Solve 2-3-5/3/2-1/3/2/5/2/3-frac{1/3{1/15}}

$$2 - \frac { 3 - \frac { 5 } { 3 / 2 } - \frac { 1 / 3 } { 2 / 5 } } { 2 / 3 - \frac { 1 / 3 } { 1 / 15 } }$$

Evaluate

$$\frac{45}{26}\approx 1.730769231$$

Solution Steps

Divide 5 by \frac{3}{2} by multiplying 5 by the reciprocal of \frac{3}{2}.

$$2-\frac{3-5\times \frac{2}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Express 5\times \frac{2}{3} as a single fraction.

$$2-\frac{3-\frac{5\times 2}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Multiply 5 and 2 to get 10.

$$2-\frac{3-\frac{10}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Convert 3 to fraction \frac{9}{3}.

$$2-\frac{\frac{9}{3}-\frac{10}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Since \frac{9}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{\frac{9-10}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Subtract 10 from 9 to get -1.

$$2-\frac{-\frac{1}{3}-\frac{\frac{1}{3}}{\frac{2}{5}}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Divide \frac{1}{3} by \frac{2}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{5}.

$$2-\frac{-\frac{1}{3}-\frac{1}{3}\times \frac{5}{2}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Multiply \frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{-\frac{1}{3}-\frac{1\times 5}{3\times 2}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 2}.

$$2-\frac{-\frac{1}{3}-\frac{5}{6}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$2-\frac{-\frac{2}{6}-\frac{5}{6}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Since -\frac{2}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{\frac{-2-5}{6}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Subtract 5 from -2 to get -7.

$$2-\frac{-\frac{7}{6}}{\frac{2}{3}-\frac{\frac{1}{3}}{\frac{1}{15}}}$$

Divide \frac{1}{3} by \frac{1}{15} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{15}.

$$2-\frac{-\frac{7}{6}}{\frac{2}{3}-\frac{1}{3}\times 15}$$

Multiply \frac{1}{3} and 15 to get \frac{15}{3}.

$$2-\frac{-\frac{7}{6}}{\frac{2}{3}-\frac{15}{3}}$$

Since \frac{2}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{-\frac{7}{6}}{\frac{2-15}{3}}$$

Subtract 15 from 2 to get -13.

$$2-\frac{-\frac{7}{6}}{-\frac{13}{3}}$$

Divide -\frac{7}{6} by -\frac{13}{3} by multiplying -\frac{7}{6} by the reciprocal of -\frac{13}{3}.

$$2-\left(-\frac{7}{6}\left(-\frac{3}{13}\right)\right)$$

Multiply -\frac{7}{6} times -\frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{-7\left(-3\right)}{6\times 13}$$

Do the multiplications in the fraction \frac{-7\left(-3\right)}{6\times 13}.

$$2-\frac{21}{78}$$

Reduce the fraction \frac{21}{78} to lowest terms by extracting and canceling out 3.

$$2-\frac{7}{26}$$

Convert 2 to fraction \frac{52}{26}.

$$\frac{52}{26}-\frac{7}{26}$$

Since \frac{52}{26} and \frac{7}{26} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-7}{26}$$

Subtract 7 from 52 to get 45.

$$\frac{45}{26}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 \cdot 13} = 1\frac{19}{26} = 1.7307692307692308$$