Solve -0.6(1.6*(-9/13)-5)-(2.9*(-9/13)-8)-4(4-1.5*(-9/13)

$$-0.6(1.6 \times (- \frac{ 9 }{ 13 } )-5)-(2.9 \times (- \frac{ 9 }{ 13 } )-8)-4(4-1.5 \times (- \frac{ 9 }{ 13 } )$$

Evaluate

$$-\frac{4213}{650}\approx -6.481538462$$

Solution Steps

Convert decimal number 1.6 to fraction \frac{16}{10}. Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$-0.6\left(\frac{8}{5}\left(-\frac{9}{13}\right)-5\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Multiply \frac{8}{5} times -\frac{9}{13} by multiplying numerator times numerator and denominator times denominator.

$$-0.6\left(\frac{8\left(-9\right)}{5\times 13}-5\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Do the multiplications in the fraction \frac{8\left(-9\right)}{5\times 13}.

$$-0.6\left(\frac{-72}{65}-5\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Fraction \frac{-72}{65} can be rewritten as -\frac{72}{65} by extracting the negative sign.

$$-0.6\left(-\frac{72}{65}-5\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Convert 5 to fraction \frac{325}{65}.

$$-0.6\left(-\frac{72}{65}-\frac{325}{65}\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Since -\frac{72}{65} and \frac{325}{65} have the same denominator, subtract them by subtracting their numerators.

$$-0.6\times \frac{-72-325}{65}-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Subtract 325 from -72 to get -397.

$$-0.6\left(-\frac{397}{65}\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Convert decimal number -0.6 to fraction -\frac{6}{10}. Reduce the fraction -\frac{6}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{5}\left(-\frac{397}{65}\right)-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Multiply -\frac{3}{5} times -\frac{397}{65} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-397\right)}{5\times 65}-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Do the multiplications in the fraction \frac{-3\left(-397\right)}{5\times 65}.

$$\frac{1191}{325}-\left(2.9\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Convert decimal number 2.9 to fraction \frac{29}{10}.

$$\frac{1191}{325}-\left(\frac{29}{10}\left(-\frac{9}{13}\right)-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Multiply \frac{29}{10} times -\frac{9}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1191}{325}-\left(\frac{29\left(-9\right)}{10\times 13}-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Do the multiplications in the fraction \frac{29\left(-9\right)}{10\times 13}.

$$\frac{1191}{325}-\left(\frac{-261}{130}-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Fraction \frac{-261}{130} can be rewritten as -\frac{261}{130} by extracting the negative sign.

$$\frac{1191}{325}-\left(-\frac{261}{130}-8\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Convert 8 to fraction \frac{1040}{130}.

$$\frac{1191}{325}-\left(-\frac{261}{130}-\frac{1040}{130}\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Since -\frac{261}{130} and \frac{1040}{130} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1191}{325}-\frac{-261-1040}{130}-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Subtract 1040 from -261 to get -1301.

$$\frac{1191}{325}-\left(-\frac{1301}{130}\right)-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

The opposite of -\frac{1301}{130} is \frac{1301}{130}.

$$\frac{1191}{325}+\frac{1301}{130}-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Least common multiple of 325 and 130 is 650. Convert \frac{1191}{325} and \frac{1301}{130} to fractions with denominator 650.

$$\frac{2382}{650}+\frac{6505}{650}-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Since \frac{2382}{650} and \frac{6505}{650} have the same denominator, add them by adding their numerators.

$$\frac{2382+6505}{650}-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Add 2382 and 6505 to get 8887.

$$\frac{8887}{650}-4\left(4-1.5\left(-\frac{9}{13}\right)\right)$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{8887}{650}-4\left(4-\frac{3}{2}\left(-\frac{9}{13}\right)\right)$$

Multiply \frac{3}{2} times -\frac{9}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8887}{650}-4\left(4-\frac{3\left(-9\right)}{2\times 13}\right)$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{2\times 13}.

$$\frac{8887}{650}-4\left(4-\frac{-27}{26}\right)$$

Fraction \frac{-27}{26} can be rewritten as -\frac{27}{26} by extracting the negative sign.

$$\frac{8887}{650}-4\left(4-\left(-\frac{27}{26}\right)\right)$$

The opposite of -\frac{27}{26} is \frac{27}{26}.

$$\frac{8887}{650}-4\left(4+\frac{27}{26}\right)$$

Convert 4 to fraction \frac{104}{26}.

$$\frac{8887}{650}-4\left(\frac{104}{26}+\frac{27}{26}\right)$$

Since \frac{104}{26} and \frac{27}{26} have the same denominator, add them by adding their numerators.

$$\frac{8887}{650}-4\times \frac{104+27}{26}$$

Add 104 and 27 to get 131.

$$\frac{8887}{650}-4\times \frac{131}{26}$$

Express 4\times \frac{131}{26} as a single fraction.

$$\frac{8887}{650}-\frac{4\times 131}{26}$$

Multiply 4 and 131 to get 524.

$$\frac{8887}{650}-\frac{524}{26}$$

Reduce the fraction \frac{524}{26} to lowest terms by extracting and canceling out 2.

$$\frac{8887}{650}-\frac{262}{13}$$

Least common multiple of 650 and 13 is 650. Convert \frac{8887}{650} and \frac{262}{13} to fractions with denominator 650.

$$\frac{8887}{650}-\frac{13100}{650}$$

Since \frac{8887}{650} and \frac{13100}{650} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8887-13100}{650}$$

Subtract 13100 from 8887 to get -4213.

$$-\frac{4213}{650}$$

Factor

$$-\frac{4213}{650} = -6\frac{313}{650} = -6.481538461538461$$