Solve (17/3-7/4)*3/2+frac{5/4}{(frac{11}{18}+frac{5}{12}+frac{7}{24})*frac{24}{25}}div-(2+frac{5}{2}-frac{3}{4})

$$\frac{ ( \frac{ 17 }{ 3 } - \frac{ 7 }{ 4 } ) \times \frac{ 3 }{ 2 } + \frac{ 5 }{ 4 } }{ ( \frac{ 11 }{ 18 } + \frac{ 5 }{ 12 } + \frac{ 7 }{ 24 } ) \times \frac{ 24 }{ 25 } } \div -(2+ \frac{ 5 }{ 2 } - \frac{ 3 }{ 4 } )$$

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{17}{3} and \frac{7}{4} to fractions with denominator 12.

$$\frac{\frac{\left(\frac{68}{12}-\frac{21}{12}\right)\times \frac{3}{2}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Since \frac{68}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{68-21}{12}\times \frac{3}{2}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Subtract 21 from 68 to get 47.

$$\frac{\frac{\frac{47}{12}\times \frac{3}{2}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Multiply \frac{47}{12} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{47\times 3}{12\times 2}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Do the multiplications in the fraction \frac{47\times 3}{12\times 2}.

$$\frac{\frac{\frac{141}{24}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Reduce the fraction \frac{141}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{\frac{47}{8}+\frac{5}{4}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Least common multiple of 8 and 4 is 8. Convert \frac{47}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{\frac{\frac{47}{8}+\frac{10}{8}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Since \frac{47}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{47+10}{8}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Add 47 and 10 to get 57.

$$\frac{\frac{\frac{57}{8}}{\left(\frac{11}{18}+\frac{5}{12}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Least common multiple of 18 and 12 is 36. Convert \frac{11}{18} and \frac{5}{12} to fractions with denominator 36.

$$\frac{\frac{\frac{57}{8}}{\left(\frac{22}{36}+\frac{15}{36}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Since \frac{22}{36} and \frac{15}{36} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{57}{8}}{\left(\frac{22+15}{36}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Add 22 and 15 to get 37.

$$\frac{\frac{\frac{57}{8}}{\left(\frac{37}{36}+\frac{7}{24}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Least common multiple of 36 and 24 is 72. Convert \frac{37}{36} and \frac{7}{24} to fractions with denominator 72.

$$\frac{\frac{\frac{57}{8}}{\left(\frac{74}{72}+\frac{21}{72}\right)\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Since \frac{74}{72} and \frac{21}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{57}{8}}{\frac{74+21}{72}\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Add 74 and 21 to get 95.

$$\frac{\frac{\frac{57}{8}}{\frac{95}{72}\times \frac{24}{25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Multiply \frac{95}{72} times \frac{24}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{57}{8}}{\frac{95\times 24}{72\times 25}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Do the multiplications in the fraction \frac{95\times 24}{72\times 25}.

$$\frac{\frac{\frac{57}{8}}{\frac{2280}{1800}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Reduce the fraction \frac{2280}{1800} to lowest terms by extracting and canceling out 120.

$$\frac{\frac{\frac{57}{8}}{\frac{19}{15}}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Divide \frac{57}{8} by \frac{19}{15} by multiplying \frac{57}{8} by the reciprocal of \frac{19}{15}.

$$\frac{\frac{57}{8}\times \frac{15}{19}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Multiply \frac{57}{8} times \frac{15}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{57\times 15}{8\times 19}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Do the multiplications in the fraction \frac{57\times 15}{8\times 19}.

$$\frac{\frac{855}{152}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Reduce the fraction \frac{855}{152} to lowest terms by extracting and canceling out 19.

$$\frac{\frac{45}{8}}{-\left(2+\frac{5}{2}-\frac{3}{4}\right)}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{45}{8}}{-\left(\frac{4}{2}+\frac{5}{2}-\frac{3}{4}\right)}$$

Since \frac{4}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{45}{8}}{-\left(\frac{4+5}{2}-\frac{3}{4}\right)}$$

Add 4 and 5 to get 9.

$$\frac{\frac{45}{8}}{-\left(\frac{9}{2}-\frac{3}{4}\right)}$$

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

$$\frac{\frac{45}{8}}{-\left(\frac{18}{4}-\frac{3}{4}\right)}$$

Since \frac{18}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{45}{8}}{-\frac{18-3}{4}}$$

Subtract 3 from 18 to get 15.

$$\frac{\frac{45}{8}}{-\frac{15}{4}}$$

Divide \frac{45}{8} by -\frac{15}{4} by multiplying \frac{45}{8} by the reciprocal of -\frac{15}{4}.

$$\frac{45}{8}\left(-\frac{4}{15}\right)$$

Multiply \frac{45}{8} times -\frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{45\left(-4\right)}{8\times 15}$$

Do the multiplications in the fraction \frac{45\left(-4\right)}{8\times 15}.

$$\frac{-180}{120}$$

Reduce the fraction \frac{-180}{120} to lowest terms by extracting and canceling out 60.

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

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$