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

$$\frac { 20 } { 50 } \times ( 11.8 + 0.2 \times 45 ) + \frac { 10 } { 50 } \times ( 11.8 \times 0.2 \times 55 )$$

Evaluate

$$34.28$$

Solution Steps

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

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

Multiply 0.2 and 45 to get 9.

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

Add 11.8 and 9 to get 20.8.

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

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.

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

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

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

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

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

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

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

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.

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

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

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

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

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

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{59}{25} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{59\times 1}{25\times 5}.

$$\frac{208}{25}+\frac{59}{125}\times 55$$

Express \frac{59}{125}\times 55 as a single fraction.

$$\frac{208}{25}+\frac{59\times 55}{125}$$

Multiply 59 and 55 to get 3245.

$$\frac{208}{25}+\frac{3245}{125}$$

Reduce the fraction \frac{3245}{125} to lowest terms by extracting and canceling out 5.

$$\frac{208}{25}+\frac{649}{25}$$

Since \frac{208}{25} and \frac{649}{25} have the same denominator, add them by adding their numerators.

$$\frac{208+649}{25}$$

Add 208 and 649 to get 857.

$$\frac{857}{25}$$

Factor

$$\frac{857}{5 ^ {2}} = 34\frac{7}{25} = 34.28$$