Solve 2/5+3/4+63/16-frac{12/5*frac{3}{4}*frac{63}{16}}{1-frac{12}{5}-frac{3}{4}-frac{3}{4}*frac{63}{16}-frac{12}{5}*frac{63}{16}}

$$\frac { \frac { 2 } { 5 } + \frac { 3 } { 4 } + \frac { 63 } { 16 } - \frac { 12 } { 5 } \cdot \frac { 3 } { 4 } \cdot \frac { 63 } { 16 } } { 1 - \frac { 12 } { 5 } - \frac { 3 } { 4 } - \frac { 3 } { 4 } \cdot \frac { 63 } { 16 } - \frac { 12 } { 5 } \cdot \frac { 63 } { 16 } }$$

Evaluate

$$\frac{640}{4657}\approx 0.137427528$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{\frac{8}{20}+\frac{15}{20}+\frac{63}{16}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Since \frac{8}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+15}{20}+\frac{63}{16}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Add 8 and 15 to get 23.

$$\frac{\frac{23}{20}+\frac{63}{16}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Least common multiple of 20 and 16 is 80. Convert \frac{23}{20} and \frac{63}{16} to fractions with denominator 80.

$$\frac{\frac{92}{80}+\frac{315}{80}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Since \frac{92}{80} and \frac{315}{80} have the same denominator, add them by adding their numerators.

$$\frac{\frac{92+315}{80}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Add 92 and 315 to get 407.

$$\frac{\frac{407}{80}-\frac{12}{5}\times \frac{3}{4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Multiply \frac{12}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{407}{80}-\frac{12\times 3}{5\times 4}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Do the multiplications in the fraction \frac{12\times 3}{5\times 4}.

$$\frac{\frac{407}{80}-\frac{36}{20}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Reduce the fraction \frac{36}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{407}{80}-\frac{9}{5}\times \frac{63}{16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Multiply \frac{9}{5} times \frac{63}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{407}{80}-\frac{9\times 63}{5\times 16}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Do the multiplications in the fraction \frac{9\times 63}{5\times 16}.

$$\frac{\frac{407}{80}-\frac{567}{80}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Since \frac{407}{80} and \frac{567}{80} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{407-567}{80}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Subtract 567 from 407 to get -160.

$$\frac{\frac{-160}{80}}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Divide -160 by 80 to get -2.

$$\frac{-2}{1-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{-2}{\frac{5}{5}-\frac{12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Since \frac{5}{5} and \frac{12}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{5-12}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Subtract 12 from 5 to get -7.

$$\frac{-2}{-\frac{7}{5}-\frac{3}{4}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Least common multiple of 5 and 4 is 20. Convert -\frac{7}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{-2}{-\frac{28}{20}-\frac{15}{20}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Since -\frac{28}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{-28-15}{20}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Subtract 15 from -28 to get -43.

$$\frac{-2}{-\frac{43}{20}-\frac{3}{4}\times \frac{63}{16}-\frac{12}{5}\times \frac{63}{16}}$$

Multiply \frac{3}{4} times \frac{63}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2}{-\frac{43}{20}-\frac{3\times 63}{4\times 16}-\frac{12}{5}\times \frac{63}{16}}$$

Do the multiplications in the fraction \frac{3\times 63}{4\times 16}.

$$\frac{-2}{-\frac{43}{20}-\frac{189}{64}-\frac{12}{5}\times \frac{63}{16}}$$

Least common multiple of 20 and 64 is 320. Convert -\frac{43}{20} and \frac{189}{64} to fractions with denominator 320.

$$\frac{-2}{-\frac{688}{320}-\frac{945}{320}-\frac{12}{5}\times \frac{63}{16}}$$

Since -\frac{688}{320} and \frac{945}{320} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{-688-945}{320}-\frac{12}{5}\times \frac{63}{16}}$$

Subtract 945 from -688 to get -1633.

$$\frac{-2}{-\frac{1633}{320}-\frac{12}{5}\times \frac{63}{16}}$$

Multiply \frac{12}{5} times \frac{63}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2}{-\frac{1633}{320}-\frac{12\times 63}{5\times 16}}$$

Do the multiplications in the fraction \frac{12\times 63}{5\times 16}.

$$\frac{-2}{-\frac{1633}{320}-\frac{756}{80}}$$

Reduce the fraction \frac{756}{80} to lowest terms by extracting and canceling out 4.

$$\frac{-2}{-\frac{1633}{320}-\frac{189}{20}}$$

Least common multiple of 320 and 20 is 320. Convert -\frac{1633}{320} and \frac{189}{20} to fractions with denominator 320.

$$\frac{-2}{-\frac{1633}{320}-\frac{3024}{320}}$$

Since -\frac{1633}{320} and \frac{3024}{320} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{-1633-3024}{320}}$$

Subtract 3024 from -1633 to get -4657.

$$\frac{-2}{-\frac{4657}{320}}$$

Divide -2 by -\frac{4657}{320} by multiplying -2 by the reciprocal of -\frac{4657}{320}.

$$-2\left(-\frac{320}{4657}\right)$$

Express -2\left(-\frac{320}{4657}\right) as a single fraction.

$$\frac{-2\left(-320\right)}{4657}$$

Multiply -2 and -320 to get 640.

$$\frac{640}{4657}$$

Factor

$$\frac{2 ^ {7} \cdot 5}{4657} = 0.137427528451793$$