Solve 7div31/4div413/20

$$7 \div 3 \frac { 1 } { 4 } \div 4 \frac { 13 } { 20 }$$

Evaluate

$$\frac{560}{1209}\approx 0.463192721$$

Solution Steps

Divide \frac{7}{\frac{3\times 4+1}{4}} by \frac{4\times 20+13}{20} by multiplying \frac{7}{\frac{3\times 4+1}{4}} by the reciprocal of \frac{4\times 20+13}{20}.

$$\frac{7\times 20}{\frac{3\times 4+1}{4}\left(4\times 20+13\right)}$$

Multiply 7 and 20 to get 140.

$$\frac{140}{\frac{3\times 4+1}{4}\left(4\times 20+13\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{140}{\frac{12+1}{4}\left(4\times 20+13\right)}$$

Add 12 and 1 to get 13.

$$\frac{140}{\frac{13}{4}\left(4\times 20+13\right)}$$

Multiply 4 and 20 to get 80.

$$\frac{140}{\frac{13}{4}\left(80+13\right)}$$

Add 80 and 13 to get 93.

$$\frac{140}{\frac{13}{4}\times 93}$$

Express \frac{13}{4}\times 93 as a single fraction.

$$\frac{140}{\frac{13\times 93}{4}}$$

Multiply 13 and 93 to get 1209.

$$\frac{140}{\frac{1209}{4}}$$

Divide 140 by \frac{1209}{4} by multiplying 140 by the reciprocal of \frac{1209}{4}.

$$140\times \frac{4}{1209}$$

Express 140\times \frac{4}{1209} as a single fraction.

$$\frac{140\times 4}{1209}$$

Multiply 140 and 4 to get 560.

$$\frac{560}{1209}$$

Factor

$$\frac{2 ^ {4} \cdot 5 \cdot 7}{3 \cdot 13 \cdot 31} = 0.46319272125723737$$