Solve 1/3-2/frac{4{5}-3/10}

$$\frac{ \frac{ 1 }{ 3 } -2 }{ \frac{ 4 }{ 5 } - \frac{ 3 }{ 10 } }$$

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{1}{3}-\frac{6}{3}}{\frac{4}{5}-\frac{3}{10}}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-6}{3}}{\frac{4}{5}-\frac{3}{10}}$$

Subtract 6 from 1 to get -5.

$$\frac{-\frac{5}{3}}{\frac{4}{5}-\frac{3}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{4}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{-\frac{5}{3}}{\frac{8}{10}-\frac{3}{10}}$$

Since \frac{8}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{5}{3}}{\frac{8-3}{10}}$$

Subtract 3 from 8 to get 5.

$$\frac{-\frac{5}{3}}{\frac{5}{10}}$$

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

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

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

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

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

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

Multiply -5 and 2 to get -10.

$$\frac{-10}{3}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$