Solve 4317/10(-5/3-4/5+5/7-40)

$$431 \frac { 7 } { 10 } ( - \frac { 5 } { 3 } - \frac { 4 } { 5 } + \frac { 5 } { 7 } - 40 )$$

Evaluate

$$-\frac{3154288}{175}\approx -18024.502857143$$

Solution Steps

Multiply 431 and 10 to get 4310.

$$\frac{4310+7}{10}\left(-\frac{5}{3}-\frac{4}{5}+\frac{5}{7}-40\right)$$

Add 4310 and 7 to get 4317.

$$\frac{4317}{10}\left(-\frac{5}{3}-\frac{4}{5}+\frac{5}{7}-40\right)$$

Least common multiple of 3 and 5 is 15. Convert -\frac{5}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{4317}{10}\left(-\frac{25}{15}-\frac{12}{15}+\frac{5}{7}-40\right)$$

Since -\frac{25}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4317}{10}\left(\frac{-25-12}{15}+\frac{5}{7}-40\right)$$

Subtract 12 from -25 to get -37.

$$\frac{4317}{10}\left(-\frac{37}{15}+\frac{5}{7}-40\right)$$

Least common multiple of 15 and 7 is 105. Convert -\frac{37}{15} and \frac{5}{7} to fractions with denominator 105.

$$\frac{4317}{10}\left(-\frac{259}{105}+\frac{75}{105}-40\right)$$

Since -\frac{259}{105} and \frac{75}{105} have the same denominator, add them by adding their numerators.

$$\frac{4317}{10}\left(\frac{-259+75}{105}-40\right)$$

Add -259 and 75 to get -184.

$$\frac{4317}{10}\left(-\frac{184}{105}-40\right)$$

Convert 40 to fraction \frac{4200}{105}.

$$\frac{4317}{10}\left(-\frac{184}{105}-\frac{4200}{105}\right)$$

Since -\frac{184}{105} and \frac{4200}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4317}{10}\times \frac{-184-4200}{105}$$

Subtract 4200 from -184 to get -4384.

$$\frac{4317}{10}\left(-\frac{4384}{105}\right)$$

Multiply \frac{4317}{10} times -\frac{4384}{105} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4317\left(-4384\right)}{10\times 105}$$

Do the multiplications in the fraction \frac{4317\left(-4384\right)}{10\times 105}.

$$\frac{-18925728}{1050}$$

Reduce the fraction \frac{-18925728}{1050} to lowest terms by extracting and canceling out 6.

$$-\frac{3154288}{175}$$

Factor

$$-\frac{3154288}{175} = -18024\frac{88}{175} = -18024.502857142856$$