Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Add $1$ and $3$ .

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

Step 4

Find the common denominator.

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Step 4.1

Write $3$ as a fraction with denominator $1$ .

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

Step 4.2

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

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

Step 4.3

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

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

Step 4.4

Write $2$ as a fraction with denominator $1$ .

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

Step 4.5

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

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

Step 4.6

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify each term.

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Step 6.1

Multiply $3$ by $2$ .

$\frac{6 + 2 \cdot 2 + 4}{2}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{6 + 4 + 4}{2}$

Step 7

Simplify the expression.

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Step 7.1

Add $6$ and $4$ .

$\frac{10 + 4}{2}$

Step 7.2

Add $10$ and $4$ .

$\frac{14}{2}$

Step 7.3

Divide $14$ by $2$ .

$7$