Solve (3/2div9/2)+(-2/3*1/3)

$$( \frac { 3 } { 2 } \div \frac { 9 } { 2 } ) + ( - \frac { 2 } { 3 } \cdot \frac { 1 } { 3 } )$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Divide \frac{3}{2} by \frac{9}{2} by multiplying \frac{3}{2} by the reciprocal of \frac{9}{2}.

$$\frac{3}{2}\times \frac{2}{9}-\frac{2}{3}\times \frac{1}{3}$$

Multiply \frac{3}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{2\times 9}-\frac{2}{3}\times \frac{1}{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{9}-\frac{2}{3}\times \frac{1}{3}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

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

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

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

$$\frac{1}{3}+\frac{-2}{9}$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$\frac{1}{3}-\frac{2}{9}$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{2}{9} to fractions with denominator 9.

$$\frac{3}{9}-\frac{2}{9}$$

Since \frac{3}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{9}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$