Solve ((5/3-3/7)*9/4)div(1/3+frac{3}{5}-frac{1}{2})divfrac{3}{10}

$$(( \frac{ 5 }{ 3 } - \frac{ 3 }{ 7 } ) \times \frac{ 9 }{ 4 } ) \div ( \frac{ 1 }{ 3 } + \frac{ 3 }{ 5 } - \frac{ 1 }{ 2 } ) \div \frac{ 3 }{ 10 }$$

Evaluate

$$\frac{150}{7}\approx 21.428571429$$

Solution Steps

Divide \frac{\left(\frac{5}{3}-\frac{3}{7}\right)\times \frac{9}{4}}{\frac{1}{3}+\frac{3}{5}-\frac{1}{2}} by \frac{3}{10} by multiplying \frac{\left(\frac{5}{3}-\frac{3}{7}\right)\times \frac{9}{4}}{\frac{1}{3}+\frac{3}{5}-\frac{1}{2}} by the reciprocal of \frac{3}{10}.

$$\frac{\left(\frac{5}{3}-\frac{3}{7}\right)\times \frac{9}{4}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Least common multiple of 3 and 7 is 21. Convert \frac{5}{3} and \frac{3}{7} to fractions with denominator 21.

$$\frac{\left(\frac{35}{21}-\frac{9}{21}\right)\times \frac{9}{4}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Since \frac{35}{21} and \frac{9}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35-9}{21}\times \frac{9}{4}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Subtract 9 from 35 to get 26.

$$\frac{\frac{26}{21}\times \frac{9}{4}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Multiply \frac{26}{21} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{26\times 9}{21\times 4}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Do the multiplications in the fraction \frac{26\times 9}{21\times 4}.

$$\frac{\frac{234}{84}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Reduce the fraction \frac{234}{84} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{39}{14}\times 10}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Express \frac{39}{14}\times 10 as a single fraction.

$$\frac{\frac{39\times 10}{14}}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Multiply 39 and 10 to get 390.

$$\frac{\frac{390}{14}}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Reduce the fraction \frac{390}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{195}{7}}{\left(\frac{1}{3}+\frac{3}{5}-\frac{1}{2}\right)\times 3}$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\frac{195}{7}}{\left(\frac{5}{15}+\frac{9}{15}-\frac{1}{2}\right)\times 3}$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{195}{7}}{\left(\frac{5+9}{15}-\frac{1}{2}\right)\times 3}$$

Add 5 and 9 to get 14.

$$\frac{\frac{195}{7}}{\left(\frac{14}{15}-\frac{1}{2}\right)\times 3}$$

Least common multiple of 15 and 2 is 30. Convert \frac{14}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{\frac{195}{7}}{\left(\frac{28}{30}-\frac{15}{30}\right)\times 3}$$

Since \frac{28}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{195}{7}}{\frac{28-15}{30}\times 3}$$

Subtract 15 from 28 to get 13.

$$\frac{\frac{195}{7}}{\frac{13}{30}\times 3}$$

Express \frac{13}{30}\times 3 as a single fraction.

$$\frac{\frac{195}{7}}{\frac{13\times 3}{30}}$$

Multiply 13 and 3 to get 39.

$$\frac{\frac{195}{7}}{\frac{39}{30}}$$

Reduce the fraction \frac{39}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{195}{7}}{\frac{13}{10}}$$

Divide \frac{195}{7} by \frac{13}{10} by multiplying \frac{195}{7} by the reciprocal of \frac{13}{10}.

$$\frac{195}{7}\times \frac{10}{13}$$

Multiply \frac{195}{7} times \frac{10}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{195\times 10}{7\times 13}$$

Do the multiplications in the fraction \frac{195\times 10}{7\times 13}.

$$\frac{1950}{91}$$

Reduce the fraction \frac{1950}{91} to lowest terms by extracting and canceling out 13.

$$\frac{150}{7}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 ^ {2}}{7} = 21\frac{3}{7} = 21.428571428571427$$