Solve ((5/8*16/25)-1/10)div(7/15+frac{9}{20})

$$(( \frac{ 5 }{ 8 } \times \frac{ 16 }{ 25 } )- \frac{ 1 }{ 10 } ) \div ( \frac{ 7 }{ 15 } + \frac{ 9 }{ 20 } )$$

Evaluate

$$\frac{18}{55}\approx 0.327272727$$

Solution Steps

Multiply \frac{5}{8} times \frac{16}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 16}{8\times 25}-\frac{1}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Do the multiplications in the fraction \frac{5\times 16}{8\times 25}.

$$\frac{\frac{80}{200}-\frac{1}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Reduce the fraction \frac{80}{200} to lowest terms by extracting and canceling out 40.

$$\frac{\frac{2}{5}-\frac{1}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{4}{10}-\frac{1}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Since \frac{4}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{10}}{\frac{7}{15}+\frac{9}{20}}$$

Least common multiple of 15 and 20 is 60. Convert \frac{7}{15} and \frac{9}{20} to fractions with denominator 60.

$$\frac{\frac{3}{10}}{\frac{28}{60}+\frac{27}{60}}$$

Since \frac{28}{60} and \frac{27}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{10}}{\frac{28+27}{60}}$$

Add 28 and 27 to get 55.

$$\frac{\frac{3}{10}}{\frac{55}{60}}$$

Reduce the fraction \frac{55}{60} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3}{10}}{\frac{11}{12}}$$

Divide \frac{3}{10} by \frac{11}{12} by multiplying \frac{3}{10} by the reciprocal of \frac{11}{12}.

$$\frac{3}{10}\times \frac{12}{11}$$

Multiply \frac{3}{10} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 12}{10\times 11}$$

Do the multiplications in the fraction \frac{3\times 12}{10\times 11}.

$$\frac{36}{110}$$

Reduce the fraction \frac{36}{110} to lowest terms by extracting and canceling out 2.

$$\frac{18}{55}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5 \cdot 11} = 0.32727272727272727$$