Solve 3/4:(2/5-3)+1/4:(-2/4)=

$$\frac { 3 } { 4 } : ( \frac { 2 } { 5 } - 3 ) + \frac { 1 } { 4 } : ( - \frac { 2 } { 4 } ) =$$

Evaluate

$$-\frac{41}{52}\approx -0.788461538$$

Solution Steps

Convert 3 to fraction \frac{15}{5}.

$$\frac{\frac{3}{4}}{\frac{2}{5}-\frac{15}{5}}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Since \frac{2}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{2-15}{5}}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Subtract 15 from 2 to get -13.

$$\frac{\frac{3}{4}}{-\frac{13}{5}}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Divide \frac{3}{4} by -\frac{13}{5} by multiplying \frac{3}{4} by the reciprocal of -\frac{13}{5}.

$$\frac{3}{4}\left(-\frac{5}{13}\right)+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Multiply \frac{3}{4} times -\frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-5\right)}{4\times 13}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{4\times 13}.

$$\frac{-15}{52}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

Fraction \frac{-15}{52} can be rewritten as -\frac{15}{52} by extracting the negative sign.

$$-\frac{15}{52}+\frac{\frac{1}{4}}{-\frac{2}{4}}$$

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

$$-\frac{15}{52}+\frac{\frac{1}{4}}{-\frac{1}{2}}$$

Divide \frac{1}{4} by -\frac{1}{2} by multiplying \frac{1}{4} by the reciprocal of -\frac{1}{2}.

$$-\frac{15}{52}+\frac{1}{4}\left(-2\right)$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

$$-\frac{15}{52}+\frac{-2}{4}$$

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

$$-\frac{15}{52}-\frac{1}{2}$$

Least common multiple of 52 and 2 is 52. Convert -\frac{15}{52} and \frac{1}{2} to fractions with denominator 52.

$$-\frac{15}{52}-\frac{26}{52}$$

Since -\frac{15}{52} and \frac{26}{52} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-26}{52}$$

Subtract 26 from -15 to get -41.

$$-\frac{41}{52}$$

Factor

$$-\frac{41}{52} = -0.7884615384615384$$