Solve (2/3-1/8*4/7)div2/7*frac{4}{9}

$$( \frac{ 2 }{ 3 } - \frac{ 1 }{ 8 } \times \frac{ 4 }{ 7 } ) \div \frac{ 2 }{ 7 } \times \frac{ 4 }{ 9 }$$

Evaluate

$$\frac{25}{27}\approx 0.925925926$$

Solution Steps

Multiply \frac{1}{8} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{3}-\frac{1\times 4}{8\times 7}}{\frac{2}{7}}\times \frac{4}{9}$$

Do the multiplications in the fraction \frac{1\times 4}{8\times 7}.

$$\frac{\frac{2}{3}-\frac{4}{56}}{\frac{2}{7}}\times \frac{4}{9}$$

Reduce the fraction \frac{4}{56} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{2}{3}-\frac{1}{14}}{\frac{2}{7}}\times \frac{4}{9}$$

Least common multiple of 3 and 14 is 42. Convert \frac{2}{3} and \frac{1}{14} to fractions with denominator 42.

$$\frac{\frac{28}{42}-\frac{3}{42}}{\frac{2}{7}}\times \frac{4}{9}$$

Since \frac{28}{42} and \frac{3}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{28-3}{42}}{\frac{2}{7}}\times \frac{4}{9}$$

Subtract 3 from 28 to get 25.

$$\frac{\frac{25}{42}}{\frac{2}{7}}\times \frac{4}{9}$$

Divide \frac{25}{42} by \frac{2}{7} by multiplying \frac{25}{42} by the reciprocal of \frac{2}{7}.

$$\frac{25}{42}\times \frac{7}{2}\times \frac{4}{9}$$

Multiply \frac{25}{42} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 7}{42\times 2}\times \frac{4}{9}$$

Do the multiplications in the fraction \frac{25\times 7}{42\times 2}.

$$\frac{175}{84}\times \frac{4}{9}$$

Reduce the fraction \frac{175}{84} to lowest terms by extracting and canceling out 7.

$$\frac{25}{12}\times \frac{4}{9}$$

Multiply \frac{25}{12} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 4}{12\times 9}$$

Do the multiplications in the fraction \frac{25\times 4}{12\times 9}.

$$\frac{100}{108}$$

Reduce the fraction \frac{100}{108} to lowest terms by extracting and canceling out 4.

$$\frac{25}{27}$$

Factor

$$\frac{5 ^ {2}}{3 ^ {3}} = 0.9259259259259259$$