Basic Math Examples

$\frac{n}{1 \frac{1}{5}} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{n}{1 \frac{1}{5}}$ .

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Step 1.1.1

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

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Step 1.1.1.1

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

$\frac{n}{1 + \frac{1}{5}} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{n}{\frac{5}{5} + \frac{1}{5}} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{n}{\frac{5 + 1}{5}} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.1.2.3

Add $5$ and $1$ .

$\frac{n}{\frac{6}{5}} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$n \frac{5}{6} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.3

Combine $n$ and $\frac{5}{6}$ .

$\frac{n \cdot 5}{6} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 1.1.4

Move $5$ to the left of $n$ .

$\frac{5 n}{6} = \frac{4 \frac{1}{6}}{6 \frac{2}{3}}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{4 \frac{1}{6}}{6 \frac{2}{3}}$ .

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Step 2.1.1

Convert $4 \frac{1}{6}$ 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.

$\frac{5 n}{6} = \frac{4 + \frac{1}{6}}{6 \frac{2}{3}}$

Step 2.1.1.2

Add $4$ and $\frac{1}{6}$ .

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Step 2.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 n}{6} = \frac{4 \cdot \frac{6}{6} + \frac{1}{6}}{6 \frac{2}{3}}$

Step 2.1.1.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{5 n}{6} = \frac{\frac{4 \cdot 6}{6} + \frac{1}{6}}{6 \frac{2}{3}}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{5 n}{6} = \frac{\frac{4 \cdot 6 + 1}{6}}{6 \frac{2}{3}}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $4$ by $6$ .

$\frac{5 n}{6} = \frac{\frac{24 + 1}{6}}{6 \frac{2}{3}}$

Step 2.1.1.2.4.2

Add $24$ and $1$ .

$\frac{5 n}{6} = \frac{\frac{25}{6}}{6 \frac{2}{3}}$

Step 2.1.2

Convert $6 \frac{2}{3}$ to an improper fraction.

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Step 2.1.2.1

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

$\frac{5 n}{6} = \frac{\frac{25}{6}}{6 + \frac{2}{3}}$

Step 2.1.2.2

Add $6$ and $\frac{2}{3}$ .

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Step 2.1.2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 n}{6} = \frac{\frac{25}{6}}{6 \cdot \frac{3}{3} + \frac{2}{3}}$

Step 2.1.2.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{5 n}{6} = \frac{\frac{25}{6}}{\frac{6 \cdot 3}{3} + \frac{2}{3}}$

Step 2.1.2.2.3

Combine the numerators over the common denominator.

$\frac{5 n}{6} = \frac{\frac{25}{6}}{\frac{6 \cdot 3 + 2}{3}}$

Step 2.1.2.2.4

Simplify the numerator.

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Step 2.1.2.2.4.1

Multiply $6$ by $3$ .

$\frac{5 n}{6} = \frac{\frac{25}{6}}{\frac{18 + 2}{3}}$

Step 2.1.2.2.4.2

Add $18$ and $2$ .

$\frac{5 n}{6} = \frac{\frac{25}{6}}{\frac{20}{3}}$

Step 2.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 n}{6} = \frac{25}{6} \cdot \frac{3}{20}$

Step 2.1.4

Cancel the common factor of $5$ .

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Step 2.1.4.1

Factor $5$ out of $25$ .

$\frac{5 n}{6} = \frac{5 (5)}{6} \cdot \frac{3}{20}$

Step 2.1.4.2

Factor $5$ out of $20$ .

$\frac{5 n}{6} = \frac{5 \cdot 5}{6} \cdot \frac{3}{5 \cdot 4}$

Step 2.1.4.3

Cancel the common factor.

$\frac{5 n}{6} = \frac{5 \cdot 5}{6} \cdot \frac{3}{5 \cdot 4}$

Step 2.1.4.4

Rewrite the expression.

$\frac{5 n}{6} = \frac{5}{6} \cdot \frac{3}{4}$

Step 2.1.5

Cancel the common factor of $3$ .

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Step 2.1.5.1

Factor $3$ out of $6$ .

$\frac{5 n}{6} = \frac{5}{3 (2)} \cdot \frac{3}{4}$

Step 2.1.5.2

Cancel the common factor.

$\frac{5 n}{6} = \frac{5}{3 \cdot 2} \cdot \frac{3}{4}$

Step 2.1.5.3

Rewrite the expression.

$\frac{5 n}{6} = \frac{5}{2} \cdot \frac{1}{4}$

Step 2.1.6

Multiply $\frac{5}{2}$ by $\frac{1}{4}$ .

$\frac{5 n}{6} = \frac{5}{2 \cdot 4}$

Step 2.1.7

Multiply $2$ by $4$ .

$\frac{5 n}{6} = \frac{5}{8}$

Step 3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} \cdot \frac{5}{8}$

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 $\frac{6}{5} \cdot \frac{5 n}{6}$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} \cdot \frac{5}{8}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 n) = \frac{6}{5} \cdot \frac{5}{8}$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 n$ .

$\frac{1}{5} (5 (n)) = \frac{6}{5} \cdot \frac{5}{8}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 n) = \frac{6}{5} \cdot \frac{5}{8}$

Step 4.1.1.2.3

Rewrite the expression.

$n = \frac{6}{5} \cdot \frac{5}{8}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6}{5} \cdot \frac{5}{8}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $6$ .

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

Step 4.2.1.1.2

Factor $2$ out of $8$ .

$n = \frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 4}$

Step 4.2.1.1.3

Cancel the common factor.

$n = \frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 4}$

Step 4.2.1.1.4

Rewrite the expression.

$n = \frac{3}{5} \cdot \frac{5}{4}$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Cancel the common factor.

$n = \frac{3}{5} \cdot \frac{5}{4}$

Step 4.2.1.2.2

Rewrite the expression.

$n = 3 (\frac{1}{4})$

Step 4.2.1.3

Combine $3$ and $\frac{1}{4}$ .

$n = \frac{3}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{3}{4}$

Decimal Form:

$n = 0.75$