Solve 1/2:1/3-33/4*2/5*(frac{5}{6}-frac{4}{9})=

$$\frac { 1 } { 2 } : \frac { 1 } { 3 } - 3 \frac { 3 } { 4 } \cdot \frac { 2 } { 5 } \cdot ( \frac { 5 } { 6 } - \frac { 4 } { 9 } ) =$$

Evaluate

$$\frac{11}{12}\approx 0.916666667$$

Solution Steps

Divide \frac{1}{2} by \frac{1}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{3}.

$$\frac{1}{2}\times 3-\frac{3\times 4+3}{4}\times \frac{2}{5}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{3}{2}-\frac{3\times 4+3}{4}\times \frac{2}{5}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Multiply 3 and 4 to get 12.

$$\frac{3}{2}-\frac{12+3}{4}\times \frac{2}{5}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Add 12 and 3 to get 15.

$$\frac{3}{2}-\frac{15}{4}\times \frac{2}{5}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Multiply \frac{15}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}-\frac{15\times 2}{4\times 5}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Do the multiplications in the fraction \frac{15\times 2}{4\times 5}.

$$\frac{3}{2}-\frac{30}{20}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Reduce the fraction \frac{30}{20} to lowest terms by extracting and canceling out 10.

$$\frac{3}{2}-\frac{3}{2}\left(\frac{5}{6}-\frac{4}{9}\right)$$

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{4}{9} to fractions with denominator 18.

$$\frac{3}{2}-\frac{3}{2}\left(\frac{15}{18}-\frac{8}{18}\right)$$

Since \frac{15}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{3}{2}\times \frac{15-8}{18}$$

Subtract 8 from 15 to get 7.

$$\frac{3}{2}-\frac{3}{2}\times \frac{7}{18}$$

Multiply \frac{3}{2} times \frac{7}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}-\frac{3\times 7}{2\times 18}$$

Do the multiplications in the fraction \frac{3\times 7}{2\times 18}.

$$\frac{3}{2}-\frac{21}{36}$$

Reduce the fraction \frac{21}{36} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}-\frac{7}{12}$$

Least common multiple of 2 and 12 is 12. Convert \frac{3}{2} and \frac{7}{12} to fractions with denominator 12.

$$\frac{18}{12}-\frac{7}{12}$$

Since \frac{18}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-7}{12}$$

Subtract 7 from 18 to get 11.

$$\frac{11}{12}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3} = 0.9166666666666666$$