Solve n*1/2*3/5-1/3*2/5+frac{3}{2}*frac{9}{5}=

$$n \cdot \frac { 1 } { 2 } \cdot \frac { 3 } { 5 } - \frac { 1 } { 3 } \cdot \frac { 2 } { 5 } + \frac { 3 } { 2 } \cdot \frac { 9 } { 5 } =$$

Evaluate

$$\frac{3n}{10}+\frac{77}{30}$$

Solution Steps

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$n\times \frac{1\times 3}{2\times 5}-\frac{1}{3}\times \frac{2}{5}+\frac{3}{2}\times \frac{9}{5}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$n\times \frac{3}{10}-\frac{1}{3}\times \frac{2}{5}+\frac{3}{2}\times \frac{9}{5}$$

Multiply \frac{1}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$n\times \frac{3}{10}-\frac{1\times 2}{3\times 5}+\frac{3}{2}\times \frac{9}{5}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 5}.

$$n\times \frac{3}{10}-\frac{2}{15}+\frac{3}{2}\times \frac{9}{5}$$

Multiply \frac{3}{2} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$n\times \frac{3}{10}-\frac{2}{15}+\frac{3\times 9}{2\times 5}$$

Do the multiplications in the fraction \frac{3\times 9}{2\times 5}.

$$n\times \frac{3}{10}-\frac{2}{15}+\frac{27}{10}$$

Least common multiple of 15 and 10 is 30. Convert -\frac{2}{15} and \frac{27}{10} to fractions with denominator 30.

$$n\times \frac{3}{10}-\frac{4}{30}+\frac{81}{30}$$

Since -\frac{4}{30} and \frac{81}{30} have the same denominator, add them by adding their numerators.

$$n\times \frac{3}{10}+\frac{-4+81}{30}$$

Add -4 and 81 to get 77.

$$n\times \frac{3}{10}+\frac{77}{30}$$

Factor

$$\frac{9n+77}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{9n+77}{30}$$

Consider 9n-4+81. Multiply and combine like terms.

$$9n+77$$

Rewrite the complete factored expression.

$$\frac{9n+77}{30}$$