Solve (-51/16+11/8)*(-5/6-3/14)

$$( - 5 \frac { 1 } { 16 } + 1 \frac { 1 } { 8 } ) \cdot ( - \frac { 5 } { 6 } - \frac { 3 } { 14 } )$$

Evaluate

$$\frac{33}{8}=4.125$$

Solution Steps

Multiply 5 and 16 to get 80.

$$\left(-\frac{80+1}{16}+\frac{1\times 8+1}{8}\right)\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Add 80 and 1 to get 81.

$$\left(-\frac{81}{16}+\frac{1\times 8+1}{8}\right)\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Multiply 1 and 8 to get 8.

$$\left(-\frac{81}{16}+\frac{8+1}{8}\right)\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Add 8 and 1 to get 9.

$$\left(-\frac{81}{16}+\frac{9}{8}\right)\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Least common multiple of 16 and 8 is 16. Convert -\frac{81}{16} and \frac{9}{8} to fractions with denominator 16.

$$\left(-\frac{81}{16}+\frac{18}{16}\right)\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Since -\frac{81}{16} and \frac{18}{16} have the same denominator, add them by adding their numerators.

$$\frac{-81+18}{16}\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Add -81 and 18 to get -63.

$$-\frac{63}{16}\left(-\frac{5}{6}-\frac{3}{14}\right)$$

Least common multiple of 6 and 14 is 42. Convert -\frac{5}{6} and \frac{3}{14} to fractions with denominator 42.

$$-\frac{63}{16}\left(-\frac{35}{42}-\frac{9}{42}\right)$$

Since -\frac{35}{42} and \frac{9}{42} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{63}{16}\times \frac{-35-9}{42}$$

Subtract 9 from -35 to get -44.

$$-\frac{63}{16}\times \frac{-44}{42}$$

Reduce the fraction \frac{-44}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{63}{16}\left(-\frac{22}{21}\right)$$

Multiply -\frac{63}{16} times -\frac{22}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\left(-22\right)}{16\times 21}$$

Do the multiplications in the fraction \frac{-63\left(-22\right)}{16\times 21}.

$$\frac{1386}{336}$$

Reduce the fraction \frac{1386}{336} to lowest terms by extracting and canceling out 42.

$$\frac{33}{8}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {3}} = 4\frac{1}{8} = 4.125$$