Solve 1/7+1/3/1-frac{1{21}}

$$\frac { \frac { 1 } { 7 } + \frac { 1 } { 3 } } { 1 - \frac { 1 } { 21 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{1}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{\frac{3}{21}+\frac{7}{21}}{1-\frac{1}{21}}$$

Since \frac{3}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+7}{21}}{1-\frac{1}{21}}$$

Add 3 and 7 to get 10.

$$\frac{\frac{10}{21}}{1-\frac{1}{21}}$$

Convert 1 to fraction \frac{21}{21}.

$$\frac{\frac{10}{21}}{\frac{21}{21}-\frac{1}{21}}$$

Since \frac{21}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10}{21}}{\frac{21-1}{21}}$$

Subtract 1 from 21 to get 20.

$$\frac{\frac{10}{21}}{\frac{20}{21}}$$

Divide \frac{10}{21} by \frac{20}{21} by multiplying \frac{10}{21} by the reciprocal of \frac{20}{21}.

$$\frac{10}{21}\times \frac{21}{20}$$

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

$$\frac{10\times 21}{21\times 20}$$

Cancel out 21 in both numerator and denominator.

$$\frac{10}{20}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

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

Factor

$$\frac{1}{2} = 0.5$$