\frac{1}{8} + \frac{8 + 3}{4} + \frac{1}{2}$

Step 1.2.4.2

Add

$8$ and

$3$ .

$\frac{1}{8} + \frac{11}{4} + \frac{1}{2}$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply

$\frac{11}{4}$ by

$\frac{2}{2}$ .

$\frac{1}{8} + \frac{11}{4} \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.2

Multiply

$\frac{11}{4}$ by

$\frac{2}{2}$ .

$\frac{1}{8} + \frac{11 \cdot 2}{4 \cdot 2} + \frac{1}{2}$

Step 2.3

Multiply

$\frac{1}{2}$ by

$\frac{4}{4}$ .

$\frac{1}{8} + \frac{11 \cdot 2}{4 \cdot 2} + \frac{1}{2} \cdot \frac{4}{4}$

Step 2.4

Multiply

$\frac{1}{2}$ by

$\frac{4}{4}$ .

$\frac{1}{8} + \frac{11 \cdot 2}{4 \cdot 2} + \frac{4}{2 \cdot 4}$

Step 2.5

Reorder the factors of

$4 \cdot 2$ .

$\frac{1}{8} + \frac{11 \cdot 2}{2 \cdot 4} + \frac{4}{2 \cdot 4}$

Step 2.6

Multiply

$2$ by

$4$ .

$\frac{1}{8} + \frac{11 \cdot 2}{8} + \frac{4}{2 \cdot 4}$

Step 2.7

Multiply

$2$ by

$4$ .

$\frac{1}{8} + \frac{11 \cdot 2}{8} + \frac{4}{8}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 + 11 \cdot 2 + 4}{8}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Multiply

$11$ by

$2$ .

$\frac{1 + 22 + 4}{8}$

Step 4.2

Add

$1$ and

$22$ .

$\frac{23 + 4}{8}$

Step 4.3

Add

$23$ and

$4$ .

$\frac{27}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{8}$

Decimal Form:

$3.375$

Mixed Number Form:

$3 \frac{3}{8}$