Solve 2/4-3/5/frac{5{18}+7/23}

$$\frac { \frac { 2 } { 4 } - \frac { 3 } { 5 } } { \frac { 5 } { 18 } + \frac { 7 } { 23 } }$$

Evaluate

$$-\frac{207}{1205}\approx -0.171784232$$

Solution Steps

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

$$\frac{\frac{1}{2}-\frac{3}{5}}{\frac{5}{18}+\frac{7}{23}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{\frac{5}{10}-\frac{6}{10}}{\frac{5}{18}+\frac{7}{23}}$$

Since \frac{5}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-6}{10}}{\frac{5}{18}+\frac{7}{23}}$$

Subtract 6 from 5 to get -1.

$$\frac{-\frac{1}{10}}{\frac{5}{18}+\frac{7}{23}}$$

Least common multiple of 18 and 23 is 414. Convert \frac{5}{18} and \frac{7}{23} to fractions with denominator 414.

$$\frac{-\frac{1}{10}}{\frac{115}{414}+\frac{126}{414}}$$

Since \frac{115}{414} and \frac{126}{414} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{10}}{\frac{115+126}{414}}$$

Add 115 and 126 to get 241.

$$\frac{-\frac{1}{10}}{\frac{241}{414}}$$

Divide -\frac{1}{10} by \frac{241}{414} by multiplying -\frac{1}{10} by the reciprocal of \frac{241}{414}.

$$-\frac{1}{10}\times \frac{414}{241}$$

Multiply -\frac{1}{10} times \frac{414}{241} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-414}{10\times 241}$$

Do the multiplications in the fraction \frac{-414}{10\times 241}.

$$\frac{-414}{2410}$$

Reduce the fraction \frac{-414}{2410} to lowest terms by extracting and canceling out 2.

$$-\frac{207}{1205}$$

Factor

$$-\frac{207}{1205} = -0.17178423236514523$$