Solve 1/2-1/3/1-frac{1{2}*1/3}

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

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

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

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

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

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

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

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

Convert 1 to fraction \frac{6}{6}.

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

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

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

Subtract 1 from 6 to get 5.

$$\frac{\frac{1}{6}}{\frac{5}{6}}$$

Divide \frac{1}{6} by \frac{5}{6} by multiplying \frac{1}{6} by the reciprocal of \frac{5}{6}.

$$\frac{1}{6}\times \frac{6}{5}$$

Multiply \frac{1}{6} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{6\times 5}$$

Cancel out 6 in both numerator and denominator.

$$\frac{1}{5}$$

Factor

$$\frac{1}{5} = 0.2$$