Solve 47/12*(-13/11)-(-11/15)*(-119/21)*(-frac{45}{64})

$$4 \frac{ 7 }{ 12 } \times (-1 \frac{ 3 }{ 11 } )-(-1 \frac{ 1 }{ 15 } ) \times (-1 \frac{ 19 }{ 21 } ) \times (- \frac{ 45 }{ 64 } )$$

Evaluate

$$-\frac{185}{42}\approx -4.404761905$$

Solution Steps

Multiply 4 and 12 to get 48.

$$\frac{48+7}{12}\left(-\frac{1\times 11+3}{11}\right)-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Add 48 and 7 to get 55.

$$\frac{55}{12}\left(-\frac{1\times 11+3}{11}\right)-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Multiply 1 and 11 to get 11.

$$\frac{55}{12}\left(-\frac{11+3}{11}\right)-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Add 11 and 3 to get 14.

$$\frac{55}{12}\left(-\frac{14}{11}\right)-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Multiply \frac{55}{12} times -\frac{14}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55\left(-14\right)}{12\times 11}-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Do the multiplications in the fraction \frac{55\left(-14\right)}{12\times 11}.

$$\frac{-770}{132}-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Reduce the fraction \frac{-770}{132} to lowest terms by extracting and canceling out 22.

$$-\frac{35}{6}-\left(-\frac{1\times 15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Multiply 1 and 15 to get 15.

$$-\frac{35}{6}-\left(-\frac{15+1}{15}\right)\left(-\frac{1\times 21+19}{21}\right)\left(-\frac{45}{64}\right)$$

Add 15 and 1 to get 16.

$$-\frac{35}{6}-\left(-\frac{16}{15}\left(-\frac{21+19}{21}\right)\left(-\frac{45}{64}\right)\right)$$

Add 21 and 19 to get 40.

$$-\frac{35}{6}-\left(-\frac{16}{15}\left(-\frac{40}{21}\right)\left(-\frac{45}{64}\right)\right)$$

Multiply -\frac{16}{15} times -\frac{40}{21} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{35}{6}-\frac{-16\left(-40\right)}{15\times 21}\left(-\frac{45}{64}\right)$$

Do the multiplications in the fraction \frac{-16\left(-40\right)}{15\times 21}.

$$-\frac{35}{6}-\frac{640}{315}\left(-\frac{45}{64}\right)$$

Reduce the fraction \frac{640}{315} to lowest terms by extracting and canceling out 5.

$$-\frac{35}{6}-\frac{128}{63}\left(-\frac{45}{64}\right)$$

Multiply \frac{128}{63} times -\frac{45}{64} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{35}{6}-\frac{128\left(-45\right)}{63\times 64}$$

Do the multiplications in the fraction \frac{128\left(-45\right)}{63\times 64}.

$$-\frac{35}{6}-\frac{-5760}{4032}$$

Reduce the fraction \frac{-5760}{4032} to lowest terms by extracting and canceling out 576.

$$-\frac{35}{6}-\left(-\frac{10}{7}\right)$$

The opposite of -\frac{10}{7} is \frac{10}{7}.

$$-\frac{35}{6}+\frac{10}{7}$$

Least common multiple of 6 and 7 is 42. Convert -\frac{35}{6} and \frac{10}{7} to fractions with denominator 42.

$$-\frac{245}{42}+\frac{60}{42}$$

Since -\frac{245}{42} and \frac{60}{42} have the same denominator, add them by adding their numerators.

$$\frac{-245+60}{42}$$

Add -245 and 60 to get -185.

$$-\frac{185}{42}$$

Factor

$$-\frac{185}{42} = -4\frac{17}{42} = -4.404761904761905$$