Solve 8/9div2/3-(5/2+(-3/4)*frac{7}{3}-frac{1}{9})

$$\frac{ 8 }{ 9 } \div \frac{ 2 }{ 3 } -( \frac{ 5 }{ 2 } +(- \frac{ 3 }{ 4 } ) \times \frac{ 7 }{ 3 } - \frac{ 1 }{ 9 } )$$

Evaluate

$$\frac{25}{36}\approx 0.694444444$$

Solution Steps

Divide \frac{8}{9} by \frac{2}{3} by multiplying \frac{8}{9} by the reciprocal of \frac{2}{3}.

$$\frac{8}{9}\times \frac{3}{2}-\left(\frac{5}{2}-\frac{3}{4}\times \frac{7}{3}-\frac{1}{9}\right)$$

Multiply \frac{8}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 3}{9\times 2}-\left(\frac{5}{2}-\frac{3}{4}\times \frac{7}{3}-\frac{1}{9}\right)$$

Do the multiplications in the fraction \frac{8\times 3}{9\times 2}.

$$\frac{24}{18}-\left(\frac{5}{2}-\frac{3}{4}\times \frac{7}{3}-\frac{1}{9}\right)$$

Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

$$\frac{4}{3}-\left(\frac{5}{2}-\frac{3}{4}\times \frac{7}{3}-\frac{1}{9}\right)$$

Multiply -\frac{3}{4} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}-\left(\frac{5}{2}+\frac{-3\times 7}{4\times 3}-\frac{1}{9}\right)$$

Do the multiplications in the fraction \frac{-3\times 7}{4\times 3}.

$$\frac{4}{3}-\left(\frac{5}{2}+\frac{-21}{12}-\frac{1}{9}\right)$$

Reduce the fraction \frac{-21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{4}{3}-\left(\frac{5}{2}-\frac{7}{4}-\frac{1}{9}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{4}{3}-\left(\frac{10}{4}-\frac{7}{4}-\frac{1}{9}\right)$$

Since \frac{10}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}-\left(\frac{10-7}{4}-\frac{1}{9}\right)$$

Subtract 7 from 10 to get 3.

$$\frac{4}{3}-\left(\frac{3}{4}-\frac{1}{9}\right)$$

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{1}{9} to fractions with denominator 36.

$$\frac{4}{3}-\left(\frac{27}{36}-\frac{4}{36}\right)$$

Since \frac{27}{36} and \frac{4}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}-\frac{27-4}{36}$$

Subtract 4 from 27 to get 23.

$$\frac{4}{3}-\frac{23}{36}$$

Least common multiple of 3 and 36 is 36. Convert \frac{4}{3} and \frac{23}{36} to fractions with denominator 36.

$$\frac{48}{36}-\frac{23}{36}$$

Since \frac{48}{36} and \frac{23}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-23}{36}$$

Subtract 23 from 48 to get 25.

$$\frac{25}{36}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3 ^ {2}} = 0.6944444444444444$$