Solve for n 2 1/10n=1 1/6

$2 \frac{1}{10} n = 1 \frac{1}{6}$

Simplify the left side.

Simplify $2 \frac{1}{10} n$ .

Convert $2 \frac{1}{10}$ to an improper fraction.

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

$(2 + \frac{1}{10}) n = 1 \frac{1}{6}$

Add $2$ and $\frac{1}{10}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$(2 \cdot \frac{10}{10} + \frac{1}{10}) n = 1 \frac{1}{6}$

Combine $2$ and $\frac{10}{10}$ .

$(\frac{2 \cdot 10}{10} + \frac{1}{10}) n = 1 \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 10 + 1}{10} n = 1 \frac{1}{6}$

Simplify the numerator.

Multiply $2$ by $10$ .

$\frac{20 + 1}{10} n = 1 \frac{1}{6}$

Add $20$ and $1$ .

$\frac{21}{10} n = 1 \frac{1}{6}$

Combine $\frac{21}{10}$ and $n$ .

$\frac{21 n}{10} = 1 \frac{1}{6}$

Simplify the right side.

Convert $1 \frac{1}{6}$ to an improper fraction.

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

$\frac{21 n}{10} = 1 + \frac{1}{6}$

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

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

$\frac{21 n}{10} = \frac{6}{6} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{21 n}{10} = \frac{6 + 1}{6}$

Add $6$ and $1$ .

$\frac{21 n}{10} = \frac{7}{6}$

Multiply both sides of the equation by $\frac{10}{21}$ .

$\frac{10}{21} \cdot \frac{21 n}{10} = \frac{10}{21} \cdot \frac{7}{6}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{21} \cdot \frac{21 n}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{21} \cdot \frac{21 n}{10} = \frac{10}{21} \cdot \frac{7}{6}$

Rewrite the expression.

$\frac{1}{21} (21 n) = \frac{10}{21} \cdot \frac{7}{6}$

Cancel the common factor of $21$ .

Factor $21$ out of $21 n$ .

$\frac{1}{21} (21 (n)) = \frac{10}{21} \cdot \frac{7}{6}$

Cancel the common factor.

$\frac{1}{21} (21 n) = \frac{10}{21} \cdot \frac{7}{6}$

Rewrite the expression.

$n = \frac{10}{21} \cdot \frac{7}{6}$

Simplify the right side.

Simplify $\frac{10}{21} \cdot \frac{7}{6}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$n = \frac{2 (5)}{21} \cdot \frac{7}{6}$

Factor $2$ out of $6$ .

$n = \frac{2 \cdot 5}{21} \cdot \frac{7}{2 \cdot 3}$

Cancel the common factor.

$n = \frac{2 \cdot 5}{21} \cdot \frac{7}{2 \cdot 3}$

Rewrite the expression.

$n = \frac{5}{21} \cdot \frac{7}{3}$

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

$n = \frac{5}{7 (3)} \cdot \frac{7}{3}$

Cancel the common factor.

$n = \frac{5}{7 \cdot 3} \cdot \frac{7}{3}$

Rewrite the expression.

$n = \frac{5}{3} \cdot \frac{1}{3}$

Multiply $\frac{5}{3}$ by $\frac{1}{3}$ .

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

Multiply $3$ by $3$ .

$n = \frac{5}{9}$

The result can be shown in multiple forms.

Exact Form:

$n = \frac{5}{9}$

Decimal Form:

$n = 0.\overline{5}$

Solve for n 2 1/10n=1 1/6

Related Questions

Support LCMGCF.com by disabling your adblocker.