Solve 1div(1/6+1/7)

$$1 \div ( \frac { 1 } { 6 } + \frac { 1 } { 7 } )$$

Evaluate

$$\frac{42}{13}\approx 3.230769231$$

Solution Steps

Least common multiple of 6 and 7 is 42. Convert \frac{1}{6} and \frac{1}{7} to fractions with denominator 42.

$$\frac{1}{\frac{7}{42}+\frac{6}{42}}$$

Since \frac{7}{42} and \frac{6}{42} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{7+6}{42}}$$

Add 7 and 6 to get 13.

$$\frac{1}{\frac{13}{42}}$$

Divide 1 by \frac{13}{42} by multiplying 1 by the reciprocal of \frac{13}{42}.

$$1\times \frac{42}{13}$$

Multiply 1 and \frac{42}{13} to get \frac{42}{13}.

$$\frac{42}{13}$$

Factor

$$\frac{2 \cdot 3 \cdot 7}{13} = 3\frac{3}{13} = 3.230769230769231$$