Solve 21/2-2/5div3/10/2frac{1{3}*frac{4}{5}}

$$\frac { 2 \frac { 1 } { 2 } - \frac { 2 } { 5 } \div \frac { 3 } { 10 } } { 2 \frac { 1 } { 3 } \times \frac { 4 } { 5 } }$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\frac{4+1}{2}-\frac{\frac{2}{5}}{\frac{3}{10}}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{2}-\frac{\frac{2}{5}}{\frac{3}{10}}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Divide \frac{2}{5} by \frac{3}{10} by multiplying \frac{2}{5} by the reciprocal of \frac{3}{10}.

$$\frac{\frac{5}{2}-\frac{2}{5}\times \frac{10}{3}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Multiply \frac{2}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{2}-\frac{2\times 10}{5\times 3}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Do the multiplications in the fraction \frac{2\times 10}{5\times 3}.

$$\frac{\frac{5}{2}-\frac{20}{15}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{5}{2}-\frac{4}{3}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{15}{6}-\frac{8}{6}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Since \frac{15}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-8}{6}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{7}{6}}{\frac{2\times 3+1}{3}\times \frac{4}{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{7}{6}}{\frac{6+1}{3}\times \frac{4}{5}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{6}}{\frac{7}{3}\times \frac{4}{5}}$$

Multiply \frac{7}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{6}}{\frac{7\times 4}{3\times 5}}$$

Do the multiplications in the fraction \frac{7\times 4}{3\times 5}.

$$\frac{\frac{7}{6}}{\frac{28}{15}}$$

Divide \frac{7}{6} by \frac{28}{15} by multiplying \frac{7}{6} by the reciprocal of \frac{28}{15}.

$$\frac{7}{6}\times \frac{15}{28}$$

Multiply \frac{7}{6} times \frac{15}{28} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 15}{6\times 28}$$

Do the multiplications in the fraction \frac{7\times 15}{6\times 28}.

$$\frac{105}{168}$$

Reduce the fraction \frac{105}{168} to lowest terms by extracting and canceling out 21.

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$