Solve (5/16-6/4-8)(5/16-6/4-5)=

$$( \frac { 5 } { 16 } - \frac { 6 } { 4 } - 8 ) ( \frac { 5 } { 16 } - \frac { 6 } { 4 } - 5 ) =$$

Evaluate

$$\frac{14553}{256}=56.84765625$$

Solution Steps

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{5}{16}-\frac{3}{2}-8\right)\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Least common multiple of 16 and 2 is 16. Convert \frac{5}{16} and \frac{3}{2} to fractions with denominator 16.

$$\left(\frac{5}{16}-\frac{24}{16}-8\right)\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Since \frac{5}{16} and \frac{24}{16} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{5-24}{16}-8\right)\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Subtract 24 from 5 to get -19.

$$\left(-\frac{19}{16}-8\right)\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Convert 8 to fraction \frac{128}{16}.

$$\left(-\frac{19}{16}-\frac{128}{16}\right)\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Since -\frac{19}{16} and \frac{128}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-19-128}{16}\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Subtract 128 from -19 to get -147.

$$-\frac{147}{16}\left(\frac{5}{16}-\frac{6}{4}-5\right)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{147}{16}\left(\frac{5}{16}-\frac{3}{2}-5\right)$$

Least common multiple of 16 and 2 is 16. Convert \frac{5}{16} and \frac{3}{2} to fractions with denominator 16.

$$-\frac{147}{16}\left(\frac{5}{16}-\frac{24}{16}-5\right)$$

Since \frac{5}{16} and \frac{24}{16} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{147}{16}\left(\frac{5-24}{16}-5\right)$$

Subtract 24 from 5 to get -19.

$$-\frac{147}{16}\left(-\frac{19}{16}-5\right)$$

Convert 5 to fraction \frac{80}{16}.

$$-\frac{147}{16}\left(-\frac{19}{16}-\frac{80}{16}\right)$$

Since -\frac{19}{16} and \frac{80}{16} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{147}{16}\times \frac{-19-80}{16}$$

Subtract 80 from -19 to get -99.

$$-\frac{147}{16}\left(-\frac{99}{16}\right)$$

Multiply -\frac{147}{16} times -\frac{99}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-147\left(-99\right)}{16\times 16}$$

Do the multiplications in the fraction \frac{-147\left(-99\right)}{16\times 16}.

$$\frac{14553}{256}$$

Factor

$$\frac{3 ^ {3} \cdot 7 ^ {2} \cdot 11}{2 ^ {8}} = 56\frac{217}{256} = 56.84765625$$