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

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

Evaluate

$$\frac{14}{5}=2.8$$

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

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

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

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

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

$$\frac{2}{5}-\frac{3}{30}+\frac{5}{2}$$

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

$$\frac{2}{5}-\frac{1}{10}+\frac{5}{2}$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{1}{10} to fractions with denominator 10.

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

Since \frac{4}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

$$\frac{3}{10}+\frac{5}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{3}{10} and \frac{5}{2} to fractions with denominator 10.

$$\frac{3}{10}+\frac{25}{10}$$

Since \frac{3}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$\frac{3+25}{10}$$

Add 3 and 25 to get 28.

$$\frac{28}{10}$$

Reduce the fraction \frac{28}{10} to lowest terms by extracting and canceling out 2.

$$\frac{14}{5}$$

Factor

$$\frac{2 \cdot 7}{5} = 2\frac{4}{5} = 2.8$$