Solve 1/frac{1{24}+0.25/30+1/10}

$$\frac{ 1 }{ \frac{ 1 }{ 24 } + \frac{ 0.25 }{ 30 } + \frac{ 1 }{ 10 } }$$

Evaluate

$$\frac{20}{3}\approx 6.666666667$$

Solution Steps

Expand \frac{0.25}{30} by multiplying both numerator and the denominator by 100.

$$\frac{1}{\frac{1}{24}+\frac{25}{3000}+\frac{1}{10}}$$

Reduce the fraction \frac{25}{3000} to lowest terms by extracting and canceling out 25.

$$\frac{1}{\frac{1}{24}+\frac{1}{120}+\frac{1}{10}}$$

Least common multiple of 24 and 120 is 120. Convert \frac{1}{24} and \frac{1}{120} to fractions with denominator 120.

$$\frac{1}{\frac{5}{120}+\frac{1}{120}+\frac{1}{10}}$$

Since \frac{5}{120} and \frac{1}{120} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{5+1}{120}+\frac{1}{10}}$$

Add 5 and 1 to get 6.

$$\frac{1}{\frac{6}{120}+\frac{1}{10}}$$

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

$$\frac{1}{\frac{1}{20}+\frac{1}{10}}$$

Least common multiple of 20 and 10 is 20. Convert \frac{1}{20} and \frac{1}{10} to fractions with denominator 20.

$$\frac{1}{\frac{1}{20}+\frac{2}{20}}$$

Since \frac{1}{20} and \frac{2}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1+2}{20}}$$

Add 1 and 2 to get 3.

$$\frac{1}{\frac{3}{20}}$$

Divide 1 by \frac{3}{20} by multiplying 1 by the reciprocal of \frac{3}{20}.

$$1\times \frac{20}{3}$$

Multiply 1 and \frac{20}{3} to get \frac{20}{3}.

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

Factor

$$\frac{5 \cdot 2 ^ {2}}{3} = 6\frac{2}{3} = 6.666666666666667$$