Solve 51/3-21/3divleft(3/4-1/2left(frac{7}{10}-frac{3}{5}right)right)

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

Evaluate

$$2$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{15+1}{3}-\frac{\frac{2\times 3+1}{3}}{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{10}-\frac{3}{5}\right)}$$

Add 15 and 1 to get 16.

$$\frac{16}{3}-\frac{\frac{2\times 3+1}{3}}{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{10}-\frac{3}{5}\right)}$$

Multiply 2 and 3 to get 6.

$$\frac{16}{3}-\frac{\frac{6+1}{3}}{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{10}-\frac{3}{5}\right)}$$

Add 6 and 1 to get 7.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{10}-\frac{3}{5}\right)}$$

Least common multiple of 10 and 5 is 10. Convert \frac{7}{10} and \frac{3}{5} to fractions with denominator 10.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{10}-\frac{6}{10}\right)}$$

Since \frac{7}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1}{2}\times \frac{7-6}{10}}$$

Subtract 6 from 7 to get 1.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1}{2}\times \frac{1}{10}}$$

Multiply \frac{1}{2} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1\times 1}{2\times 10}}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 10}.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{3}{4}-\frac{1}{20}}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{15}{20}-\frac{1}{20}}$$

Since \frac{15}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{15-1}{20}}$$

Subtract 1 from 15 to get 14.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{14}{20}}$$

Reduce the fraction \frac{14}{20} to lowest terms by extracting and canceling out 2.

$$\frac{16}{3}-\frac{\frac{7}{3}}{\frac{7}{10}}$$

Divide \frac{7}{3} by \frac{7}{10} by multiplying \frac{7}{3} by the reciprocal of \frac{7}{10}.

$$\frac{16}{3}-\frac{7}{3}\times \frac{10}{7}$$

Multiply \frac{7}{3} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{3}-\frac{7\times 10}{3\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{16}{3}-\frac{10}{3}$$

Since \frac{16}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-10}{3}$$

Subtract 10 from 16 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$