Solve -2/3*3/5+5/2-3/5*frac{1}{6}

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

Evaluate

$$2$$

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

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

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

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

Least common multiple of 5 and 2 is 10. Convert -\frac{2}{5} and \frac{5}{2} to fractions with denominator 10.

$$-\frac{4}{10}+\frac{25}{10}-\frac{3}{5}\times \frac{1}{6}$$

Since -\frac{4}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$\frac{-4+25}{10}-\frac{3}{5}\times \frac{1}{6}$$

Add -4 and 25 to get 21.

$$\frac{21}{10}-\frac{3}{5}\times \frac{1}{6}$$

Multiply \frac{3}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{10}-\frac{3\times 1}{5\times 6}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 6}.

$$\frac{21}{10}-\frac{3}{30}$$

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

$$\frac{21}{10}-\frac{1}{10}$$

Since \frac{21}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-1}{10}$$

Subtract 1 from 21 to get 20.

$$\frac{20}{10}$$

Divide 20 by 10 to get 2.

$$2$$

Factor

$$2$$