Solve 4/21+3/7/frac{4{7}-5/14}=

$$\frac { \frac { 4 } { 21 } + \frac { 3 } { 7 } } { \frac { 4 } { 7 } - \frac { 5 } { 14 } } =$$

Evaluate

$$\frac{26}{9}\approx 2.888888889$$

Solution Steps

Least common multiple of 21 and 7 is 21. Convert \frac{4}{21} and \frac{3}{7} to fractions with denominator 21.

$$\frac{\frac{4}{21}+\frac{9}{21}}{\frac{4}{7}-\frac{5}{14}}$$

Since \frac{4}{21} and \frac{9}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+9}{21}}{\frac{4}{7}-\frac{5}{14}}$$

Add 4 and 9 to get 13.

$$\frac{\frac{13}{21}}{\frac{4}{7}-\frac{5}{14}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{4}{7} and \frac{5}{14} to fractions with denominator 14.

$$\frac{\frac{13}{21}}{\frac{8}{14}-\frac{5}{14}}$$

Since \frac{8}{14} and \frac{5}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{21}}{\frac{8-5}{14}}$$

Subtract 5 from 8 to get 3.

$$\frac{\frac{13}{21}}{\frac{3}{14}}$$

Divide \frac{13}{21} by \frac{3}{14} by multiplying \frac{13}{21} by the reciprocal of \frac{3}{14}.

$$\frac{13}{21}\times \frac{14}{3}$$

Multiply \frac{13}{21} times \frac{14}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 14}{21\times 3}$$

Do the multiplications in the fraction \frac{13\times 14}{21\times 3}.

$$\frac{182}{63}$$

Reduce the fraction \frac{182}{63} to lowest terms by extracting and canceling out 7.

$$\frac{26}{9}$$

Factor

$$\frac{2 \cdot 13}{3 ^ {2}} = 2\frac{8}{9} = 2.888888888888889$$