Solve 5/6div31/4div13/30

$$\frac { 5 } { 6 } \div 3 \frac { 1 } { 4 } \div 1 \frac { 3 } { 30 }$$

Evaluate

$$\frac{100}{429}\approx 0.233100233$$

Solution Steps

Divide \frac{\frac{5}{6}}{\frac{3\times 4+1}{4}} by \frac{1\times 30+3}{30} by multiplying \frac{\frac{5}{6}}{\frac{3\times 4+1}{4}} by the reciprocal of \frac{1\times 30+3}{30}.

$$\frac{\frac{5}{6}\times 30}{\frac{3\times 4+1}{4}\left(1\times 30+3\right)}$$

Express \frac{5}{6}\times 30 as a single fraction.

$$\frac{\frac{5\times 30}{6}}{\frac{3\times 4+1}{4}\left(1\times 30+3\right)}$$

Multiply 5 and 30 to get 150.

$$\frac{\frac{150}{6}}{\frac{3\times 4+1}{4}\left(1\times 30+3\right)}$$

Divide 150 by 6 to get 25.

$$\frac{25}{\frac{3\times 4+1}{4}\left(1\times 30+3\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{25}{\frac{12+1}{4}\left(1\times 30+3\right)}$$

Add 12 and 1 to get 13.

$$\frac{25}{\frac{13}{4}\left(1\times 30+3\right)}$$

Multiply 1 and 30 to get 30.

$$\frac{25}{\frac{13}{4}\left(30+3\right)}$$

Add 30 and 3 to get 33.

$$\frac{25}{\frac{13}{4}\times 33}$$

Express \frac{13}{4}\times 33 as a single fraction.

$$\frac{25}{\frac{13\times 33}{4}}$$

Multiply 13 and 33 to get 429.

$$\frac{25}{\frac{429}{4}}$$

Divide 25 by \frac{429}{4} by multiplying 25 by the reciprocal of \frac{429}{4}.

$$25\times \frac{4}{429}$$

Express 25\times \frac{4}{429} as a single fraction.

$$\frac{25\times 4}{429}$$

Multiply 25 and 4 to get 100.

$$\frac{100}{429}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 \cdot 11 \cdot 13} = 0.2331002331002331$$