Pre-Algebra Examples

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

Step 1

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

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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 $\frac{3}{4}$ .

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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.

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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.

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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.

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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:

$3 \frac{3}{8}$