Solve 6.75div3+27/40(67/12-317/36)*(2.5-41/3div0.65)

$$6.75 \div 3+ \frac{ 27 }{ 40 } ( 6 \frac { 7 } { 12 } - 3 \frac { 17 } { 36 } ) \times (2.5- 4 \frac { 1 } { 3 } \div 0.65)$$

Evaluate

$$-6.5$$

Solution Steps

Expand \frac{6.75}{3} by multiplying both numerator and the denominator by 100.

$$\frac{675}{300}+\frac{27}{40}\left(\frac{6\times 12+7}{12}-\frac{3\times 36+17}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Reduce the fraction \frac{675}{300} to lowest terms by extracting and canceling out 75.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{6\times 12+7}{12}-\frac{3\times 36+17}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Multiply 6 and 12 to get 72.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{72+7}{12}-\frac{3\times 36+17}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Add 72 and 7 to get 79.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{79}{12}-\frac{3\times 36+17}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Multiply 3 and 36 to get 108.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{79}{12}-\frac{108+17}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Add 108 and 17 to get 125.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{79}{12}-\frac{125}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Least common multiple of 12 and 36 is 36. Convert \frac{79}{12} and \frac{125}{36} to fractions with denominator 36.

$$\frac{9}{4}+\frac{27}{40}\left(\frac{237}{36}-\frac{125}{36}\right)\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Since \frac{237}{36} and \frac{125}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}+\frac{27}{40}\times \frac{237-125}{36}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Subtract 125 from 237 to get 112.

$$\frac{9}{4}+\frac{27}{40}\times \frac{112}{36}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Reduce the fraction \frac{112}{36} to lowest terms by extracting and canceling out 4.

$$\frac{9}{4}+\frac{27}{40}\times \frac{28}{9}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Multiply \frac{27}{40} times \frac{28}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{4}+\frac{27\times 28}{40\times 9}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Do the multiplications in the fraction \frac{27\times 28}{40\times 9}.

$$\frac{9}{4}+\frac{756}{360}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Reduce the fraction \frac{756}{360} to lowest terms by extracting and canceling out 36.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{\frac{4\times 3+1}{3}}{0.65}\right)$$

Express \frac{\frac{4\times 3+1}{3}}{0.65} as a single fraction.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{4\times 3+1}{3\times 0.65}\right)$$

Multiply 4 and 3 to get 12.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{12+1}{3\times 0.65}\right)$$

Add 12 and 1 to get 13.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{13}{3\times 0.65}\right)$$

Multiply 3 and 0.65 to get 1.95.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{13}{1.95}\right)$$

Expand \frac{13}{1.95} by multiplying both numerator and the denominator by 100.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{1300}{195}\right)$$

Reduce the fraction \frac{1300}{195} to lowest terms by extracting and canceling out 65.

$$\frac{9}{4}+\frac{21}{10}\left(2.5-\frac{20}{3}\right)$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{4}+\frac{21}{10}\left(\frac{5}{2}-\frac{20}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{20}{3} to fractions with denominator 6.

$$\frac{9}{4}+\frac{21}{10}\left(\frac{15}{6}-\frac{40}{6}\right)$$

Since \frac{15}{6} and \frac{40}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}+\frac{21}{10}\times \frac{15-40}{6}$$

Subtract 40 from 15 to get -25.

$$\frac{9}{4}+\frac{21}{10}\left(-\frac{25}{6}\right)$$

Multiply \frac{21}{10} times -\frac{25}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{4}+\frac{21\left(-25\right)}{10\times 6}$$

Do the multiplications in the fraction \frac{21\left(-25\right)}{10\times 6}.

$$\frac{9}{4}+\frac{-525}{60}$$

Reduce the fraction \frac{-525}{60} to lowest terms by extracting and canceling out 15.

$$\frac{9}{4}-\frac{35}{4}$$

Since \frac{9}{4} and \frac{35}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-35}{4}$$

Subtract 35 from 9 to get -26.

$$\frac{-26}{4}$$

Reduce the fraction \frac{-26}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{2}$$

Factor

$$-6.5$$