Solve 7/4-9/8+3/5-frac{7/10-frac{3}{2}}{frac{15}{16}*frac{4}{9}*frac{25}{21}*frac{28}{5}}

$$\frac { \frac { 7 } { 4 } - \frac { 9 } { 8 } + \frac { 3 } { 5 } - \frac { 7 } { 10 } - \frac { 3 } { 2 } } { \frac { 15 } { 16 } \cdot \frac { 4 } { 9 } \cdot \frac { 25 } { 21 } \cdot \frac { 28 } { 5 } }$$

Evaluate

$$-\frac{351}{1000}=-0.351$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{9}{8} to fractions with denominator 8.

$$\frac{\frac{14}{8}-\frac{9}{8}+\frac{3}{5}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Since \frac{14}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-9}{8}+\frac{3}{5}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Subtract 9 from 14 to get 5.

$$\frac{\frac{5}{8}+\frac{3}{5}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Least common multiple of 8 and 5 is 40. Convert \frac{5}{8} and \frac{3}{5} to fractions with denominator 40.

$$\frac{\frac{25}{40}+\frac{24}{40}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Since \frac{25}{40} and \frac{24}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+24}{40}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Add 25 and 24 to get 49.

$$\frac{\frac{49}{40}-\frac{7}{10}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Least common multiple of 40 and 10 is 40. Convert \frac{49}{40} and \frac{7}{10} to fractions with denominator 40.

$$\frac{\frac{49}{40}-\frac{28}{40}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Since \frac{49}{40} and \frac{28}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49-28}{40}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Subtract 28 from 49 to get 21.

$$\frac{\frac{21}{40}-\frac{3}{2}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Least common multiple of 40 and 2 is 40. Convert \frac{21}{40} and \frac{3}{2} to fractions with denominator 40.

$$\frac{\frac{21}{40}-\frac{60}{40}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Since \frac{21}{40} and \frac{60}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-60}{40}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Subtract 60 from 21 to get -39.

$$\frac{-\frac{39}{40}}{\frac{15}{16}\times \frac{4}{9}\times \frac{25}{21}\times \frac{28}{5}}$$

Multiply \frac{15}{16} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{39}{40}}{\frac{15\times 4}{16\times 9}\times \frac{25}{21}\times \frac{28}{5}}$$

Do the multiplications in the fraction \frac{15\times 4}{16\times 9}.

$$\frac{-\frac{39}{40}}{\frac{60}{144}\times \frac{25}{21}\times \frac{28}{5}}$$

Reduce the fraction \frac{60}{144} to lowest terms by extracting and canceling out 12.

$$\frac{-\frac{39}{40}}{\frac{5}{12}\times \frac{25}{21}\times \frac{28}{5}}$$

Multiply \frac{5}{12} times \frac{25}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{39}{40}}{\frac{5\times 25}{12\times 21}\times \frac{28}{5}}$$

Do the multiplications in the fraction \frac{5\times 25}{12\times 21}.

$$\frac{-\frac{39}{40}}{\frac{125}{252}\times \frac{28}{5}}$$

Multiply \frac{125}{252} times \frac{28}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{39}{40}}{\frac{125\times 28}{252\times 5}}$$

Do the multiplications in the fraction \frac{125\times 28}{252\times 5}.

$$\frac{-\frac{39}{40}}{\frac{3500}{1260}}$$

Reduce the fraction \frac{3500}{1260} to lowest terms by extracting and canceling out 140.

$$\frac{-\frac{39}{40}}{\frac{25}{9}}$$

Divide -\frac{39}{40} by \frac{25}{9} by multiplying -\frac{39}{40} by the reciprocal of \frac{25}{9}.

$$-\frac{39}{40}\times \frac{9}{25}$$

Multiply -\frac{39}{40} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39\times 9}{40\times 25}$$

Do the multiplications in the fraction \frac{-39\times 9}{40\times 25}.

$$\frac{-351}{1000}$$

Fraction \frac{-351}{1000} can be rewritten as -\frac{351}{1000} by extracting the negative sign.

$$-\frac{351}{1000}$$

Factor

$$-\frac{351}{1000} = -0.351$$