Solve 2/3*(2-51/2div214/15)

$$\frac{ 2 }{ 3 } \times (2- 5 \frac { 1 } { 2 } \div 2 \frac { 14 } { 15 } )$$

Evaluate

$$\frac{1}{12}\approx 0.083333333$$

Solution Steps

Divide \frac{5\times 2+1}{2} by \frac{2\times 15+14}{15} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{2\times 15+14}{15}.

$$\frac{2}{3}\left(2-\frac{\left(5\times 2+1\right)\times 15}{2\left(2\times 15+14\right)}\right)$$

Multiply 5 and 2 to get 10.

$$\frac{2}{3}\left(2-\frac{\left(10+1\right)\times 15}{2\left(2\times 15+14\right)}\right)$$

Add 10 and 1 to get 11.

$$\frac{2}{3}\left(2-\frac{11\times 15}{2\left(2\times 15+14\right)}\right)$$

Multiply 11 and 15 to get 165.

$$\frac{2}{3}\left(2-\frac{165}{2\left(2\times 15+14\right)}\right)$$

Multiply 2 and 15 to get 30.

$$\frac{2}{3}\left(2-\frac{165}{2\left(30+14\right)}\right)$$

Add 30 and 14 to get 44.

$$\frac{2}{3}\left(2-\frac{165}{2\times 44}\right)$$

Multiply 2 and 44 to get 88.

$$\frac{2}{3}\left(2-\frac{165}{88}\right)$$

Reduce the fraction \frac{165}{88} to lowest terms by extracting and canceling out 11.

$$\frac{2}{3}\left(2-\frac{15}{8}\right)$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{2}{3}\left(\frac{16}{8}-\frac{15}{8}\right)$$

Since \frac{16}{8} and \frac{15}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{16-15}{8}$$

Subtract 15 from 16 to get 1.

$$\frac{2}{3}\times \frac{1}{8}$$

Multiply \frac{2}{3} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{3\times 8}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 8}.

$$\frac{2}{24}$$

Reduce the fraction \frac{2}{24} to lowest terms by extracting and canceling out 2.

$$\frac{1}{12}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$$