Solve 20/50left(11.8+0.2*45right)+10/5011.8+0.2*55

$$\frac{ 20 }{ 50 } \left( 11.8+0.2 \cdot 45 \right) + \frac{ 10 }{ 50 } 11.8+0.2 \cdot 55$$

Evaluate

$$21.68$$

Solution Steps

Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.

$$\frac{2}{5}\left(11.8+0.2\times 45\right)+\frac{10}{50}\times 11.8+0.2\times 55$$

Multiply 0.2 and 45 to get 9.

$$\frac{2}{5}\left(11.8+9\right)+\frac{10}{50}\times 11.8+0.2\times 55$$

Add 11.8 and 9 to get 20.8.

$$\frac{2}{5}\times 20.8+\frac{10}{50}\times 11.8+0.2\times 55$$

Convert decimal number 20.8 to fraction \frac{208}{10}. Reduce the fraction \frac{208}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}\times \frac{104}{5}+\frac{10}{50}\times 11.8+0.2\times 55$$

Multiply \frac{2}{5} times \frac{104}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 104}{5\times 5}+\frac{10}{50}\times 11.8+0.2\times 55$$

Do the multiplications in the fraction \frac{2\times 104}{5\times 5}.

$$\frac{208}{25}+\frac{10}{50}\times 11.8+0.2\times 55$$

Reduce the fraction \frac{10}{50} to lowest terms by extracting and canceling out 10.

$$\frac{208}{25}+\frac{1}{5}\times 11.8+0.2\times 55$$

Convert decimal number 11.8 to fraction \frac{118}{10}. Reduce the fraction \frac{118}{10} to lowest terms by extracting and canceling out 2.

$$\frac{208}{25}+\frac{1}{5}\times \frac{59}{5}+0.2\times 55$$

Multiply \frac{1}{5} times \frac{59}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{208}{25}+\frac{1\times 59}{5\times 5}+0.2\times 55$$

Do the multiplications in the fraction \frac{1\times 59}{5\times 5}.

$$\frac{208}{25}+\frac{59}{25}+0.2\times 55$$

Since \frac{208}{25} and \frac{59}{25} have the same denominator, add them by adding their numerators.

$$\frac{208+59}{25}+0.2\times 55$$

Add 208 and 59 to get 267.

$$\frac{267}{25}+0.2\times 55$$

Multiply 0.2 and 55 to get 11.

$$\frac{267}{25}+11$$

Convert 11 to fraction \frac{275}{25}.

$$\frac{267}{25}+\frac{275}{25}$$

Since \frac{267}{25} and \frac{275}{25} have the same denominator, add them by adding their numerators.

$$\frac{267+275}{25}$$

Add 267 and 275 to get 542.

$$\frac{542}{25}$$

Factor

$$\frac{2 \cdot 271}{5 ^ {2}} = 21\frac{17}{25} = 21.68$$