Solve 1div(2-3/4*8/9div5/6)

$$1 \div ( 2 - \frac { 3 } { 4 } \times \frac { 8 } { 9 } \div \frac { 5 } { 6 } )$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2-\frac{\frac{3\times 8}{4\times 9}}{\frac{5}{6}}}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\frac{1}{2-\frac{\frac{24}{36}}{\frac{5}{6}}}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{1}{2-\frac{\frac{2}{3}}{\frac{5}{6}}}$$

Divide \frac{2}{3} by \frac{5}{6} by multiplying \frac{2}{3} by the reciprocal of \frac{5}{6}.

$$\frac{1}{2-\frac{2}{3}\times \frac{6}{5}}$$

Multiply \frac{2}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2-\frac{2\times 6}{3\times 5}}$$

Do the multiplications in the fraction \frac{2\times 6}{3\times 5}.

$$\frac{1}{2-\frac{12}{15}}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2-\frac{4}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{1}{\frac{10}{5}-\frac{4}{5}}$$

Since \frac{10}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{10-4}{5}}$$

Subtract 4 from 10 to get 6.

$$\frac{1}{\frac{6}{5}}$$

Divide 1 by \frac{6}{5} by multiplying 1 by the reciprocal of \frac{6}{5}.

$$1\times \frac{5}{6}$$

Multiply 1 and \frac{5}{6} to get \frac{5}{6}.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$