Solve 4/5div[(5/8-1/3)div12]=

$$\frac { 4 } { 5 } \div [ ( \frac { 5 } { 8 } - \frac { 1 } { 3 } ) \div 12 ] =$$

Evaluate

$$\frac{1152}{35}\approx 32.914285714$$

Solution Steps

Divide \frac{4}{5} by \frac{\frac{5}{8}-\frac{1}{3}}{12} by multiplying \frac{4}{5} by the reciprocal of \frac{\frac{5}{8}-\frac{1}{3}}{12}.

$$\frac{4\times 12}{5\left(\frac{5}{8}-\frac{1}{3}\right)}$$

Multiply 4 and 12 to get 48.

$$\frac{48}{5\left(\frac{5}{8}-\frac{1}{3}\right)}$$

Least common multiple of 8 and 3 is 24. Convert \frac{5}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{48}{5\left(\frac{15}{24}-\frac{8}{24}\right)}$$

Since \frac{15}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48}{5\times \frac{15-8}{24}}$$

Subtract 8 from 15 to get 7.

$$\frac{48}{5\times \frac{7}{24}}$$

Express 5\times \frac{7}{24} as a single fraction.

$$\frac{48}{\frac{5\times 7}{24}}$$

Multiply 5 and 7 to get 35.

$$\frac{48}{\frac{35}{24}}$$

Divide 48 by \frac{35}{24} by multiplying 48 by the reciprocal of \frac{35}{24}.

$$48\times \frac{24}{35}$$

Express 48\times \frac{24}{35} as a single fraction.

$$\frac{48\times 24}{35}$$

Multiply 48 and 24 to get 1152.

$$\frac{1152}{35}$$

Factor

$$\frac{2 ^ {7} \cdot 3 ^ {2}}{5 \cdot 7} = 32\frac{32}{35} = 32.91428571428571$$