Solve (3-3/4)(3-7/9)/(5-frac{5{6})}

$$\frac { ( 3 - \frac { 3 } { 4 } ) ( 3 - \frac { 7 } { 9 } ) } { ( 5 - \frac { 5 } { 6 } ) }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$\frac{\left(\frac{12}{4}-\frac{3}{4}\right)\left(3-\frac{7}{9}\right)}{5-\frac{5}{6}}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-3}{4}\left(3-\frac{7}{9}\right)}{5-\frac{5}{6}}$$

Subtract 3 from 12 to get 9.

$$\frac{\frac{9}{4}\left(3-\frac{7}{9}\right)}{5-\frac{5}{6}}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{\frac{9}{4}\left(\frac{27}{9}-\frac{7}{9}\right)}{5-\frac{5}{6}}$$

Since \frac{27}{9} and \frac{7}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{4}\times \frac{27-7}{9}}{5-\frac{5}{6}}$$

Subtract 7 from 27 to get 20.

$$\frac{\frac{9}{4}\times \frac{20}{9}}{5-\frac{5}{6}}$$

Multiply \frac{9}{4} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 20}{4\times 9}}{5-\frac{5}{6}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{\frac{20}{4}}{5-\frac{5}{6}}$$

Divide 20 by 4 to get 5.

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

Convert 5 to fraction \frac{30}{6}.

$$\frac{5}{\frac{30}{6}-\frac{5}{6}}$$

Since \frac{30}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{\frac{30-5}{6}}$$

Subtract 5 from 30 to get 25.

$$\frac{5}{\frac{25}{6}}$$

Divide 5 by \frac{25}{6} by multiplying 5 by the reciprocal of \frac{25}{6}.

$$5\times \frac{6}{25}$$

Express 5\times \frac{6}{25} as a single fraction.

$$\frac{5\times 6}{25}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{25}$$

Reduce the fraction \frac{30}{25} to lowest terms by extracting and canceling out 5.

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

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$