Solve (-9/16)*(-31/3)+8/13div(-12/13)

$$( - \frac { 9 } { 16 } ) \times ( - 3 \frac { 1 } { 3 } ) + \frac { 8 } { 13 } \div ( - \frac { 12 } { 13 } )$$

Evaluate

$$\frac{29}{24}\approx 1.208333333$$

Solution Steps

Multiply 3 and 3 to get 9.

$$-\frac{9}{16}\left(-\frac{9+1}{3}\right)+\frac{\frac{8}{13}}{-\frac{12}{13}}$$

Add 9 and 1 to get 10.

$$-\frac{9}{16}\left(-\frac{10}{3}\right)+\frac{\frac{8}{13}}{-\frac{12}{13}}$$

Multiply -\frac{9}{16} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\left(-10\right)}{16\times 3}+\frac{\frac{8}{13}}{-\frac{12}{13}}$$

Do the multiplications in the fraction \frac{-9\left(-10\right)}{16\times 3}.

$$\frac{90}{48}+\frac{\frac{8}{13}}{-\frac{12}{13}}$$

Reduce the fraction \frac{90}{48} to lowest terms by extracting and canceling out 6.

$$\frac{15}{8}+\frac{\frac{8}{13}}{-\frac{12}{13}}$$

Divide \frac{8}{13} by -\frac{12}{13} by multiplying \frac{8}{13} by the reciprocal of -\frac{12}{13}.

$$\frac{15}{8}+\frac{8}{13}\left(-\frac{13}{12}\right)$$

Multiply \frac{8}{13} times -\frac{13}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{8}+\frac{8\left(-13\right)}{13\times 12}$$

Do the multiplications in the fraction \frac{8\left(-13\right)}{13\times 12}.

$$\frac{15}{8}+\frac{-104}{156}$$

Reduce the fraction \frac{-104}{156} to lowest terms by extracting and canceling out 52.

$$\frac{15}{8}-\frac{2}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{15}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{45}{24}-\frac{16}{24}$$

Since \frac{45}{24} and \frac{16}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-16}{24}$$

Subtract 16 from 45 to get 29.

$$\frac{29}{24}$$

Factor

$$\frac{29}{2 ^ {3} \cdot 3} = 1\frac{5}{24} = 1.2083333333333333$$