Solve 7/20div(13/8div11/27)

$$\frac { 7 } { 20 } \div ( 1 \frac { 3 } { 8 } \div \frac { 11 } { 27 } )$$

Evaluate

$$\frac{14}{135}\approx 0.103703704$$

Solution Steps

Divide \frac{7}{20} by \frac{\frac{1\times 8+3}{8}}{\frac{11}{27}} by multiplying \frac{7}{20} by the reciprocal of \frac{\frac{1\times 8+3}{8}}{\frac{11}{27}}.

$$\frac{7\times \frac{11}{27}}{20\times \frac{1\times 8+3}{8}}$$

Express 7\times \frac{11}{27} as a single fraction.

$$\frac{\frac{7\times 11}{27}}{20\times \frac{1\times 8+3}{8}}$$

Multiply 7 and 11 to get 77.

$$\frac{\frac{77}{27}}{20\times \frac{1\times 8+3}{8}}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{77}{27}}{20\times \frac{8+3}{8}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{77}{27}}{20\times \frac{11}{8}}$$

Express 20\times \frac{11}{8} as a single fraction.

$$\frac{\frac{77}{27}}{\frac{20\times 11}{8}}$$

Multiply 20 and 11 to get 220.

$$\frac{\frac{77}{27}}{\frac{220}{8}}$$

Reduce the fraction \frac{220}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{77}{27}}{\frac{55}{2}}$$

Divide \frac{77}{27} by \frac{55}{2} by multiplying \frac{77}{27} by the reciprocal of \frac{55}{2}.

$$\frac{77}{27}\times \frac{2}{55}$$

Multiply \frac{77}{27} times \frac{2}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{77\times 2}{27\times 55}$$

Do the multiplications in the fraction \frac{77\times 2}{27\times 55}.

$$\frac{154}{1485}$$

Reduce the fraction \frac{154}{1485} to lowest terms by extracting and canceling out 11.

$$\frac{14}{135}$$

Factor

$$\frac{2 \cdot 7}{3 ^ {3} \cdot 5} = 0.1037037037037037$$