Solve 21/3div11/6*(3/4-2/5*1frac{1}{4})

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

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Divide \frac{2\times 3+1}{3} by \frac{1\times 6+1}{6} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{1\times 6+1}{6}.

$$\frac{\left(2\times 3+1\right)\times 6}{3\left(1\times 6+1\right)}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\left(1+2\times 3\right)}{1+6}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{2\left(1+6\right)}{1+6}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{2\times 7}{1+6}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{14}{1+6}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{14}{7}\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Divide 14 by 7 to get 2.

$$2\left(\frac{3}{4}-\frac{2}{5}\times \frac{1\times 4+1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$2\left(\frac{3}{4}-\frac{2}{5}\times \frac{4+1}{4}\right)$$

Add 4 and 1 to get 5.

$$2\left(\frac{3}{4}-\frac{2}{5}\times \frac{5}{4}\right)$$

Multiply \frac{2}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$2\left(\frac{3}{4}-\frac{2\times 5}{5\times 4}\right)$$

Cancel out 5 in both numerator and denominator.

$$2\left(\frac{3}{4}-\frac{2}{4}\right)$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{3-2}{4}$$

Subtract 2 from 3 to get 1.

$$2\times \frac{1}{4}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$