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

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{3}{10}-\frac{2}{15}+\frac{3}{2}$$

Least common multiple of 10 and 15 is 30. Convert \frac{3}{10} and \frac{2}{15} to fractions with denominator 30.

$$\frac{9}{30}-\frac{4}{30}+\frac{3}{2}$$

Since \frac{9}{30} and \frac{4}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-4}{30}+\frac{3}{2}$$

Subtract 4 from 9 to get 5.

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

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}+\frac{3}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{1}{6}+\frac{9}{6}$$

Since \frac{1}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+9}{6}$$

Add 1 and 9 to get 10.

$$\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$