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

$$\frac { 3 } { 2 } + \frac { 1 } { 3 } \cdot \frac { 1 } { 2 } - \frac { 4 } { 5 } : 3 - \frac { 5 } { 3 }$$

Evaluate

$$-\frac{4}{15}\approx -0.266666667$$

Solution Steps

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

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

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

$$\frac{3}{2}+\frac{1}{6}-\frac{\frac{4}{5}}{3}-\frac{5}{3}$$

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

$$\frac{9}{6}+\frac{1}{6}-\frac{\frac{4}{5}}{3}-\frac{5}{3}$$

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

$$\frac{9+1}{6}-\frac{\frac{4}{5}}{3}-\frac{5}{3}$$

Add 9 and 1 to get 10.

$$\frac{10}{6}-\frac{\frac{4}{5}}{3}-\frac{5}{3}$$

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

$$\frac{5}{3}-\frac{\frac{4}{5}}{3}-\frac{5}{3}$$

Express \frac{\frac{4}{5}}{3} as a single fraction.

$$\frac{5}{3}-\frac{4}{5\times 3}-\frac{5}{3}$$

Multiply 5 and 3 to get 15.

$$\frac{5}{3}-\frac{4}{15}-\frac{5}{3}$$

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

$$\frac{25}{15}-\frac{4}{15}-\frac{5}{3}$$

Since \frac{25}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-4}{15}-\frac{5}{3}$$

Subtract 4 from 25 to get 21.

$$\frac{21}{15}-\frac{5}{3}$$

Reduce the fraction \frac{21}{15} to lowest terms by extracting and canceling out 3.

$$\frac{7}{5}-\frac{5}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{7}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{21}{15}-\frac{25}{15}$$

Since \frac{21}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-25}{15}$$

Subtract 25 from 21 to get -4.

$$-\frac{4}{15}$$

Factor

$$-\frac{4}{15} = -0.26666666666666666$$