Solve 47/12*(-13/11)-(-11/15)*(-45/64)

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

Evaluate

$$-\frac{79}{12}\approx -6.583333333$$

Solution Steps

Multiply 4 and 12 to get 48.

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

Add 48 and 7 to get 55.

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

Multiply 1 and 11 to get 11.

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

Add 11 and 3 to get 14.

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

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

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

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

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

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

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

Multiply 1 and 15 to get 15.

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

Add 15 and 1 to get 16.

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

Multiply -\frac{16}{15} times -\frac{45}{64} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-16\left(-45\right)}{15\times 64}.

$$-\frac{35}{6}-\frac{720}{960}$$

Reduce the fraction \frac{720}{960} to lowest terms by extracting and canceling out 240.

$$-\frac{35}{6}-\frac{3}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{35}{6} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{70}{12}-\frac{9}{12}$$

Since -\frac{70}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-70-9}{12}$$

Subtract 9 from -70 to get -79.

$$-\frac{79}{12}$$

Factor

$$-\frac{79}{12} = -6\frac{7}{12} = -6.583333333333333$$