Solve 2/5+3/10/frac{6{7}-1/14}=

$$\frac { \frac { 2 } { 5 } + \frac { 3 } { 10 } } { \frac { 6 } { 7 } - \frac { 1 } { 14 } } =$$

Evaluate

$$\frac{49}{55}\approx 0.890909091$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{4}{10}+\frac{3}{10}}{\frac{6}{7}-\frac{1}{14}}$$

Since \frac{4}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+3}{10}}{\frac{6}{7}-\frac{1}{14}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{10}}{\frac{6}{7}-\frac{1}{14}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{6}{7} and \frac{1}{14} to fractions with denominator 14.

$$\frac{\frac{7}{10}}{\frac{12}{14}-\frac{1}{14}}$$

Since \frac{12}{14} and \frac{1}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{10}}{\frac{12-1}{14}}$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{7}{10}}{\frac{11}{14}}$$

Divide \frac{7}{10} by \frac{11}{14} by multiplying \frac{7}{10} by the reciprocal of \frac{11}{14}.

$$\frac{7}{10}\times \frac{14}{11}$$

Multiply \frac{7}{10} times \frac{14}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 14}{10\times 11}$$

Do the multiplications in the fraction \frac{7\times 14}{10\times 11}.

$$\frac{98}{110}$$

Reduce the fraction \frac{98}{110} to lowest terms by extracting and canceling out 2.

$$\frac{49}{55}$$

Factor

$$\frac{7 ^ {2}}{5 \cdot 11} = 0.8909090909090909$$