Solve 8/5{5/4+frac{8/3}}

$$\frac{ 8 }{ \frac{ 5 }{ \frac{ 5 }{ 4 } + \frac{ 8 }{ 3 } } }$$

Evaluate

$$\frac{94}{15}\approx 6.266666667$$

Solution Steps

Divide 8 by \frac{5}{\frac{5}{4}+\frac{8}{3}} by multiplying 8 by the reciprocal of \frac{5}{\frac{5}{4}+\frac{8}{3}}.

$$\frac{8\left(\frac{5}{4}+\frac{8}{3}\right)}{5}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{8\left(\frac{15}{12}+\frac{32}{12}\right)}{5}$$

Since \frac{15}{12} and \frac{32}{12} have the same denominator, add them by adding their numerators.

$$\frac{8\times \frac{15+32}{12}}{5}$$

Add 15 and 32 to get 47.

$$\frac{8\times \frac{47}{12}}{5}$$

Express 8\times \frac{47}{12} as a single fraction.

$$\frac{\frac{8\times 47}{12}}{5}$$

Multiply 8 and 47 to get 376.

$$\frac{\frac{376}{12}}{5}$$

Reduce the fraction \frac{376}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{94}{3}}{5}$$

Express \frac{\frac{94}{3}}{5} as a single fraction.

$$\frac{94}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{94}{15}$$

Factor

$$\frac{2 \cdot 47}{3 \cdot 5} = 6\frac{4}{15} = 6.266666666666667$$