Solve 8/3*2/frac{1{2}*3/2}(4*15/2)frac{1}{3}

$$\frac { \frac { 8 } { 3 } \cdot 2 } { \frac { 1 } { 2 } \cdot \frac { 3 } { 2 } } ( 4 \cdot \frac { 15 } { 2 } ) \frac { 1 } { 3 }$$

Evaluate

$$\frac{640}{9}\approx 71.111111111$$

Solution Steps

Express \frac{8}{3}\times 2 as a single fraction.

$$\frac{\frac{8\times 2}{3}}{\frac{1}{2}\times \frac{3}{2}}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

Multiply 8 and 2 to get 16.

$$\frac{\frac{16}{3}}{\frac{1}{2}\times \frac{3}{2}}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

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

$$\frac{\frac{16}{3}}{\frac{1\times 3}{2\times 2}}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

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

$$\frac{\frac{16}{3}}{\frac{3}{4}}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

Divide \frac{16}{3} by \frac{3}{4} by multiplying \frac{16}{3} by the reciprocal of \frac{3}{4}.

$$\frac{16}{3}\times \frac{4}{3}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

Multiply \frac{16}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 4}{3\times 3}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{16\times 4}{3\times 3}.

$$\frac{64}{9}\times 4\times \frac{15}{2}\times \frac{1}{3}$$

Express \frac{64}{9}\times 4 as a single fraction.

$$\frac{64\times 4}{9}\times \frac{15}{2}\times \frac{1}{3}$$

Multiply 64 and 4 to get 256.

$$\frac{256}{9}\times \frac{15}{2}\times \frac{1}{3}$$

Multiply \frac{256}{9} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{256\times 15}{9\times 2}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{256\times 15}{9\times 2}.

$$\frac{3840}{18}\times \frac{1}{3}$$

Reduce the fraction \frac{3840}{18} to lowest terms by extracting and canceling out 6.

$$\frac{640}{3}\times \frac{1}{3}$$

Multiply \frac{640}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{640\times 1}{3\times 3}$$

Do the multiplications in the fraction \frac{640\times 1}{3\times 3}.

$$\frac{640}{9}$$

Factor

$$\frac{2 ^ {7} \cdot 5}{3 ^ {2}} = 71\frac{1}{9} = 71.11111111111111$$