Simplify (2 1/2÷1 2/3)÷(-3 1/3)

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

Step 1

Convert

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

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

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

Add

$2$ and

$\frac{1}{2}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Combine

$2$ and

$\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$2$ by

$2$ .

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

Add

$4$ and

$1$ .

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

Step 2

Convert

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

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

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

Add

$1$ and

$\frac{2}{3}$ .

Write

$1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add

$3$ and

$2$ .

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

Step 3

Convert

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

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

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

Add

$3$ and

$\frac{1}{3}$ .

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

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

Combine

$3$ and

$\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$3$ by

$3$ .

$\frac{5}{2} \div \frac{5}{3} \div (- \frac{9 + 1}{3})$

Add

$9$ and

$1$ .

$\frac{5}{2} \div \frac{5}{3} \div (- \frac{10}{3})$

Step 4

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \div \frac{5}{3} (- \frac{3}{10})$

Step 5

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{3}{5} (- \frac{3}{10})$

Step 6

Cancel the common factor of

$5$ .

Cancel the common factor.

$\frac{5}{2} \cdot \frac{3}{5} (- \frac{3}{10})$

Rewrite the expression.

$\frac{1}{2} \cdot 3 (- \frac{3}{10})$

Step 7

Combine

$\frac{1}{2}$ and

$3$ .

$\frac{3}{2} (- \frac{3}{10})$

Step 8

Multiply

$\frac{3}{2} (- \frac{3}{10})$ .

Multiply

$\frac{3}{2}$ by

$\frac{3}{10}$ .

$- \frac{3 \cdot 3}{2 \cdot 10}$

Multiply

$3$ by

$3$ .

$- \frac{9}{2 \cdot 10}$

Multiply

$2$ by

$10$ .

$- \frac{9}{20}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{20}$

Decimal Form:

$- 0.45$

Simplify (2 1/2÷1 2/3)÷(-3 1/3)

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