Solve (0.04/0.1-0.04/0.3)div(0.3+0.3+0.1)

$$( \frac{ 0.04 }{ 0.1 } - \frac{ 0.04 }{ 0.3 } ) \div (0.3+0.3+0.1)$$

Evaluate

$$\frac{8}{21}\approx 0.380952381$$

Solution Steps

Expand \frac{0.04}{0.1} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{4}{10}-\frac{0.04}{0.3}}{0.3+0.3+0.1}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{5}-\frac{0.04}{0.3}}{0.3+0.3+0.1}$$

Expand \frac{0.04}{0.3} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{2}{5}-\frac{4}{30}}{0.3+0.3+0.1}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{5}-\frac{2}{15}}{0.3+0.3+0.1}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{2}{15} to fractions with denominator 15.

$$\frac{\frac{6}{15}-\frac{2}{15}}{0.3+0.3+0.1}$$

Since \frac{6}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-2}{15}}{0.3+0.3+0.1}$$

Subtract 2 from 6 to get 4.

$$\frac{\frac{4}{15}}{0.3+0.3+0.1}$$

Add 0.3 and 0.3 to get 0.6.

$$\frac{\frac{4}{15}}{0.6+0.1}$$

Add 0.6 and 0.1 to get 0.7.

$$\frac{\frac{4}{15}}{0.7}$$

Express \frac{\frac{4}{15}}{0.7} as a single fraction.

$$\frac{4}{15\times 0.7}$$

Multiply 15 and 0.7 to get 10.5.

$$\frac{4}{10.5}$$

Expand \frac{4}{10.5} by multiplying both numerator and the denominator by 10.

$$\frac{40}{105}$$

Reduce the fraction \frac{40}{105} to lowest terms by extracting and canceling out 5.

$$\frac{8}{21}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 7} = 0.38095238095238093$$