Solve 1/2-2/7/frac{1{10}+1/5}

$$\frac{ \frac{ 1 }{ 2 } - \frac{ 2 }{ 7 } }{ \frac{ 1 }{ 10 } + \frac{ 1 }{ 5 } }$$

Evaluate

$$\frac{5}{7}\approx 0.714285714$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{2}{7} to fractions with denominator 14.

$$\frac{\frac{7}{14}-\frac{4}{14}}{\frac{1}{10}+\frac{1}{5}}$$

Since \frac{7}{14} and \frac{4}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-4}{14}}{\frac{1}{10}+\frac{1}{5}}$$

Subtract 4 from 7 to get 3.

$$\frac{\frac{3}{14}}{\frac{1}{10}+\frac{1}{5}}$$

Least common multiple of 10 and 5 is 10. Convert \frac{1}{10} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{3}{14}}{\frac{1}{10}+\frac{2}{10}}$$

Since \frac{1}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{14}}{\frac{1+2}{10}}$$

Add 1 and 2 to get 3.

$$\frac{\frac{3}{14}}{\frac{3}{10}}$$

Divide \frac{3}{14} by \frac{3}{10} by multiplying \frac{3}{14} by the reciprocal of \frac{3}{10}.

$$\frac{3}{14}\times \frac{10}{3}$$

Multiply \frac{3}{14} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{14\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{10}{14}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{7}$$

Factor

$$\frac{5}{7} = 0.7142857142857143$$