Basic Math Examples

$\frac{6}{8} \div 5 \frac{2}{5}$

Step 1

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

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Step 1.1

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

$\frac{6}{8} \div (5 + \frac{2}{5})$

Step 1.2

Add $5$ and $\frac{2}{5}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6}{8} \div (5 \cdot \frac{5}{5} + \frac{2}{5})$

Step 1.2.2

Combine $5$ and $\frac{5}{5}$ .

$\frac{6}{8} \div (\frac{5 \cdot 5}{5} + \frac{2}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6}{8} \div \frac{5 \cdot 5 + 2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $5$ .

$\frac{6}{8} \div \frac{25 + 2}{5}$

Step 1.2.4.2

Add $25$ and $2$ .

$\frac{6}{8} \div \frac{27}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{8} \cdot \frac{5}{27}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{8} \cdot \frac{5}{27}$

Step 3.2

Factor $3$ out of $27$ .

$\frac{3 \cdot 2}{8} \cdot \frac{5}{3 \cdot 9}$

Step 3.3

Cancel the common factor.

$\frac{3 \cdot 2}{8} \cdot \frac{5}{3 \cdot 9}$

Step 3.4

Rewrite the expression.

$\frac{2}{8} \cdot \frac{5}{9}$

Step 4

Multiply $\frac{2}{8}$ by $\frac{5}{9}$ .

$\frac{2 \cdot 5}{8 \cdot 9}$

Step 5

Multiply.

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Step 5.1

Multiply $2$ by $5$ .

$\frac{10}{8 \cdot 9}$

Step 5.2

Multiply $8$ by $9$ .

$\frac{10}{72}$

Step 6

Cancel the common factor of $10$ and $72$ .

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Step 6.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{72}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $72$ .

$\frac{2 \cdot 5}{2 \cdot 36}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 36}$

Step 6.2.3

Rewrite the expression.

$\frac{5}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{36}$

Decimal Form:

$0.13\overline{8}$