Solve 24/9:(2/3-2/7)

$$2 \frac { 4 } { 9 } : ( \frac { 2 } { 3 } - \frac { 2 } { 7 } )$$

Evaluate

$$\frac{77}{12}\approx 6.416666667$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\frac{\frac{18+4}{9}}{\frac{2}{3}-\frac{2}{7}}$$

Add 18 and 4 to get 22.

$$\frac{\frac{22}{9}}{\frac{2}{3}-\frac{2}{7}}$$

Least common multiple of 3 and 7 is 21. Convert \frac{2}{3} and \frac{2}{7} to fractions with denominator 21.

$$\frac{\frac{22}{9}}{\frac{14}{21}-\frac{6}{21}}$$

Since \frac{14}{21} and \frac{6}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{22}{9}}{\frac{14-6}{21}}$$

Subtract 6 from 14 to get 8.

$$\frac{\frac{22}{9}}{\frac{8}{21}}$$

Divide \frac{22}{9} by \frac{8}{21} by multiplying \frac{22}{9} by the reciprocal of \frac{8}{21}.

$$\frac{22}{9}\times \frac{21}{8}$$

Multiply \frac{22}{9} times \frac{21}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 21}{9\times 8}$$

Do the multiplications in the fraction \frac{22\times 21}{9\times 8}.

$$\frac{462}{72}$$

Reduce the fraction \frac{462}{72} to lowest terms by extracting and canceling out 6.

$$\frac{77}{12}$$

Factor

$$\frac{7 \cdot 11}{2 ^ {2} \cdot 3} = 6\frac{5}{12} = 6.416666666666667$$