Evaluate (1/2)÷((2/3)÷(3/4)-(4/5*5/6))

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} - \frac{4}{5} \cdot \frac{5}{6}}$

Step 3

Simplify the denominator.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} + \frac{- 4}{5} \cdot \frac{5}{6}}$

Factor $2$ out of $- 4$ .

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

Factor $2$ out of $6$ .

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} + \frac{2 \cdot - 2}{5} \cdot \frac{5}{2 \cdot 3}}$

Cancel the common factor.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} + \frac{2 \cdot - 2}{5} \cdot \frac{5}{2 \cdot 3}}$

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} + \frac{- 2}{5} \cdot \frac{5}{3}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} + \frac{- 2}{5} \cdot \frac{5}{3}}$

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} - 2 \cdot \frac{1}{3}}$

Combine $- 2$ and $\frac{1}{3}$ .

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

Move the negative in front of the fraction.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \div \frac{3}{4} - \frac{2}{3}}$

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} \cdot \frac{1}{\frac{2}{3} \cdot \frac{4}{3} - \frac{2}{3}}$

Multiply $\frac{2}{3} \cdot \frac{4}{3}$ .

Multiply $\frac{2}{3}$ by $\frac{4}{3}$ .

$\frac{1}{2} \cdot \frac{1}{\frac{2 \cdot 4}{3 \cdot 3} - \frac{2}{3}}$

Multiply $2$ by $4$ .

$\frac{1}{2} \cdot \frac{1}{\frac{8}{3 \cdot 3} - \frac{2}{3}}$

Multiply $3$ by $3$ .

$\frac{1}{2} \cdot \frac{1}{\frac{8}{9} - \frac{2}{3}}$

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

$\frac{1}{2} \cdot \frac{1}{\frac{8}{9} - \frac{2}{3} \cdot \frac{3}{3}}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{1}{2} \cdot \frac{1}{\frac{8}{9} - \frac{2 \cdot 3}{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{1}{2} \cdot \frac{1}{\frac{8}{9} - \frac{2 \cdot 3}{9}}$

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{1}{\frac{8 - 2 \cdot 3}{9}}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$\frac{1}{2} \cdot \frac{1}{\frac{8 - 6}{9}}$

Subtract $6$ from $8$ .

$\frac{1}{2} \cdot \frac{1}{\frac{2}{9}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} (1 (\frac{9}{2}))$

Step 5

Multiply $\frac{9}{2}$ by $1$ .

$\frac{1}{2} \cdot \frac{9}{2}$

Step 6

Multiply $\frac{1}{2} \cdot \frac{9}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{9}{2}$ .

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

Multiply $2$ by $2$ .

$\frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$

Evaluate (1/2)÷((2/3)÷(3/4)-(4/5*5/6))

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