Convert to a Simplified Fraction 1/6+3^2-(2/3)÷1 3/5

$\frac{1}{6} + 3^{2} - \frac{2}{3} \div 1 \frac{3}{5}$

Step 1

Convert $1 \frac{3}{5}$ to an improper fraction.

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

$\frac{1}{6} + 3^{2} - \frac{2}{3} \div (1 + \frac{3}{5})$

Add $1$ and $\frac{3}{5}$ .

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

$\frac{1}{6} + 3^{2} - \frac{2}{3} \div (\frac{5}{5} + \frac{3}{5})$

Combine the numerators over the common denominator.

$\frac{1}{6} + 3^{2} - \frac{2}{3} \div \frac{5 + 3}{5}$

Add $5$ and $3$ .

$\frac{1}{6} + 3^{2} - \frac{2}{3} \div \frac{8}{5}$

Step 2

Simplify each term.

Raise $3$ to the power of $2$ .

$\frac{1}{6} + 9 - \frac{2}{3} \div \frac{8}{5}$

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{6} + 9 - (\frac{2}{3} \cdot \frac{5}{8})$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{1}{6} + 9 - (\frac{2}{3} \cdot \frac{5}{2 (4)})$

Cancel the common factor.

$\frac{1}{6} + 9 - (\frac{2}{3} \cdot \frac{5}{2 \cdot 4})$

Rewrite the expression.

$\frac{1}{6} + 9 - (\frac{1}{3} \cdot \frac{5}{4})$

Multiply $\frac{1}{3}$ by $\frac{5}{4}$ .

$\frac{1}{6} + 9 - \frac{5}{3 \cdot 4}$

Multiply $3$ by $4$ .

$\frac{1}{6} + 9 - \frac{5}{12}$

Step 3

Find the common denominator.

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{1}{6} \cdot \frac{2}{2} + 9 - \frac{5}{12}$

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{2}{6 \cdot 2} + 9 - \frac{5}{12}$

Write $9$ as a fraction with denominator $1$ .

$\frac{2}{6 \cdot 2} + \frac{9}{1} - \frac{5}{12}$

Multiply $\frac{9}{1}$ by $\frac{12}{12}$ .

$\frac{2}{6 \cdot 2} + \frac{9}{1} \cdot \frac{12}{12} - \frac{5}{12}$

Multiply $\frac{9}{1}$ by $\frac{12}{12}$ .

$\frac{2}{6 \cdot 2} + \frac{9 \cdot 12}{12} - \frac{5}{12}$

Reorder the factors of $6 \cdot 2$ .

$\frac{2}{2 \cdot 6} + \frac{9 \cdot 12}{12} - \frac{5}{12}$

Multiply $2$ by $6$ .

$\frac{2}{12} + \frac{9 \cdot 12}{12} - \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 + 9 \cdot 12 - 5}{12}$

Step 5

Multiply $9$ by $12$ .

$\frac{2 + 108 - 5}{12}$

Step 6

Add $2$ and $108$ .

$\frac{110 - 5}{12}$

Step 7

Subtract $5$ from $110$ .

$\frac{105}{12}$

Step 8

Cancel the common factor of $105$ and $12$ .

Factor $3$ out of $105$ .

$\frac{3 (35)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$\frac{3 \cdot 35}{3 \cdot 4}$

Cancel the common factor.

$\frac{3 \cdot 35}{3 \cdot 4}$

Rewrite the expression.

$\frac{35}{4}$

Convert to a Simplified Fraction 1/6+3^2-(2/3)÷1 3/5

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