Solve (24/-7)-(-3/-4)/1+(frac{24{7})-(-3/4)}

$$\frac { ( \frac { 24 } { - 7 } ) - ( \frac { - 3 } { - 4 } ) } { 1 + ( \frac { 24 } { 7 } ) - ( \frac { - 3 } { 4 } ) }$$

Evaluate

$$-\frac{117}{145}\approx -0.806896552$$

Solution Steps

Fraction \frac{24}{-7} can be rewritten as -\frac{24}{7} by extracting the negative sign.

$$\frac{-\frac{24}{7}-\frac{-3}{-4}}{1+\frac{24}{7}-\frac{-3}{4}}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

$$\frac{-\frac{24}{7}-\frac{3}{4}}{1+\frac{24}{7}-\frac{-3}{4}}$$

Least common multiple of 7 and 4 is 28. Convert -\frac{24}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{-\frac{96}{28}-\frac{21}{28}}{1+\frac{24}{7}-\frac{-3}{4}}$$

Since -\frac{96}{28} and \frac{21}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-96-21}{28}}{1+\frac{24}{7}-\frac{-3}{4}}$$

Subtract 21 from -96 to get -117.

$$\frac{-\frac{117}{28}}{1+\frac{24}{7}-\frac{-3}{4}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{-\frac{117}{28}}{\frac{7}{7}+\frac{24}{7}-\frac{-3}{4}}$$

Since \frac{7}{7} and \frac{24}{7} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{117}{28}}{\frac{7+24}{7}-\frac{-3}{4}}$$

Add 7 and 24 to get 31.

$$\frac{-\frac{117}{28}}{\frac{31}{7}-\frac{-3}{4}}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{-\frac{117}{28}}{\frac{31}{7}-\left(-\frac{3}{4}\right)}$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$\frac{-\frac{117}{28}}{\frac{31}{7}+\frac{3}{4}}$$

Least common multiple of 7 and 4 is 28. Convert \frac{31}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{-\frac{117}{28}}{\frac{124}{28}+\frac{21}{28}}$$

Since \frac{124}{28} and \frac{21}{28} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{117}{28}}{\frac{124+21}{28}}$$

Add 124 and 21 to get 145.

$$\frac{-\frac{117}{28}}{\frac{145}{28}}$$

Divide -\frac{117}{28} by \frac{145}{28} by multiplying -\frac{117}{28} by the reciprocal of \frac{145}{28}.

$$-\frac{117}{28}\times \frac{28}{145}$$

Multiply -\frac{117}{28} times \frac{28}{145} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-117\times 28}{28\times 145}$$

Cancel out 28 in both numerator and denominator.

$$\frac{-117}{145}$$

Fraction \frac{-117}{145} can be rewritten as -\frac{117}{145} by extracting the negative sign.

$$-\frac{117}{145}$$

Factor

$$-\frac{117}{145} = -0.8068965517241379$$