Solve 7/4left(-8/5-9/8-5/6+frac{4}{3}right)

$$\frac{ 7 }{ 4 } \left( - \frac{ 8 }{ 5 } - \frac{ 9 }{ 8 } - \frac{ 5 }{ 6 } + \frac{ 4 }{ 3 } \right)$$

Evaluate

$$-\frac{623}{160}=-3.89375$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert -\frac{8}{5} and \frac{9}{8} to fractions with denominator 40.

$$\frac{7}{4}\left(-\frac{64}{40}-\frac{45}{40}-\frac{5}{6}+\frac{4}{3}\right)$$

Since -\frac{64}{40} and \frac{45}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}\left(\frac{-64-45}{40}-\frac{5}{6}+\frac{4}{3}\right)$$

Subtract 45 from -64 to get -109.

$$\frac{7}{4}\left(-\frac{109}{40}-\frac{5}{6}+\frac{4}{3}\right)$$

Least common multiple of 40 and 6 is 120. Convert -\frac{109}{40} and \frac{5}{6} to fractions with denominator 120.

$$\frac{7}{4}\left(-\frac{327}{120}-\frac{100}{120}+\frac{4}{3}\right)$$

Since -\frac{327}{120} and \frac{100}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}\left(\frac{-327-100}{120}+\frac{4}{3}\right)$$

Subtract 100 from -327 to get -427.

$$\frac{7}{4}\left(-\frac{427}{120}+\frac{4}{3}\right)$$

Least common multiple of 120 and 3 is 120. Convert -\frac{427}{120} and \frac{4}{3} to fractions with denominator 120.

$$\frac{7}{4}\left(-\frac{427}{120}+\frac{160}{120}\right)$$

Since -\frac{427}{120} and \frac{160}{120} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}\times \frac{-427+160}{120}$$

Add -427 and 160 to get -267.

$$\frac{7}{4}\times \frac{-267}{120}$$

Reduce the fraction \frac{-267}{120} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}\left(-\frac{89}{40}\right)$$

Multiply \frac{7}{4} times -\frac{89}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-89\right)}{4\times 40}$$

Do the multiplications in the fraction \frac{7\left(-89\right)}{4\times 40}.

$$\frac{-623}{160}$$

Fraction \frac{-623}{160} can be rewritten as -\frac{623}{160} by extracting the negative sign.

$$-\frac{623}{160}$$

Factor

$$-\frac{623}{160} = -3\frac{143}{160} = -3.89375$$