Solve 6/5-3/2+1/4/frac{2{3}-frac{6}{4}+2}

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

Evaluate

$$-\frac{3}{70}\approx -0.042857143$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{12}{10}-\frac{15}{10}+\frac{1}{4}}{\frac{2}{3}-\frac{6}{4}+2}$$

Since \frac{12}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-15}{10}+\frac{1}{4}}{\frac{2}{3}-\frac{6}{4}+2}$$

Subtract 15 from 12 to get -3.

$$\frac{-\frac{3}{10}+\frac{1}{4}}{\frac{2}{3}-\frac{6}{4}+2}$$

Least common multiple of 10 and 4 is 20. Convert -\frac{3}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{-\frac{6}{20}+\frac{5}{20}}{\frac{2}{3}-\frac{6}{4}+2}$$

Since -\frac{6}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-6+5}{20}}{\frac{2}{3}-\frac{6}{4}+2}$$

Add -6 and 5 to get -1.

$$\frac{-\frac{1}{20}}{\frac{2}{3}-\frac{6}{4}+2}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{20}}{\frac{2}{3}-\frac{3}{2}+2}$$

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

$$\frac{-\frac{1}{20}}{\frac{4}{6}-\frac{9}{6}+2}$$

Since \frac{4}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{20}}{\frac{4-9}{6}+2}$$

Subtract 9 from 4 to get -5.

$$\frac{-\frac{1}{20}}{-\frac{5}{6}+2}$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{-\frac{1}{20}}{-\frac{5}{6}+\frac{12}{6}}$$

Since -\frac{5}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{20}}{\frac{-5+12}{6}}$$

Add -5 and 12 to get 7.

$$\frac{-\frac{1}{20}}{\frac{7}{6}}$$

Divide -\frac{1}{20} by \frac{7}{6} by multiplying -\frac{1}{20} by the reciprocal of \frac{7}{6}.

$$-\frac{1}{20}\times \frac{6}{7}$$

Multiply -\frac{1}{20} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6}{20\times 7}$$

Do the multiplications in the fraction \frac{-6}{20\times 7}.

$$\frac{-6}{140}$$

Reduce the fraction \frac{-6}{140} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{70}$$

Factor

$$-\frac{3}{70} = -0.04285714285714286$$