Basic Math Examples

$\frac{n}{\frac{10}{9}} = \frac{81}{\frac{10}{7 \frac{1}{5}}}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{n}{\frac{10}{9}}$ .

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Step 1.1.1

Multiply the numerator by the reciprocal of the denominator.

$n \frac{9}{10} = \frac{81}{\frac{10}{7 \frac{1}{5}}}$

Step 1.1.2

Combine $n$ and $\frac{9}{10}$ .

$\frac{n \cdot 9}{10} = \frac{81}{\frac{10}{7 \frac{1}{5}}}$

Step 1.1.3

Move $9$ to the left of $n$ .

$\frac{9 n}{10} = \frac{81}{\frac{10}{7 \frac{1}{5}}}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{81}{\frac{10}{7 \frac{1}{5}}}$ .

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Step 2.1.1

Convert $7 \frac{1}{5}$ to an improper fraction.

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Step 2.1.1.1

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

$\frac{9 n}{10} = \frac{81}{\frac{10}{7 + \frac{1}{5}}}$

Step 2.1.1.2

Add $7$ and $\frac{1}{5}$ .

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Step 2.1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9 n}{10} = \frac{81}{\frac{10}{7 \cdot \frac{5}{5} + \frac{1}{5}}}$

Step 2.1.1.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{9 n}{10} = \frac{81}{\frac{10}{\frac{7 \cdot 5}{5} + \frac{1}{5}}}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{9 n}{10} = \frac{81}{\frac{10}{\frac{7 \cdot 5 + 1}{5}}}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $7$ by $5$ .

$\frac{9 n}{10} = \frac{81}{\frac{10}{\frac{35 + 1}{5}}}$

Step 2.1.1.2.4.2

Add $35$ and $1$ .

$\frac{9 n}{10} = \frac{81}{\frac{10}{\frac{36}{5}}}$

Step 2.1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 n}{10} = 81 \frac{\frac{36}{5}}{10}$

Step 2.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 n}{10} = 81 (\frac{36}{5} \cdot \frac{1}{10})$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Factor $2$ out of $36$ .

$\frac{9 n}{10} = 81 (\frac{2 (18)}{5} \cdot \frac{1}{10})$

Step 2.1.4.2

Factor $2$ out of $10$ .

$\frac{9 n}{10} = 81 (\frac{2 \cdot 18}{5} \cdot \frac{1}{2 \cdot 5})$

Step 2.1.4.3

Cancel the common factor.

$\frac{9 n}{10} = 81 (\frac{2 \cdot 18}{5} \cdot \frac{1}{2 \cdot 5})$

Step 2.1.4.4

Rewrite the expression.

$\frac{9 n}{10} = 81 (\frac{18}{5} \cdot \frac{1}{5})$

Step 2.1.5

Multiply $\frac{18}{5}$ by $\frac{1}{5}$ .

$\frac{9 n}{10} = 81 \frac{18}{5 \cdot 5}$

Step 2.1.6

Multiply $5$ by $5$ .

$\frac{9 n}{10} = 81 (\frac{18}{25})$

Step 2.1.7

Multiply $81 (\frac{18}{25})$ .

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Step 2.1.7.1

Combine $81$ and $\frac{18}{25}$ .

$\frac{9 n}{10} = \frac{81 \cdot 18}{25}$

Step 2.1.7.2

Multiply $81$ by $18$ .

$\frac{9 n}{10} = \frac{1458}{25}$

Step 3

Multiply both sides of the equation by $\frac{10}{9}$ .

$\frac{10}{9} \cdot \frac{9 n}{10} = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{10}{9} \cdot \frac{9 n}{10}$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{10}{9} \cdot \frac{9 n}{10} = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 n) = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4.1.1.2

Cancel the common factor of $9$ .

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Step 4.1.1.2.1

Factor $9$ out of $9 n$ .

$\frac{1}{9} (9 (n)) = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 n) = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4.1.1.2.3

Rewrite the expression.

$n = \frac{10}{9} \cdot \frac{1458}{25}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{10}{9} \cdot \frac{1458}{25}$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Factor $5$ out of $10$ .

$n = \frac{5 (2)}{9} \cdot \frac{1458}{25}$

Step 4.2.1.1.2

Factor $5$ out of $25$ .

$n = \frac{5 \cdot 2}{9} \cdot \frac{1458}{5 \cdot 5}$

Step 4.2.1.1.3

Cancel the common factor.

$n = \frac{5 \cdot 2}{9} \cdot \frac{1458}{5 \cdot 5}$

Step 4.2.1.1.4

Rewrite the expression.

$n = \frac{2}{9} \cdot \frac{1458}{5}$

Step 4.2.1.2

Cancel the common factor of $9$ .

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Step 4.2.1.2.1

Factor $9$ out of $1458$ .

$n = \frac{2}{9} \cdot \frac{9 (162)}{5}$

Step 4.2.1.2.2

Cancel the common factor.

$n = \frac{2}{9} \cdot \frac{9 \cdot 162}{5}$

Step 4.2.1.2.3

Rewrite the expression.

$n = 2 (\frac{162}{5})$

Step 4.2.1.3

Combine $2$ and $\frac{162}{5}$ .

$n = \frac{2 \cdot 162}{5}$

Step 4.2.1.4

Multiply $2$ by $162$ .

$n = \frac{324}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{324}{5}$

Decimal Form:

$n = 64.8$

Mixed Number Form:

$n = 64 \frac{4}{5}$