Solve 10.8*(2/3-3/4+7/9)

$$10.8 \times ( \frac { 2 } { 3 } - \frac { 3 } { 4 } + \frac { 7 } { 9 } )$$

Evaluate

$$7.5$$

Solution Steps

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

$$10.8\left(\frac{8}{12}-\frac{9}{12}+\frac{7}{9}\right)$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$10.8\left(\frac{8-9}{12}+\frac{7}{9}\right)$$

Subtract 9 from 8 to get -1.

$$10.8\left(-\frac{1}{12}+\frac{7}{9}\right)$$

Least common multiple of 12 and 9 is 36. Convert -\frac{1}{12} and \frac{7}{9} to fractions with denominator 36.

$$10.8\left(-\frac{3}{36}+\frac{28}{36}\right)$$

Since -\frac{3}{36} and \frac{28}{36} have the same denominator, add them by adding their numerators.

$$10.8\times \frac{-3+28}{36}$$

Add -3 and 28 to get 25.

$$10.8\times \frac{25}{36}$$

Convert decimal number 10.8 to fraction \frac{108}{10}. Reduce the fraction \frac{108}{10} to lowest terms by extracting and canceling out 2.

$$\frac{54}{5}\times \frac{25}{36}$$

Multiply \frac{54}{5} times \frac{25}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{54\times 25}{5\times 36}$$

Do the multiplications in the fraction \frac{54\times 25}{5\times 36}.

$$\frac{1350}{180}$$

Reduce the fraction \frac{1350}{180} to lowest terms by extracting and canceling out 90.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$