Solve 2/3-3/2*(2/3-3/2)+frac{1}{3}*(frac{3}{2}-3)=

$$\frac { 2 } { 3 } - \frac { 3 } { 2 } \cdot ( \frac { 2 } { 3 } - \frac { 3 } { 2 } ) + \frac { 1 } { 3 } \cdot ( \frac { 3 } { 2 } - 3 ) =$$

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{3}{2} to fractions with denominator 6.

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

Since \frac{4}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 9 from 4 to get -5.

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

Multiply \frac{3}{2} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\left(-5\right)}{2\times 6}.

$$\frac{2}{3}-\frac{-15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Reduce the fraction \frac{-15}{12} to lowest terms by extracting and canceling out 3.

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

The opposite of -\frac{5}{4} is \frac{5}{4}.

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

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Add 8 and 15 to get 23.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-\frac{6}{2}\right)$$

Since \frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23}{12}+\frac{1}{3}\times \frac{3-6}{2}$$

Subtract 6 from 3 to get -3.

$$\frac{23}{12}+\frac{1}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{1}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23}{12}+\frac{1\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{3\times 2}.

$$\frac{23}{12}+\frac{-3}{6}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{23}{12}-\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{23}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{23}{12}-\frac{6}{12}$$

Since \frac{23}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-6}{12}$$

Subtract 6 from 23 to get 17.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$