Basic Math Examples

8 - 4 \frac{1}{2}

$8 - 4 \frac{1}{2}$

Step 1

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

8 - (4 + \frac{1}{2})

$8 - (4 + \frac{1}{2})$

Step 1.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

8 - (4 \cdot \frac{2}{2} + \frac{1}{2})

$8 - (4 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

8 - (\frac{4 \cdot 2}{2} + \frac{1}{2})

$8 - (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

8 - \frac{4 \cdot 2 + 1}{2}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

2

$2$ .

8 - \frac{8 + 1}{2}

$8 - \frac{8 + 1}{2}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

8 - \frac{9}{2}

$8 - \frac{9}{2}$

8 - \frac{9}{2}

$8 - \frac{9}{2}$

8 - \frac{9}{2}

$8 - \frac{9}{2}$

8 - \frac{9}{2}

$8 - \frac{9}{2}$

Step 2

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

8 \cdot \frac{2}{2} - \frac{9}{2}

$8 \cdot \frac{2}{2} - \frac{9}{2}$

Step 3

Combine

8

$8$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8 \cdot 2}{2} - \frac{9}{2}

$\frac{8 \cdot 2}{2} - \frac{9}{2}$

Step 4

Combine the numerators over the common denominator.

\frac{8 \cdot 2 - 9}{2}

$\frac{8 \cdot 2 - 9}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

8

$8$ by

2

$2$ .

\frac{16 - 9}{2}

$\frac{16 - 9}{2}$

Step 5.2

Subtract

9

$9$ from

16

$16$ .

\frac{7}{2}

$\frac{7}{2}$

\frac{7}{2}

$\frac{7}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{7}{2}

$\frac{7}{2}$

Decimal Form:

3.5

$3.5$

Mixed Number Form:

3 \frac{1}{2}

$3 \frac{1}{2}$