Solve 1/3-1/5/frac{2{9}+5/6}=

$$\frac { \frac { 1 } { 3 } - \frac { 1 } { 5 } } { \frac { 2 } { 9 } + \frac { 5 } { 6 } } =$$

Evaluate

$$\frac{12}{95}\approx 0.126315789$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{\frac{5}{15}-\frac{3}{15}}{\frac{2}{9}+\frac{5}{6}}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-3}{15}}{\frac{2}{9}+\frac{5}{6}}$$

Subtract 3 from 5 to get 2.

$$\frac{\frac{2}{15}}{\frac{2}{9}+\frac{5}{6}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{2}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{\frac{2}{15}}{\frac{4}{18}+\frac{15}{18}}$$

Since \frac{4}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{15}}{\frac{4+15}{18}}$$

Add 4 and 15 to get 19.

$$\frac{\frac{2}{15}}{\frac{19}{18}}$$

Divide \frac{2}{15} by \frac{19}{18} by multiplying \frac{2}{15} by the reciprocal of \frac{19}{18}.

$$\frac{2}{15}\times \frac{18}{19}$$

Multiply \frac{2}{15} times \frac{18}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 18}{15\times 19}$$

Do the multiplications in the fraction \frac{2\times 18}{15\times 19}.

$$\frac{36}{285}$$

Reduce the fraction \frac{36}{285} to lowest terms by extracting and canceling out 3.

$$\frac{12}{95}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5 \cdot 19} = 0.12631578947368421$$