Solve 3-1/2-(-2)/35/2-23/2

$$3 - \frac { 1 } { 2 } - \frac { ( - 2 ) } { 3 } \frac { 5 } { 2 } - 2 \frac { 3 } { 2 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

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

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{5}{2}-\left(-\frac{2}{3}\times \frac{5}{2}\right)-\frac{2\times 2+3}{2}$$

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

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

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

$$\frac{5}{2}-\frac{-10}{6}-\frac{2\times 2+3}{2}$$

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

$$\frac{5}{2}-\left(-\frac{5}{3}\right)-\frac{2\times 2+3}{2}$$

The opposite of -\frac{5}{3} is \frac{5}{3}.

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

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

$$\frac{15}{6}+\frac{10}{6}-\frac{2\times 2+3}{2}$$

Since \frac{15}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+10}{6}-\frac{2\times 2+3}{2}$$

Add 15 and 10 to get 25.

$$\frac{25}{6}-\frac{2\times 2+3}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{25}{6}-\frac{4+3}{2}$$

Add 4 and 3 to get 7.

$$\frac{25}{6}-\frac{7}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{25}{6} and \frac{7}{2} to fractions with denominator 6.

$$\frac{25}{6}-\frac{21}{6}$$

Since \frac{25}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-21}{6}$$

Subtract 21 from 25 to get 4.

$$\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$