Solve 8/3div2/frac{1{2}div3/2}div(4*15/2)divfrac{1}{3}

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

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Divide \frac{\frac{\frac{\frac{8}{3}}{2}}{\frac{\frac{1}{2}}{\frac{3}{2}}}}{4\times \frac{15}{2}} by \frac{1}{3} by multiplying \frac{\frac{\frac{\frac{8}{3}}{2}}{\frac{\frac{1}{2}}{\frac{3}{2}}}}{4\times \frac{15}{2}} by the reciprocal of \frac{1}{3}.

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

Divide \frac{\frac{8}{3}}{2} by \frac{\frac{1}{2}}{\frac{3}{2}} by multiplying \frac{\frac{8}{3}}{2} by the reciprocal of \frac{\frac{1}{2}}{\frac{3}{2}}.

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

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

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

Cancel out 3 in both numerator and denominator.

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

Divide 8 by 2 to get 4.

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

Cancel out 2 and 2.

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

Anything divided by one gives itself.

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

Multiply 4 and 3 to get 12.

$$\frac{12}{4\times \frac{15}{2}}$$

Express 4\times \frac{15}{2} as a single fraction.

$$\frac{12}{\frac{4\times 15}{2}}$$

Multiply 4 and 15 to get 60.

$$\frac{12}{\frac{60}{2}}$$

Divide 60 by 2 to get 30.

$$\frac{12}{30}$$

Reduce the fraction \frac{12}{30} to lowest terms by extracting and canceling out 6.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$