Solve left(9/4-3/2right)left(7/9+2/6right)-frac{4}{3}=

$$\left( \frac{ 9 }{ 4 } - \frac{ 3 }{ 2 } \right) \left( \frac{ 7 }{ 9 } + \frac{ 2 }{ 6 } \right) - \frac{ 4 }{ 3 } =$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{3}{2} to fractions with denominator 4.

$$\left(\frac{9}{4}-\frac{6}{4}\right)\left(\frac{7}{9}+\frac{2}{6}\right)-\frac{4}{3}$$

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

$$\frac{9-6}{4}\left(\frac{7}{9}+\frac{2}{6}\right)-\frac{4}{3}$$

Subtract 6 from 9 to get 3.

$$\frac{3}{4}\left(\frac{7}{9}+\frac{2}{6}\right)-\frac{4}{3}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 9 and 3 is 9. Convert \frac{7}{9} and \frac{1}{3} to fractions with denominator 9.

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

Since \frac{7}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\times \frac{7+3}{9}-\frac{4}{3}$$

Add 7 and 3 to get 10.

$$\frac{3}{4}\times \frac{10}{9}-\frac{4}{3}$$

Multiply \frac{3}{4} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{4\times 9}-\frac{4}{3}$$

Do the multiplications in the fraction \frac{3\times 10}{4\times 9}.

$$\frac{30}{36}-\frac{4}{3}$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{5}{6}-\frac{4}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{4}{3} to fractions with denominator 6.

$$\frac{5}{6}-\frac{8}{6}$$

Since \frac{5}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-8}{6}$$

Subtract 8 from 5 to get -3.

$$\frac{-3}{6}$$

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

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

Factor

$$-\frac{1}{2} = -0.5$$