Basic Math Examples

\frac{5}{8} \div 6 \frac{5}{6}

$\frac{5}{8} \div 6 \frac{5}{6}$

Step 1

Convert

6 \frac{5}{6}

$6 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

\frac{5}{8} \div (6 + \frac{5}{6})

$\frac{5}{8} \div (6 + \frac{5}{6})$

Step 1.2

Add

6

$6$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5}{8} \div (6 \cdot \frac{6}{6} + \frac{5}{6})

$\frac{5}{8} \div (6 \cdot \frac{6}{6} + \frac{5}{6})$

Step 1.2.2

Combine

6

$6$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5}{8} \div (\frac{6 \cdot 6}{6} + \frac{5}{6})

$\frac{5}{8} \div (\frac{6 \cdot 6}{6} + \frac{5}{6})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5}{8} \div \frac{6 \cdot 6 + 5}{6}

$\frac{5}{8} \div \frac{6 \cdot 6 + 5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

6

$6$ .

\frac{5}{8} \div \frac{36 + 5}{6}

$\frac{5}{8} \div \frac{36 + 5}{6}$

Step 1.2.4.2

Add

36

$36$ and

5

$5$ .

\frac{5}{8} \div \frac{41}{6}

$\frac{5}{8} \div \frac{41}{6}$

\frac{5}{8} \div \frac{41}{6}

$\frac{5}{8} \div \frac{41}{6}$

\frac{5}{8} \div \frac{41}{6}

$\frac{5}{8} \div \frac{41}{6}$

\frac{5}{8} \div \frac{41}{6}

$\frac{5}{8} \div \frac{41}{6}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{5}{8} \cdot \frac{6}{41}

$\frac{5}{8} \cdot \frac{6}{41}$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

8

$8$ .

\frac{5}{2 (4)} \cdot \frac{6}{41}

$\frac{5}{2 (4)} \cdot \frac{6}{41}$

Step 3.2

Factor

2

$2$ out of

6

$6$ .

\frac{5}{2 \cdot 4} \cdot \frac{2 \cdot 3}{41}

$\frac{5}{2 \cdot 4} \cdot \frac{2 \cdot 3}{41}$

Step 3.3

Cancel the common factor.

$\frac{5}{2 \cdot 4} \cdot \frac{2 \cdot 3}{41}$

Step 3.4

Rewrite the expression.

$\frac{5}{4} \cdot \frac{3}{41}$

Step 4

Multiply

$\frac{5}{4}$ by

$\frac{3}{41}$ .

$\frac{5 \cdot 3}{4 \cdot 41}$

Step 5

Multiply.

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Step 5.1

Multiply

$5$ by

$3$ .

$\frac{15}{4 \cdot 41}$

Step 5.2

Multiply

$4$ by

$41$ .

$\frac{15}{164}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{164}$

Decimal Form:

$0.09\overline{14634}$