Solve 1/frac{1{15}+1/35}

$$\frac { 1 } { \frac { 1 } { 15 } + \frac { 1 } { 35 } }$$

Evaluate

$$\frac{21}{2}=10.5$$

Solution Steps

Least common multiple of 15 and 35 is 105. Convert \frac{1}{15} and \frac{1}{35} to fractions with denominator 105.

$$\frac{1}{\frac{7}{105}+\frac{3}{105}}$$

Since \frac{7}{105} and \frac{3}{105} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{7+3}{105}}$$

Add 7 and 3 to get 10.

$$\frac{1}{\frac{10}{105}}$$

Reduce the fraction \frac{10}{105} to lowest terms by extracting and canceling out 5.

$$\frac{1}{\frac{2}{21}}$$

Divide 1 by \frac{2}{21} by multiplying 1 by the reciprocal of \frac{2}{21}.

$$1\times \frac{21}{2}$$

Multiply 1 and \frac{21}{2} to get \frac{21}{2}.

$$\frac{21}{2}$$

Factor

$$\frac{3 \cdot 7}{2} = 10\frac{1}{2} = 10.5$$