Evaluate 2 1/6-1 2/9÷3 2/3

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

Step 1

Convert $2 \frac{1}{6}$ to an improper fraction.

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

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

Add $2$ and $\frac{1}{6}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Combine $2$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $6$ .

$\frac{12 + 1}{6} - 1 \frac{2}{9} \div 3 \frac{2}{3}$

Add $12$ and $1$ .

$\frac{13}{6} - 1 \frac{2}{9} \div 3 \frac{2}{3}$

Step 2

Convert $1 \frac{2}{9}$ to an improper fraction.

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

$\frac{13}{6} - (1 + \frac{2}{9}) \div 3 \frac{2}{3}$

Add $1$ and $\frac{2}{9}$ .

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

$\frac{13}{6} - (\frac{9}{9} + \frac{2}{9}) \div 3 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{13}{6} - \frac{9 + 2}{9} \div 3 \frac{2}{3}$

Add $9$ and $2$ .

$\frac{13}{6} - \frac{11}{9} \div 3 \frac{2}{3}$

Step 3

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

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

$\frac{13}{6} - \frac{11}{9} \div (3 + \frac{2}{3})$

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

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

$\frac{13}{6} - \frac{11}{9} \div (3 \cdot \frac{3}{3} + \frac{2}{3})$

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

$\frac{13}{6} - \frac{11}{9} \div (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{13}{6} - \frac{11}{9} \div \frac{3 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{13}{6} - \frac{11}{9} \div \frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{13}{6} - \frac{11}{9} \div \frac{11}{3}$

Step 4

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{6} - (\frac{11}{9} \cdot \frac{3}{11})$

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{13}{6} - (\frac{11}{9} \cdot \frac{3}{11})$

Rewrite the expression.

$\frac{13}{6} - (\frac{1}{9} \cdot 3)$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{13}{6} - (\frac{1}{3 (3)} \cdot 3)$

Cancel the common factor.

$\frac{13}{6} - (\frac{1}{3 \cdot 3} \cdot 3)$

Rewrite the expression.

$\frac{13}{6} - \frac{1}{3}$

Step 5

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{6} - \frac{1}{3} \cdot \frac{2}{2}$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{13}{6} - \frac{2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{13}{6} - \frac{2}{6}$

Step 7

Combine the numerators over the common denominator.

$\frac{13 - 2}{6}$

Step 8

Subtract $2$ from $13$ .

$\frac{11}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{6}$

Decimal Form:

$1.8\overline{3}$

Mixed Number Form:

$1 \frac{5}{6}$

Evaluate 2 1/6-1 2/9÷3 2/3

Related Questions

Support LCMGCF.com by disabling your adblocker.