Solve 51/9:15/10

$$5 \frac { 1 } { 9 } : 1 \frac { 5 } { 10 }$$

Evaluate

$$\frac{92}{27}\approx 3.407407407$$

Solution Steps

Divide \frac{5\times 9+1}{9} by \frac{1\times 10+5}{10} by multiplying \frac{5\times 9+1}{9} by the reciprocal of \frac{1\times 10+5}{10}.

$$\frac{\left(5\times 9+1\right)\times 10}{9\left(1\times 10+5\right)}$$

Multiply 5 and 9 to get 45.

$$\frac{\left(45+1\right)\times 10}{9\left(1\times 10+5\right)}$$

Add 45 and 1 to get 46.

$$\frac{46\times 10}{9\left(1\times 10+5\right)}$$

Multiply 46 and 10 to get 460.

$$\frac{460}{9\left(1\times 10+5\right)}$$

Multiply 1 and 10 to get 10.

$$\frac{460}{9\left(10+5\right)}$$

Add 10 and 5 to get 15.

$$\frac{460}{9\times 15}$$

Multiply 9 and 15 to get 135.

$$\frac{460}{135}$$

Reduce the fraction \frac{460}{135} to lowest terms by extracting and canceling out 5.

$$\frac{92}{27}$$

Factor

$$\frac{2 ^ {2} \cdot 23}{3 ^ {3}} = 3\frac{11}{27} = 3.4074074074074074$$