Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{2}

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

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 1}{2} \div \frac{5}{8}

$\frac{4 + 1}{2} \div \frac{5}{8}$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{5}{2} \cdot \frac{8}{5}

$\frac{5}{2} \cdot \frac{8}{5}$

Step 3

Cancel the common factor of

5

$5$ .

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Step 3.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{8}{5}$

Step 3.2

Rewrite the expression.

$\frac{1}{2} \cdot 8$

Step 4

Cancel the common factor of

$2$ .

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Step 4.1

Factor

$2$ out of

$8$ .

$\frac{1}{2} \cdot (2 (4))$

Step 4.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 4)$

Step 4.3

Rewrite the expression.

$4$