Solve frac{frac{8/3/2/frac{frac{1{2}}{3/2}}}{4-frac{15}{2}}}{frac{1}{3}}

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

Evaluate

$$-\frac{24}{7}\approx -3.428571429$$

Solution Steps

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

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

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}}.

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

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

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

Cancel out 3 in both numerator and denominator.

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

Divide 8 by 2 to get 4.

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

Cancel out 2 and 2.

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

Anything divided by one gives itself.

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

Multiply 4 and 3 to get 12.

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

Convert 4 to fraction \frac{8}{2}.

$$\frac{12}{\frac{8}{2}-\frac{15}{2}}$$

Since \frac{8}{2} and \frac{15}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{\frac{8-15}{2}}$$

Subtract 15 from 8 to get -7.

$$\frac{12}{-\frac{7}{2}}$$

Divide 12 by -\frac{7}{2} by multiplying 12 by the reciprocal of -\frac{7}{2}.

$$12\left(-\frac{2}{7}\right)$$

Express 12\left(-\frac{2}{7}\right) as a single fraction.

$$\frac{12\left(-2\right)}{7}$$

Multiply 12 and -2 to get -24.

$$\frac{-24}{7}$$

Fraction \frac{-24}{7} can be rewritten as -\frac{24}{7} by extracting the negative sign.

$$-\frac{24}{7}$$

Factor

$$-\frac{24}{7} = -3\frac{3}{7} = -3.4285714285714284$$