Solve 14/11:12/13

$$1 \frac { 4 } { 11 } : 1 \frac { 2 } { 13 }$$

Evaluate

$$\frac{13}{11}\approx 1.181818182$$

Solution Steps

Divide \frac{1\times 11+4}{11} by \frac{1\times 13+2}{13} by multiplying \frac{1\times 11+4}{11} by the reciprocal of \frac{1\times 13+2}{13}.

$$\frac{\left(1\times 11+4\right)\times 13}{11\left(1\times 13+2\right)}$$

Multiply 1 and 11 to get 11.

$$\frac{\left(11+4\right)\times 13}{11\left(1\times 13+2\right)}$$

Add 11 and 4 to get 15.

$$\frac{15\times 13}{11\left(1\times 13+2\right)}$$

Multiply 15 and 13 to get 195.

$$\frac{195}{11\left(1\times 13+2\right)}$$

Multiply 1 and 13 to get 13.

$$\frac{195}{11\left(13+2\right)}$$

Add 13 and 2 to get 15.

$$\frac{195}{11\times 15}$$

Multiply 11 and 15 to get 165.

$$\frac{195}{165}$$

Reduce the fraction \frac{195}{165} to lowest terms by extracting and canceling out 15.

$$\frac{13}{11}$$

Factor

$$\frac{13}{11} = 1\frac{2}{11} = 1.1818181818181819$$