Solve 3/2-1/2*10/3-2:12/7

$$\frac { 3 } { 2 } - \frac { 1 } { 2 } \cdot \frac { 10 } { 3 } - 2 : \frac { 12 } { 7 }$$

Evaluate

$$-\frac{4}{3}\approx -1.333333333$$

Solution Steps

Multiply \frac{1}{2} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}-\frac{1\times 10}{2\times 3}-\frac{2}{\frac{12}{7}}$$

Do the multiplications in the fraction \frac{1\times 10}{2\times 3}.

$$\frac{3}{2}-\frac{10}{6}-\frac{2}{\frac{12}{7}}$$

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

$$\frac{3}{2}-\frac{5}{3}-\frac{2}{\frac{12}{7}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{5}{3} to fractions with denominator 6.

$$\frac{9}{6}-\frac{10}{6}-\frac{2}{\frac{12}{7}}$$

Since \frac{9}{6} and \frac{10}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-10}{6}-\frac{2}{\frac{12}{7}}$$

Subtract 10 from 9 to get -1.

$$-\frac{1}{6}-\frac{2}{\frac{12}{7}}$$

Divide 2 by \frac{12}{7} by multiplying 2 by the reciprocal of \frac{12}{7}.

$$-\frac{1}{6}-2\times \frac{7}{12}$$

Express 2\times \frac{7}{12} as a single fraction.

$$-\frac{1}{6}-\frac{2\times 7}{12}$$

Multiply 2 and 7 to get 14.

$$-\frac{1}{6}-\frac{14}{12}$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{6}-\frac{7}{6}$$

Since -\frac{1}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-7}{6}$$

Subtract 7 from -1 to get -8.

$$\frac{-8}{6}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{4}{3} = -1\frac{1}{3} = -1.3333333333333333$$