Pre-Algebra Examples

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

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

Step 1

Convert

1 \frac{1}{2}

$1 \frac{1}{2}$ 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

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

Step 1.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 2

Combine the numerators over the common denominator.

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

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

Step 3

Add

1

$1$ and

3

$3$ .

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

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

Step 4

Find the common denominator.

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Step 4.1

Write

3

$3$ as a fraction with denominator

1

$1$ .

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

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

Step 4.2

Multiply

\frac{3}{1}

$\frac{3}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.3

Multiply

\frac{3}{1}

$\frac{3}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.4

Write

2

$2$ as a fraction with denominator

1

$1$ .

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

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

Step 4.5

Multiply

\frac{2}{1}

$\frac{2}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.6

Multiply

\frac{2}{1}

$\frac{2}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

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

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

Step 6

Simplify each term.

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Step 6.1

Multiply

3

$3$ by

2

$2$ .

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

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

Step 6.2

Multiply

2

$2$ by

2

$2$ .

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

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

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

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

Step 7

Simplify the expression.

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Step 7.1

Add

6

$6$ and

4

$4$ .

\frac{10 + 4}{2}

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

Step 7.2

Add

10

$10$ and

4

$4$ .

\frac{14}{2}

$\frac{14}{2}$

Step 7.3

Divide

14

$14$ by

2

$2$ .

7

$7$

7

$7$