Solve for n 9 1/3=5/3n

$9 \frac{1}{3} = \frac{5}{3} n$

Simplify the left side.

Convert $9 \frac{1}{3}$ to an improper fraction.

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

$9 + \frac{1}{3} = \frac{5}{3} n$

Add $9$ and $\frac{1}{3}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$9 \cdot \frac{3}{3} + \frac{1}{3} = \frac{5}{3} n$

Combine $9$ and $\frac{3}{3}$ .

$\frac{9 \cdot 3}{3} + \frac{1}{3} = \frac{5}{3} n$

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 + 1}{3} = \frac{5}{3} n$

Simplify the numerator.

Multiply $9$ by $3$ .

$\frac{27 + 1}{3} = \frac{5}{3} n$

Add $27$ and $1$ .

$\frac{28}{3} = \frac{5}{3} n$

Simplify the right side.

Combine $\frac{5}{3}$ and $n$ .

$\frac{28}{3} = \frac{5 n}{3}$

Rewrite the equation as $\frac{5 n}{3} = \frac{28}{3}$ .

$\frac{5 n}{3} = \frac{28}{3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 n = 28$

Divide each term in $5 n = 28$ by $5$ and simplify.

Divide each term in $5 n = 28$ by $5$ .

$\frac{5 n}{5} = \frac{28}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{28}{5}$

Divide $n$ by $1$ .

$n = \frac{28}{5}$

The result can be shown in multiple forms.

Exact Form:

$n = \frac{28}{5}$

Decimal Form:

$n = 5.6$

Mixed Number Form:

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