Solve 31/12:59/20

$$3 \frac { 1 } { 12 } : 5 \frac { 9 } { 20 }$$

Evaluate

$$\frac{185}{327}\approx 0.565749235$$

Solution Steps

Divide \frac{3\times 12+1}{12} by \frac{5\times 20+9}{20} by multiplying \frac{3\times 12+1}{12} by the reciprocal of \frac{5\times 20+9}{20}.

$$\frac{\left(3\times 12+1\right)\times 20}{12\left(5\times 20+9\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5\left(1+3\times 12\right)}{3\left(9+5\times 20\right)}$$

Multiply 3 and 12 to get 36.

$$\frac{5\left(1+36\right)}{3\left(9+5\times 20\right)}$$

Add 1 and 36 to get 37.

$$\frac{5\times 37}{3\left(9+5\times 20\right)}$$

Multiply 5 and 37 to get 185.

$$\frac{185}{3\left(9+5\times 20\right)}$$

Multiply 5 and 20 to get 100.

$$\frac{185}{3\left(9+100\right)}$$

Add 9 and 100 to get 109.

$$\frac{185}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{185}{327}$$

Factor

$$\frac{5 \cdot 37}{3 \cdot 109} = 0.5657492354740061$$