Solve ri2/5+1/4/frac{2{3}-4/5}

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

Evaluate

$$-\frac{39ir}{8}$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{1}{4} to fractions with denominator 20.

$$ri\times \frac{\frac{8}{20}+\frac{5}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Since \frac{8}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$ri\times \frac{\frac{8+5}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Add 8 and 5 to get 13.

$$ri\times \frac{\frac{13}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$ri\times \frac{\frac{13}{20}}{\frac{10}{15}-\frac{12}{15}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$ri\times \frac{\frac{13}{20}}{\frac{10-12}{15}}$$

Subtract 12 from 10 to get -2.

$$ri\times \frac{\frac{13}{20}}{-\frac{2}{15}}$$

Divide \frac{13}{20} by -\frac{2}{15} by multiplying \frac{13}{20} by the reciprocal of -\frac{2}{15}.

$$ri\times \frac{13}{20}\left(-\frac{15}{2}\right)$$

Multiply \frac{13}{20} times -\frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$ri\times \frac{13\left(-15\right)}{20\times 2}$$

Do the multiplications in the fraction \frac{13\left(-15\right)}{20\times 2}.

$$ri\times \frac{-195}{40}$$

Reduce the fraction \frac{-195}{40} to lowest terms by extracting and canceling out 5.

$$r\times \left(-\frac{39}{8}i\right)$$

Expand

$$-\frac{39ir}{8}$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{1}{4} to fractions with denominator 20.

$$ri\times \frac{\frac{8}{20}+\frac{5}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Since \frac{8}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$ri\times \frac{\frac{8+5}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Add 8 and 5 to get 13.

$$ri\times \frac{\frac{13}{20}}{\frac{2}{3}-\frac{4}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$ri\times \frac{\frac{13}{20}}{\frac{10}{15}-\frac{12}{15}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$ri\times \frac{\frac{13}{20}}{\frac{10-12}{15}}$$

Subtract 12 from 10 to get -2.

$$ri\times \frac{\frac{13}{20}}{-\frac{2}{15}}$$

Divide \frac{13}{20} by -\frac{2}{15} by multiplying \frac{13}{20} by the reciprocal of -\frac{2}{15}.

$$ri\times \frac{13}{20}\left(-\frac{15}{2}\right)$$

Multiply \frac{13}{20} times -\frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$ri\times \frac{13\left(-15\right)}{20\times 2}$$

Do the multiplications in the fraction \frac{13\left(-15\right)}{20\times 2}.

$$ri\times \frac{-195}{40}$$

Reduce the fraction \frac{-195}{40} to lowest terms by extracting and canceling out 5.

$$r\times \left(-\frac{39}{8}i\right)$$