Basic Math Examples

2 \frac{5}{8} \div \frac{1}{2}

$2 \frac{5}{8} \div \frac{1}{2}$

Step 1

Convert

2 \frac{5}{8}

$2 \frac{5}{8}$ to an improper fraction.

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Step 1.1

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

(2 + \frac{5}{8}) \div \frac{1}{2}

$(2 + \frac{5}{8}) \div \frac{1}{2}$

Step 1.2

Add

2

$2$ and

\frac{5}{8}

$\frac{5}{8}$ .

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Step 1.2.1

To write

2

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

\frac{8}{8}

$\frac{8}{8}$ .

(2 \cdot \frac{8}{8} + \frac{5}{8}) \div \frac{1}{2}

$(2 \cdot \frac{8}{8} + \frac{5}{8}) \div \frac{1}{2}$

Step 1.2.2

Combine

2

$2$ and

\frac{8}{8}

$\frac{8}{8}$ .

(\frac{2 \cdot 8}{8} + \frac{5}{8}) \div \frac{1}{2}

$(\frac{2 \cdot 8}{8} + \frac{5}{8}) \div \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 8 + 5}{8} \div \frac{1}{2}

$\frac{2 \cdot 8 + 5}{8} \div \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

8

$8$ .

\frac{16 + 5}{8} \div \frac{1}{2}

$\frac{16 + 5}{8} \div \frac{1}{2}$

Step 1.2.4.2

Add

16

$16$ and

5

$5$ .

\frac{21}{8} \div \frac{1}{2}

$\frac{21}{8} \div \frac{1}{2}$

\frac{21}{8} \div \frac{1}{2}

$\frac{21}{8} \div \frac{1}{2}$

\frac{21}{8} \div \frac{1}{2}

$\frac{21}{8} \div \frac{1}{2}$

\frac{21}{8} \div \frac{1}{2}

$\frac{21}{8} \div \frac{1}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{21}{8} \cdot 2

$\frac{21}{8} \cdot 2$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

8

$8$ .

\frac{21}{2 (4)} \cdot 2

$\frac{21}{2 (4)} \cdot 2$

Step 3.2

Cancel the common factor.

$\frac{21}{2 \cdot 4} \cdot 2$

Step 3.3

Rewrite the expression.

$\frac{21}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{4}$

Decimal Form:

$5.25$

Mixed Number Form:

$5 \frac{1}{4}$