Solve (21/5*0.876-5/8)*10/81*(14/100-0.34)

$$( 2 \frac { 1 } { 5 } \cdot 0.876 - \frac { 5 } { 8 } ) \cdot \frac { 10 } { 81 } \cdot ( \frac { 14 } { 100 } - 0.34 )$$

Evaluate

$$-\frac{6511}{202500}\approx -0.032153086$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\left(\frac{10+1}{5}\times 0.876-\frac{5}{8}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Add 10 and 1 to get 11.

$$\left(\frac{11}{5}\times 0.876-\frac{5}{8}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Convert decimal number 0.876 to fraction \frac{876}{1000}. Reduce the fraction \frac{876}{1000} to lowest terms by extracting and canceling out 4.

$$\left(\frac{11}{5}\times \frac{219}{250}-\frac{5}{8}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Multiply \frac{11}{5} times \frac{219}{250} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{11\times 219}{5\times 250}-\frac{5}{8}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Do the multiplications in the fraction \frac{11\times 219}{5\times 250}.

$$\left(\frac{2409}{1250}-\frac{5}{8}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Least common multiple of 1250 and 8 is 5000. Convert \frac{2409}{1250} and \frac{5}{8} to fractions with denominator 5000.

$$\left(\frac{9636}{5000}-\frac{3125}{5000}\right)\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Since \frac{9636}{5000} and \frac{3125}{5000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9636-3125}{5000}\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Subtract 3125 from 9636 to get 6511.

$$\frac{6511}{5000}\times \frac{10}{81}\left(\frac{14}{100}-0.34\right)$$

Multiply \frac{6511}{5000} times \frac{10}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6511\times 10}{5000\times 81}\left(\frac{14}{100}-0.34\right)$$

Do the multiplications in the fraction \frac{6511\times 10}{5000\times 81}.

$$\frac{65110}{405000}\left(\frac{14}{100}-0.34\right)$$

Reduce the fraction \frac{65110}{405000} to lowest terms by extracting and canceling out 10.

$$\frac{6511}{40500}\left(\frac{14}{100}-0.34\right)$$

Reduce the fraction \frac{14}{100} to lowest terms by extracting and canceling out 2.

$$\frac{6511}{40500}\left(\frac{7}{50}-0.34\right)$$

Convert decimal number 0.34 to fraction \frac{34}{100}. Reduce the fraction \frac{34}{100} to lowest terms by extracting and canceling out 2.

$$\frac{6511}{40500}\left(\frac{7}{50}-\frac{17}{50}\right)$$

Since \frac{7}{50} and \frac{17}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6511}{40500}\times \frac{7-17}{50}$$

Subtract 17 from 7 to get -10.

$$\frac{6511}{40500}\times \frac{-10}{50}$$

Reduce the fraction \frac{-10}{50} to lowest terms by extracting and canceling out 10.

$$\frac{6511}{40500}\left(-\frac{1}{5}\right)$$

Multiply \frac{6511}{40500} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6511\left(-1\right)}{40500\times 5}$$

Do the multiplications in the fraction \frac{6511\left(-1\right)}{40500\times 5}.

$$\frac{-6511}{202500}$$

Fraction \frac{-6511}{202500} can be rewritten as -\frac{6511}{202500} by extracting the negative sign.

$$-\frac{6511}{202500}$$

Factor

$$-\frac{6511}{202500} = -0.032153086419753084$$