Solve 3/10div11/5-1/6

$$\frac { 3 } { 10 } \div 1 \frac { 1 } { 5 } - \frac { 1 } { 6 }$$

Evaluate

$$\frac{1}{12}\approx 0.083333333$$

Solution Steps

Divide \frac{3}{10} by \frac{1\times 5+1}{5} by multiplying \frac{3}{10} by the reciprocal of \frac{1\times 5+1}{5}.

$$\frac{3\times 5}{10\left(1\times 5+1\right)}-\frac{1}{6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{2\left(1+5\right)}-\frac{1}{6}$$

Add 1 and 5 to get 6.

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

Multiply 2 and 6 to get 12.

$$\frac{3}{12}-\frac{1}{6}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

$$\frac{1}{12}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$$