Basic Math Examples

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

Step 1

Convert

$8 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$8$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

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

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$8$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$8$ by

$2$ .

$\frac{16 + 1}{2} \div 2 \frac{1}{4}$

Step 1.2.4.2

Add

$16$ and

$1$ .

$\frac{17}{2} \div 2 \frac{1}{4}$

Step 2

Convert

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

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Step 2.1

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

$\frac{17}{2} \div (2 + \frac{1}{4})$

Step 2.2

Add

$2$ and

$\frac{1}{4}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{17}{2} \div (2 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

$2$ and

$\frac{4}{4}$ .

$\frac{17}{2} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{17}{2} \div \frac{2 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$4$ .

$\frac{17}{2} \div \frac{8 + 1}{4}$

Step 2.2.4.2

Add

$8$ and

$1$ .

$\frac{17}{2} \div \frac{9}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{17}{2} \cdot \frac{4}{9}$

Step 4

Cancel the common factor of

$2$ .

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Step 4.1

Factor

$2$ out of

$4$ .

$\frac{17}{2} \cdot \frac{2 (2)}{9}$

Step 4.2

Cancel the common factor.

$\frac{17}{2} \cdot \frac{2 \cdot 2}{9}$

Step 4.3

Rewrite the expression.

$17 (\frac{2}{9})$

Step 5

Combine

$17$ and

$\frac{2}{9}$ .

$\frac{17 \cdot 2}{9}$

Step 6

Multiply

$17$ by

$2$ .

$\frac{34}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{34}{9}$

Decimal Form:

$3.\overline{7}$

Mixed Number Form:

$3 \frac{7}{9}$