Solve {l}{text{17}(-48)*(12/3-3/8+5/24)}{-(-48)*23/7}

$$\left. \begin{array} { l } { \text { 17 } ( - 48 ) \times ( 1 \frac { 2 } { 3 } - \frac { 3 } { 8 } + \frac { 5 } { 24 } ) } \\ { - ( - 48 ) \times \frac { 23 } { 7 } } \end{array} \right.$$

Evaluate

$$-\frac{7464}{7}\approx -1066.285714286$$

Solution Steps

Multiply 17 and -48 to get -816.

$$-816\left(\frac{3+2}{3}-\frac{3}{8}+\frac{5}{24}\right)-\left(-48\times \frac{23}{7}\right)$$

Add 3 and 2 to get 5.

$$-816\left(\frac{5}{3}-\frac{3}{8}+\frac{5}{24}\right)-\left(-48\times \frac{23}{7}\right)$$

Least common multiple of 3 and 8 is 24. Convert \frac{5}{3} and \frac{3}{8} to fractions with denominator 24.

$$-816\left(\frac{40}{24}-\frac{9}{24}+\frac{5}{24}\right)-\left(-48\times \frac{23}{7}\right)$$

Since \frac{40}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$-816\left(\frac{40-9}{24}+\frac{5}{24}\right)-\left(-48\times \frac{23}{7}\right)$$

Subtract 9 from 40 to get 31.

$$-816\left(\frac{31}{24}+\frac{5}{24}\right)-\left(-48\times \frac{23}{7}\right)$$

Since \frac{31}{24} and \frac{5}{24} have the same denominator, add them by adding their numerators.

$$-816\times \frac{31+5}{24}-\left(-48\times \frac{23}{7}\right)$$

Add 31 and 5 to get 36.

$$-816\times \frac{36}{24}-\left(-48\times \frac{23}{7}\right)$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$-816\times \frac{3}{2}-\left(-48\times \frac{23}{7}\right)$$

Express -816\times \frac{3}{2} as a single fraction.

$$\frac{-816\times 3}{2}-\left(-48\times \frac{23}{7}\right)$$

Multiply -816 and 3 to get -2448.

$$\frac{-2448}{2}-\left(-48\times \frac{23}{7}\right)$$

Divide -2448 by 2 to get -1224.

$$-1224-\left(-48\times \frac{23}{7}\right)$$

Express -48\times \frac{23}{7} as a single fraction.

$$-1224-\frac{-48\times 23}{7}$$

Multiply -48 and 23 to get -1104.

$$-1224-\frac{-1104}{7}$$

Fraction \frac{-1104}{7} can be rewritten as -\frac{1104}{7} by extracting the negative sign.

$$-1224-\left(-\frac{1104}{7}\right)$$

The opposite of -\frac{1104}{7} is \frac{1104}{7}.

$$-1224+\frac{1104}{7}$$

Convert -1224 to fraction -\frac{8568}{7}.

$$-\frac{8568}{7}+\frac{1104}{7}$$

Since -\frac{8568}{7} and \frac{1104}{7} have the same denominator, add them by adding their numerators.

$$\frac{-8568+1104}{7}$$

Add -8568 and 1104 to get -7464.

$$-\frac{7464}{7}$$

Factor

$$-\frac{7464}{7} = -1066\frac{2}{7} = -1066.2857142857142$$