Solve (-5/2):(-4/3)-13/8:(-4/3)

$$( - \frac { 5 } { 2 } ) : ( - \frac { 4 } { 3 } ) - \frac { 13 } { 8 } : ( - \frac { 4 } { 3 } )$$

Evaluate

$$\frac{99}{32}=3.09375$$

Solution Steps

Divide -\frac{5}{2} by -\frac{4}{3} by multiplying -\frac{5}{2} by the reciprocal of -\frac{4}{3}.

$$-\frac{5}{2}\left(-\frac{3}{4}\right)-\frac{\frac{13}{8}}{-\frac{4}{3}}$$

Multiply -\frac{5}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-3\right)}{2\times 4}-\frac{\frac{13}{8}}{-\frac{4}{3}}$$

Do the multiplications in the fraction \frac{-5\left(-3\right)}{2\times 4}.

$$\frac{15}{8}-\frac{\frac{13}{8}}{-\frac{4}{3}}$$

Divide \frac{13}{8} by -\frac{4}{3} by multiplying \frac{13}{8} by the reciprocal of -\frac{4}{3}.

$$\frac{15}{8}-\frac{13}{8}\left(-\frac{3}{4}\right)$$

Multiply \frac{13}{8} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{8}-\frac{13\left(-3\right)}{8\times 4}$$

Do the multiplications in the fraction \frac{13\left(-3\right)}{8\times 4}.

$$\frac{15}{8}-\frac{-39}{32}$$

Fraction \frac{-39}{32} can be rewritten as -\frac{39}{32} by extracting the negative sign.

$$\frac{15}{8}-\left(-\frac{39}{32}\right)$$

The opposite of -\frac{39}{32} is \frac{39}{32}.

$$\frac{15}{8}+\frac{39}{32}$$

Least common multiple of 8 and 32 is 32. Convert \frac{15}{8} and \frac{39}{32} to fractions with denominator 32.

$$\frac{60}{32}+\frac{39}{32}$$

Since \frac{60}{32} and \frac{39}{32} have the same denominator, add them by adding their numerators.

$$\frac{60+39}{32}$$

Add 60 and 39 to get 99.

$$\frac{99}{32}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 ^ {5}} = 3\frac{3}{32} = 3.09375$$