Solve 10/21*7/20div5/6-1/6

$$\frac { 10 } { 21 } \times \frac { 7 } { 20 } \div \frac { 5 } { 6 } - \frac { 1 } { 6 }$$

Evaluate

$$\frac{1}{30}\approx 0.033333333$$

Solution Steps

Multiply \frac{10}{21} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10\times 7}{21\times 20}}{\frac{5}{6}}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{10\times 7}{21\times 20}.

$$\frac{\frac{70}{420}}{\frac{5}{6}}-\frac{1}{6}$$

Reduce the fraction \frac{70}{420} to lowest terms by extracting and canceling out 70.

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

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

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

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

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

Cancel out 6 in both numerator and denominator.

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

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{6}{30}-\frac{5}{30}$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{30}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{30}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 5} = 0.03333333333333333$$