Solve 15/8div(5/12div1/8+3/8)

$$\frac{ 15 }{ 8 } \div ( \frac{ 5 }{ 12 } \div \frac{ 1 }{ 8 } + \frac{ 3 }{ 8 } )$$

Evaluate

$$\frac{45}{89}\approx 0.505617978$$

Solution Steps

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

$$\frac{\frac{15}{8}}{\frac{5}{12}\times 8+\frac{3}{8}}$$

Express \frac{5}{12}\times 8 as a single fraction.

$$\frac{\frac{15}{8}}{\frac{5\times 8}{12}+\frac{3}{8}}$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{15}{8}}{\frac{40}{12}+\frac{3}{8}}$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{15}{8}}{\frac{10}{3}+\frac{3}{8}}$$

Least common multiple of 3 and 8 is 24. Convert \frac{10}{3} and \frac{3}{8} to fractions with denominator 24.

$$\frac{\frac{15}{8}}{\frac{80}{24}+\frac{9}{24}}$$

Since \frac{80}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15}{8}}{\frac{80+9}{24}}$$

Add 80 and 9 to get 89.

$$\frac{\frac{15}{8}}{\frac{89}{24}}$$

Divide \frac{15}{8} by \frac{89}{24} by multiplying \frac{15}{8} by the reciprocal of \frac{89}{24}.

$$\frac{15}{8}\times \frac{24}{89}$$

Multiply \frac{15}{8} times \frac{24}{89} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 24}{8\times 89}$$

Do the multiplications in the fraction \frac{15\times 24}{8\times 89}.

$$\frac{360}{712}$$

Reduce the fraction \frac{360}{712} to lowest terms by extracting and canceling out 8.

$$\frac{45}{89}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{89} = 0.5056179775280899$$