Solve 1/2-1/3/frac{1{4}+1/5}=

$$\frac { \frac { 1 } { 2 } - \frac { 1 } { 3 } } { \frac { 1 } { 4 } + \frac { 1 } { 5 } } =$$

Evaluate

$$\frac{10}{27}\approx 0.37037037$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}-\frac{2}{6}}{\frac{1}{4}+\frac{1}{5}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{6}}{\frac{1}{4}+\frac{1}{5}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{6}}{\frac{1}{4}+\frac{1}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{1}{6}}{\frac{5}{20}+\frac{4}{20}}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{6}}{\frac{5+4}{20}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{1}{6}}{\frac{9}{20}}$$

Divide \frac{1}{6} by \frac{9}{20} by multiplying \frac{1}{6} by the reciprocal of \frac{9}{20}.

$$\frac{1}{6}\times \frac{20}{9}$$

Multiply \frac{1}{6} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 20}{6\times 9}$$

Do the multiplications in the fraction \frac{1\times 20}{6\times 9}.

$$\frac{20}{54}$$

Reduce the fraction \frac{20}{54} to lowest terms by extracting and canceling out 2.

$$\frac{10}{27}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {3}} = 0.37037037037037035$$