Solve (0.3*1/4)div(0.3*0.25+0.2div3+0.1div12)

$$(0.3 \times \frac{ 1 }{ 4 } ) \div (0.3 \times 0.25+0.2 \div 3+0.1 \div 12)$$

Evaluate

$$0.5$$

Solution Steps

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{\frac{3}{10}\times \frac{1}{4}}{0.3\times 0.25+\frac{0.2}{3}+\frac{0.1}{12}}$$

Multiply \frac{3}{10} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 1}{10\times 4}}{0.3\times 0.25+\frac{0.2}{3}+\frac{0.1}{12}}$$

Do the multiplications in the fraction \frac{3\times 1}{10\times 4}.

$$\frac{\frac{3}{40}}{0.3\times 0.25+\frac{0.2}{3}+\frac{0.1}{12}}$$

Multiply 0.3 and 0.25 to get 0.075.

$$\frac{\frac{3}{40}}{0.075+\frac{0.2}{3}+\frac{0.1}{12}}$$

Expand \frac{0.2}{3} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{3}{40}}{0.075+\frac{2}{30}+\frac{0.1}{12}}$$

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

$$\frac{\frac{3}{40}}{0.075+\frac{1}{15}+\frac{0.1}{12}}$$

Convert decimal number 0.075 to fraction \frac{75}{1000}. Reduce the fraction \frac{75}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{3}{40}}{\frac{3}{40}+\frac{1}{15}+\frac{0.1}{12}}$$

Least common multiple of 40 and 15 is 120. Convert \frac{3}{40} and \frac{1}{15} to fractions with denominator 120.

$$\frac{\frac{3}{40}}{\frac{9}{120}+\frac{8}{120}+\frac{0.1}{12}}$$

Since \frac{9}{120} and \frac{8}{120} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{40}}{\frac{9+8}{120}+\frac{0.1}{12}}$$

Add 9 and 8 to get 17.

$$\frac{\frac{3}{40}}{\frac{17}{120}+\frac{0.1}{12}}$$

Expand \frac{0.1}{12} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{3}{40}}{\frac{17}{120}+\frac{1}{120}}$$

Since \frac{17}{120} and \frac{1}{120} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{40}}{\frac{17+1}{120}}$$

Add 17 and 1 to get 18.

$$\frac{\frac{3}{40}}{\frac{18}{120}}$$

Reduce the fraction \frac{18}{120} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{3}{40}}{\frac{3}{20}}$$

Divide \frac{3}{40} by \frac{3}{20} by multiplying \frac{3}{40} by the reciprocal of \frac{3}{20}.

$$\frac{3}{40}\times \frac{20}{3}$$

Multiply \frac{3}{40} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 20}{40\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{20}{40}$$

Reduce the fraction \frac{20}{40} to lowest terms by extracting and canceling out 20.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$