Solve (4/3+3/4+6/5+1):(-12/5)

$$( \frac { 4 } { 3 } + \frac { 3 } { 4 } + \frac { 6 } { 5 } + 1 ) : ( - \frac { 12 } { 5 } )$$

Evaluate

$$-\frac{257}{144}\approx -1.784722222$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{16}{12}+\frac{9}{12}+\frac{6}{5}+1}{-\frac{12}{5}}$$

Since \frac{16}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+9}{12}+\frac{6}{5}+1}{-\frac{12}{5}}$$

Add 16 and 9 to get 25.

$$\frac{\frac{25}{12}+\frac{6}{5}+1}{-\frac{12}{5}}$$

Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{6}{5} to fractions with denominator 60.

$$\frac{\frac{125}{60}+\frac{72}{60}+1}{-\frac{12}{5}}$$

Since \frac{125}{60} and \frac{72}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{125+72}{60}+1}{-\frac{12}{5}}$$

Add 125 and 72 to get 197.

$$\frac{\frac{197}{60}+1}{-\frac{12}{5}}$$

Convert 1 to fraction \frac{60}{60}.

$$\frac{\frac{197}{60}+\frac{60}{60}}{-\frac{12}{5}}$$

Since \frac{197}{60} and \frac{60}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{197+60}{60}}{-\frac{12}{5}}$$

Add 197 and 60 to get 257.

$$\frac{\frac{257}{60}}{-\frac{12}{5}}$$

Divide \frac{257}{60} by -\frac{12}{5} by multiplying \frac{257}{60} by the reciprocal of -\frac{12}{5}.

$$\frac{257}{60}\left(-\frac{5}{12}\right)$$

Multiply \frac{257}{60} times -\frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{257\left(-5\right)}{60\times 12}$$

Do the multiplications in the fraction \frac{257\left(-5\right)}{60\times 12}.

$$\frac{-1285}{720}$$

Reduce the fraction \frac{-1285}{720} to lowest terms by extracting and canceling out 5.

$$-\frac{257}{144}$$

Factor

$$-\frac{257}{144} = -1\frac{113}{144} = -1.7847222222222223$$