Solve 15(2)+(3/2)-2/3-(2/3)2/4

$$15 ( 2 ) + ( \frac { 3 } { 2 } ) - \frac { 2 } { 3 } - ( \frac { 2 } { 3 } ) \frac { 2 } { 4 }$$

Evaluate

$$\frac{61}{2}=30.5$$

Solution Steps

Multiply 15 and 2 to get 30.

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

Convert 30 to fraction \frac{60}{2}.

$$\frac{60}{2}+\frac{3}{2}-\frac{2}{3}-\frac{2}{3}\times \frac{2}{4}$$

Since \frac{60}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{60+3}{2}-\frac{2}{3}-\frac{2}{3}\times \frac{2}{4}$$

Add 60 and 3 to get 63.

$$\frac{63}{2}-\frac{2}{3}-\frac{2}{3}\times \frac{2}{4}$$

Least common multiple of 2 and 3 is 6. Convert \frac{63}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{189}{6}-\frac{4}{6}-\frac{2}{3}\times \frac{2}{4}$$

Since \frac{189}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{189-4}{6}-\frac{2}{3}\times \frac{2}{4}$$

Subtract 4 from 189 to get 185.

$$\frac{185}{6}-\frac{2}{3}\times \frac{2}{4}$$

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

$$\frac{185}{6}-\frac{2}{3}\times \frac{1}{2}$$

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

$$\frac{185}{6}-\frac{2\times 1}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{185}{6}-\frac{1}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{185}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{185}{6}-\frac{2}{6}$$

Since \frac{185}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{185-2}{6}$$

Subtract 2 from 185 to get 183.

$$\frac{183}{6}$$

Reduce the fraction \frac{183}{6} to lowest terms by extracting and canceling out 3.

$$\frac{61}{2}$$

Factor

$$\frac{61}{2} = 30\frac{1}{2} = 30.5$$