Solve 12/9div22/5

$$1 \frac { 2 } { 9 } \div 2 \frac { 2 } { 5 }$$

Evaluate

$$\frac{55}{108}\approx 0.509259259$$

Solution Steps

Divide \frac{1\times 9+2}{9} by \frac{2\times 5+2}{5} by multiplying \frac{1\times 9+2}{9} by the reciprocal of \frac{2\times 5+2}{5}.

$$\frac{\left(1\times 9+2\right)\times 5}{9\left(2\times 5+2\right)}$$

Multiply 1 and 9 to get 9.

$$\frac{\left(9+2\right)\times 5}{9\left(2\times 5+2\right)}$$

Add 9 and 2 to get 11.

$$\frac{11\times 5}{9\left(2\times 5+2\right)}$$

Multiply 11 and 5 to get 55.

$$\frac{55}{9\left(2\times 5+2\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{55}{9\left(10+2\right)}$$

Add 10 and 2 to get 12.

$$\frac{55}{9\times 12}$$

Multiply 9 and 12 to get 108.

$$\frac{55}{108}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {2} \cdot 3 ^ {3}} = 0.5092592592592593$$