Solve 1/frac{1{35}-1/65}

$$\frac { 1 } { \frac { 1 } { 35 } - \frac { 1 } { 65 } }$$

Evaluate

$$\frac{455}{6}\approx 75.833333333$$

Solution Steps

Least common multiple of 35 and 65 is 455. Convert \frac{1}{35} and \frac{1}{65} to fractions with denominator 455.

$$\frac{1}{\frac{13}{455}-\frac{7}{455}}$$

Since \frac{13}{455} and \frac{7}{455} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{13-7}{455}}$$

Subtract 7 from 13 to get 6.

$$\frac{1}{\frac{6}{455}}$$

Divide 1 by \frac{6}{455} by multiplying 1 by the reciprocal of \frac{6}{455}.

$$1\times \frac{455}{6}$$

Multiply 1 and \frac{455}{6} to get \frac{455}{6}.

$$\frac{455}{6}$$

Factor

$$\frac{5 \cdot 7 \cdot 13}{2 \cdot 3} = 75\frac{5}{6} = 75.83333333333333$$