Solve (4/5-8/15div22/3)*12/3

$$( \frac{ 4 }{ 5 } - \frac{ 8 }{ 15 } \div 2 \frac { 2 } { 3 } ) \times 1 \frac { 2 } { 3 }$$

Evaluate

$$1$$

Solution Steps

Divide \frac{8}{15} by \frac{2\times 3+2}{3} by multiplying \frac{8}{15} by the reciprocal of \frac{2\times 3+2}{3}.

$$\left(\frac{4}{5}-\frac{8\times 3}{15\left(2\times 3+2\right)}\right)\times \frac{1\times 3+2}{3}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{4}{5}-\frac{8}{5\left(2+2\times 3\right)}\right)\times \frac{1\times 3+2}{3}$$

Multiply 2 and 3 to get 6.

$$\left(\frac{4}{5}-\frac{8}{5\left(2+6\right)}\right)\times \frac{1\times 3+2}{3}$$

Add 2 and 6 to get 8.

$$\left(\frac{4}{5}-\frac{8}{5\times 8}\right)\times \frac{1\times 3+2}{3}$$

Multiply 5 and 8 to get 40.

$$\left(\frac{4}{5}-\frac{8}{40}\right)\times \frac{1\times 3+2}{3}$$

Reduce the fraction \frac{8}{40} to lowest terms by extracting and canceling out 8.

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

Since \frac{4}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

$$\frac{3}{5}\times \frac{1\times 3+2}{3}$$

Multiply 1 and 3 to get 3.

$$\frac{3}{5}\times \frac{3+2}{3}$$

Add 3 and 2 to get 5.

$$\frac{3}{5}\times \frac{5}{3}$$

Cancel out \frac{3}{5} and its reciprocal \frac{5}{3}.

$$1$$

Factor

$$1$$