Solve 1/2+1/4*1/5div1/6-frac{1}{7}

$$\frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } \times \frac{ 1 }{ 5 } \div \frac{ 1 }{ 6 } - \frac{ 1 }{ 7 }$$

Evaluate

$$\frac{23}{35}\approx 0.657142857$$

Solution Steps

Multiply \frac{1}{4} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{\frac{1\times 1}{4\times 5}}{\frac{1}{6}}-\frac{1}{7}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 5}.

$$\frac{1}{2}+\frac{\frac{1}{20}}{\frac{1}{6}}-\frac{1}{7}$$

Divide \frac{1}{20} by \frac{1}{6} by multiplying \frac{1}{20} by the reciprocal of \frac{1}{6}.

$$\frac{1}{2}+\frac{1}{20}\times 6-\frac{1}{7}$$

Multiply \frac{1}{20} and 6 to get \frac{6}{20}.

$$\frac{1}{2}+\frac{6}{20}-\frac{1}{7}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{3}{10}-\frac{1}{7}$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{5}{10}+\frac{3}{10}-\frac{1}{7}$$

Since \frac{5}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{10}-\frac{1}{7}$$

Add 5 and 3 to get 8.

$$\frac{8}{10}-\frac{1}{7}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}-\frac{1}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{4}{5} and \frac{1}{7} to fractions with denominator 35.

$$\frac{28}{35}-\frac{5}{35}$$

Since \frac{28}{35} and \frac{5}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-5}{35}$$

Subtract 5 from 28 to get 23.

$$\frac{23}{35}$$

Factor

$$\frac{23}{5 \cdot 7} = 0.6571428571428571$$