Pre-Algebra Examples

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

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

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.

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

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

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 2

Convert

1 \frac{1}{2}

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

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Step 2.1

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

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

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

Step 2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

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

Step 2.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 3

Convert

1 \frac{1}{2}

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

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Step 3.1

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

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

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

Step 3.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 3.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 3.2.2

Combine the numerators over the common denominator.

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

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

Step 3.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify by adding numbers.

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Step 5.1

Add

3

$3$ and

3

$3$ .

\frac{6 + 3}{2}

$\frac{6 + 3}{2}$

Step 5.2

Add

6

$6$ and

3

$3$ .

\frac{9}{2}

$\frac{9}{2}$

\frac{9}{2}

$\frac{9}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{9}{2}

$\frac{9}{2}$

Decimal Form:

4.5

$4.5$

Mixed Number Form:

4 \frac{1}{2}

$4 \frac{1}{2}$