Solve (3/87-1/5)*5/8-3/87*(frac{5}{8}-frac{87}{2})

$$( \frac { 3 } { 87 } - \frac { 1 } { 5 } ) \cdot \frac { 5 } { 8 } - \frac { 3 } { 87 } \cdot ( \frac { 5 } { 8 } - \frac { 87 } { 2 } )$$

Evaluate

$$\frac{11}{8}=1.375$$

Solution Steps

Reduce the fraction \frac{3}{87} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{29}-\frac{1}{5}\right)\times \frac{5}{8}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Least common multiple of 29 and 5 is 145. Convert \frac{1}{29} and \frac{1}{5} to fractions with denominator 145.

$$\left(\frac{5}{145}-\frac{29}{145}\right)\times \frac{5}{8}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Since \frac{5}{145} and \frac{29}{145} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-29}{145}\times \frac{5}{8}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Subtract 29 from 5 to get -24.

$$-\frac{24}{145}\times \frac{5}{8}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Multiply -\frac{24}{145} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-24\times 5}{145\times 8}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Do the multiplications in the fraction \frac{-24\times 5}{145\times 8}.

$$\frac{-120}{1160}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Reduce the fraction \frac{-120}{1160} to lowest terms by extracting and canceling out 40.

$$-\frac{3}{29}-\frac{3}{87}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Reduce the fraction \frac{3}{87} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{29}-\frac{1}{29}\left(\frac{5}{8}-\frac{87}{2}\right)$$

Least common multiple of 8 and 2 is 8. Convert \frac{5}{8} and \frac{87}{2} to fractions with denominator 8.

$$-\frac{3}{29}-\frac{1}{29}\left(\frac{5}{8}-\frac{348}{8}\right)$$

Since \frac{5}{8} and \frac{348}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{29}-\frac{1}{29}\times \frac{5-348}{8}$$

Subtract 348 from 5 to get -343.

$$-\frac{3}{29}-\frac{1}{29}\left(-\frac{343}{8}\right)$$

Multiply \frac{1}{29} times -\frac{343}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{29}-\frac{1\left(-343\right)}{29\times 8}$$

Do the multiplications in the fraction \frac{1\left(-343\right)}{29\times 8}.

$$-\frac{3}{29}-\frac{-343}{232}$$

Fraction \frac{-343}{232} can be rewritten as -\frac{343}{232} by extracting the negative sign.

$$-\frac{3}{29}-\left(-\frac{343}{232}\right)$$

The opposite of -\frac{343}{232} is \frac{343}{232}.

$$-\frac{3}{29}+\frac{343}{232}$$

Least common multiple of 29 and 232 is 232. Convert -\frac{3}{29} and \frac{343}{232} to fractions with denominator 232.

$$-\frac{24}{232}+\frac{343}{232}$$

Since -\frac{24}{232} and \frac{343}{232} have the same denominator, add them by adding their numerators.

$$\frac{-24+343}{232}$$

Add -24 and 343 to get 319.

$$\frac{319}{232}$$

Reduce the fraction \frac{319}{232} to lowest terms by extracting and canceling out 29.

$$\frac{11}{8}$$

Factor

$$\frac{11}{2 ^ {3}} = 1\frac{3}{8} = 1.375$$