Solve 0.2/0.2*0.2+0.3*2div3+0.4*0.6

$$\frac{ 0.2 }{ 0.2 \times 0.2+0.3 \times 2 \div 3+0.4 \times 0.6 }$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Multiply 0.2 and 0.2 to get 0.04.

$$\frac{0.2}{0.04+\frac{0.3\times 2}{3}+0.4\times 0.6}$$

Multiply 0.3 and 2 to get 0.6.

$$\frac{0.2}{0.04+\frac{0.6}{3}+0.4\times 0.6}$$

Expand \frac{0.6}{3} by multiplying both numerator and the denominator by 10.

$$\frac{0.2}{0.04+\frac{6}{30}+0.4\times 0.6}$$

Reduce the fraction \frac{6}{30} to lowest terms by extracting and canceling out 6.

$$\frac{0.2}{0.04+\frac{1}{5}+0.4\times 0.6}$$

Convert decimal number 0.04 to fraction \frac{4}{100}. Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{0.2}{\frac{1}{25}+\frac{1}{5}+0.4\times 0.6}$$

Least common multiple of 25 and 5 is 25. Convert \frac{1}{25} and \frac{1}{5} to fractions with denominator 25.

$$\frac{0.2}{\frac{1}{25}+\frac{5}{25}+0.4\times 0.6}$$

Since \frac{1}{25} and \frac{5}{25} have the same denominator, add them by adding their numerators.

$$\frac{0.2}{\frac{1+5}{25}+0.4\times 0.6}$$

Add 1 and 5 to get 6.

$$\frac{0.2}{\frac{6}{25}+0.4\times 0.6}$$

Multiply 0.4 and 0.6 to get 0.24.

$$\frac{0.2}{\frac{6}{25}+0.24}$$

Convert decimal number 0.24 to fraction \frac{24}{100}. Reduce the fraction \frac{24}{100} to lowest terms by extracting and canceling out 4.

$$\frac{0.2}{\frac{6}{25}+\frac{6}{25}}$$

Since \frac{6}{25} and \frac{6}{25} have the same denominator, add them by adding their numerators.

$$\frac{0.2}{\frac{6+6}{25}}$$

Add 6 and 6 to get 12.

$$\frac{0.2}{\frac{12}{25}}$$

Divide 0.2 by \frac{12}{25} by multiplying 0.2 by the reciprocal of \frac{12}{25}.

$$0.2\times \frac{25}{12}$$

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.

$$\frac{1}{5}\times \frac{25}{12}$$

Multiply \frac{1}{5} times \frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 25}{5\times 12}$$

Do the multiplications in the fraction \frac{1\times 25}{5\times 12}.

$$\frac{25}{60}$$

Reduce the fraction \frac{25}{60} to lowest terms by extracting and canceling out 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{3 \cdot 2 ^ {2}} = 0.4166666666666667$$