Combine 2-(1.5-1/3)÷(1/6)-(2 1/3-2 1/2)

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (2 \frac{1}{3} - 2 \frac{1}{2})$

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (2 + \frac{1}{3} - 2 \frac{1}{2})$

Add $2$ and $\frac{1}{3}$ .

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (2 \cdot \frac{3}{3} + \frac{1}{3} - 2 \frac{1}{2})$

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{2 \cdot 3}{3} + \frac{1}{3} - 2 \frac{1}{2})$

Combine the numerators over the common denominator.

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{2 \cdot 3 + 1}{3} - 2 \frac{1}{2})$

Simplify the numerator.

Multiply $2$ by $3$ .

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{6 + 1}{3} - 2 \frac{1}{2})$

Add $6$ and $1$ .

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - 2 \frac{1}{2})$

Step 2

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

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - (2 + \frac{1}{2}))$

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

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - (2 \cdot \frac{2}{2} + \frac{1}{2}))$

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

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - (\frac{2 \cdot 2}{2} + \frac{1}{2}))$

Combine the numerators over the common denominator.

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{2 \cdot 2 + 1}{2})$

Simplify the numerator.

Multiply $2$ by $2$ .

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{4 + 1}{2})$

Add $4$ and $1$ .

$2 - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{5}{2})$

Step 3

Find the common denominator.

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{5}{2})$

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

$\frac{2}{1} \cdot \frac{\frac{1}{6}}{\frac{1}{6}} - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{5}{2})$

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

$\frac{2 (\frac{1}{6})}{\frac{1}{6}} - (1.5 - \frac{1}{3}) \div \frac{1}{6} - (\frac{7}{3} - \frac{5}{2})$

Write $- (\frac{7}{3} - \frac{5}{2})$ as a fraction with denominator $1$ .

$\frac{2 (\frac{1}{6})}{\frac{1}{6}} - (1.5 - \frac{1}{3}) \div \frac{1}{6} + \frac{- (\frac{7}{3} - \frac{5}{2})}{1}$

Multiply $\frac{- (\frac{7}{3} - \frac{5}{2})}{1}$ by $\frac{\frac{1}{6}}{\frac{1}{6}}$ .

$\frac{2 (\frac{1}{6})}{\frac{1}{6}} - (1.5 - \frac{1}{3}) \div \frac{1}{6} + \frac{- (\frac{7}{3} - \frac{5}{2})}{1} \cdot \frac{\frac{1}{6}}{\frac{1}{6}}$

Multiply $\frac{- (\frac{7}{3} - \frac{5}{2})}{1}$ by $\frac{\frac{1}{6}}{\frac{1}{6}}$ .

$\frac{2 (\frac{1}{6})}{\frac{1}{6}} - (1.5 - \frac{1}{3}) \div \frac{1}{6} + \frac{- (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (\frac{1}{6}) - (1.5 - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Step 5

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{2 \frac{1}{2 (3)} - (1.5 - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Cancel the common factor.

$\frac{2 \frac{1}{2 \cdot 3} - (1.5 - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Rewrite the expression.

$\frac{\frac{1}{3} - (1.5 - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

To write $1.5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{1}{3} - (1.5 \cdot \frac{3}{3} - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Combine $1.5$ and $\frac{3}{3}$ .

$\frac{\frac{1}{3} - (\frac{1.5 \cdot 3}{3} - \frac{1}{3}) - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Combine the numerators over the common denominator.

$\frac{\frac{1}{3} - \frac{1.5 \cdot 3 - 1}{3} - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Simplify the numerator.

Multiply $1.5$ by $3$ .

$\frac{\frac{1}{3} - \frac{4.5 - 1}{3} - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Subtract $1$ from $4.5$ .

$\frac{\frac{1}{3} - \frac{3.5}{3} - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Divide $3.5$ by $3$ .

$\frac{\frac{1}{3} - 1 \cdot 1.1\overline{6} - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

Multiply $- 1$ by $1.1\overline{6}$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7}{3} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

To write $\frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7}{3} \cdot \frac{2}{2} - \frac{5}{2}) \frac{1}{6}}{\frac{1}{6}}$

To write $- \frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7}{3} \cdot \frac{2}{2} - \frac{5}{2} \cdot \frac{3}{3}) \frac{1}{6}}{\frac{1}{6}}$

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

Multiply $\frac{7}{3}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7 \cdot 2}{3 \cdot 2} - \frac{5}{2} \cdot \frac{3}{3}) \frac{1}{6}}{\frac{1}{6}}$

Multiply $3$ by $2$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7 \cdot 2}{6} - \frac{5}{2} \cdot \frac{3}{3}) \frac{1}{6}}{\frac{1}{6}}$

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7 \cdot 2}{6} - \frac{5 \cdot 3}{2 \cdot 3}) \frac{1}{6}}{\frac{1}{6}}$

Multiply $2$ by $3$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - (\frac{7 \cdot 2}{6} - \frac{5 \cdot 3}{6}) \frac{1}{6}}{\frac{1}{6}}$

Combine the numerators over the common denominator.

$\frac{\frac{1}{3} - 1.1\overline{6} - \frac{7 \cdot 2 - 5 \cdot 3}{6} \cdot \frac{1}{6}}{\frac{1}{6}}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - \frac{14 - 5 \cdot 3}{6} \cdot \frac{1}{6}}{\frac{1}{6}}$

Multiply $- 5$ by $3$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - \frac{14 - 15}{6} \cdot \frac{1}{6}}{\frac{1}{6}}$

Subtract $15$ from $14$ .

$\frac{\frac{1}{3} - 1.1\overline{6} - \frac{- 1}{6} \cdot \frac{1}{6}}{\frac{1}{6}}$

Move the negative in front of the fraction.

$\frac{\frac{1}{3} - 1.1\overline{6} - - \frac{1}{6} \frac{1}{6}}{\frac{1}{6}}$

Multiply $- - \frac{1}{6}$ .

Multiply $- 1$ by $- 1$ .

$\frac{\frac{1}{3} - 1.1\overline{6} + 1 (\frac{1}{6}) \frac{1}{6}}{\frac{1}{6}}$

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

$\frac{\frac{1}{3} - 1.1\overline{6} + \frac{1}{6} \cdot \frac{1}{6}}{\frac{1}{6}}$

Multiply $\frac{1}{6} \cdot \frac{1}{6}$ .

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

$\frac{\frac{1}{3} - 1.1\overline{6} + \frac{1}{6 \cdot 6}}{\frac{1}{6}}$

Multiply $6$ by $6$ .

$\frac{\frac{1}{3} - 1.1\overline{6} + \frac{1}{36}}{\frac{1}{6}}$

Step 6

Find the common denominator.

Multiply $\frac{1}{3}$ by $\frac{12}{12}$ .

$\frac{\frac{1}{3} \cdot \frac{12}{12} - 1.1\overline{6} + \frac{1}{36}}{\frac{1}{6}}$

Multiply $\frac{1}{3}$ by $\frac{12}{12}$ .

$\frac{\frac{12}{3 \cdot 12} - 1.1\overline{6} + \frac{1}{36}}{\frac{1}{6}}$

Write $- 1.1\overline{6}$ as a fraction with denominator $1$ .

$\frac{\frac{12}{3 \cdot 12} + \frac{- 1.1\overline{6}}{1} + \frac{1}{36}}{\frac{1}{6}}$

Multiply $\frac{- 1.1\overline{6}}{1}$ by $\frac{36}{36}$ .

$\frac{\frac{12}{3 \cdot 12} + \frac{- 1.1\overline{6}}{1} \cdot \frac{36}{36} + \frac{1}{36}}{\frac{1}{6}}$

Multiply $\frac{- 1.1\overline{6}}{1}$ by $\frac{36}{36}$ .

$\frac{\frac{12}{3 \cdot 12} + \frac{- 1.1\overline{6} \cdot 36}{36} + \frac{1}{36}}{\frac{1}{6}}$

Multiply $3$ by $12$ .

$\frac{\frac{12}{36} + \frac{- 1.1\overline{6} \cdot 36}{36} + \frac{1}{36}}{\frac{1}{6}}$

Step 7

Combine the numerators over the common denominator.

$\frac{\frac{12 - 1.1\overline{6} \cdot 36 + 1}{36}}{\frac{1}{6}}$

Step 8

Simplify the expression.

Multiply $- 1.1\overline{6}$ by $36$ .

$\frac{\frac{12 - 42 + 1}{36}}{\frac{1}{6}}$

Subtract $42$ from $12$ .

$\frac{\frac{- 30 + 1}{36}}{\frac{1}{6}}$

Add $- 30$ and $1$ .

$\frac{\frac{- 29}{36}}{\frac{1}{6}}$

Divide $- 29$ by $36$ .

$\frac{- 0.80\overline{5}}{\frac{1}{6}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$- 0.80\overline{5} \cdot 6$

Step 10

Multiply $- 0.80\overline{5}$ by $6$ .

$- 4.8\overline{3}$

Combine 2-(1.5-1/3)÷(1/6)-(2 1/3-2 1/2)

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