Solve [2.08(3)-25/6]-(23/4-31/8-21/6)

$$[ 2.08 ( 3 ) - 2 \frac { 5 } { 6 } ] - ( 2 \frac { 3 } { 4 } - 3 \frac { 1 } { 8 } - 2 \frac { 1 } { 6 } )$$

Evaluate

$$\frac{3569}{600}\approx 5.948333333$$

Solution Steps

Multiply 2.08 and 3 to get 6.24.

$$6.24-\frac{2\times 6+5}{6}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Multiply 2 and 6 to get 12.

$$6.24-\frac{12+5}{6}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Add 12 and 5 to get 17.

$$6.24-\frac{17}{6}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Convert decimal number 6.24 to fraction \frac{624}{100}. Reduce the fraction \frac{624}{100} to lowest terms by extracting and canceling out 4.

$$\frac{156}{25}-\frac{17}{6}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Least common multiple of 25 and 6 is 150. Convert \frac{156}{25} and \frac{17}{6} to fractions with denominator 150.

$$\frac{936}{150}-\frac{425}{150}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Since \frac{936}{150} and \frac{425}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{936-425}{150}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Subtract 425 from 936 to get 511.

$$\frac{511}{150}-\left(\frac{2\times 4+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{511}{150}-\left(\frac{8+3}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Add 8 and 3 to get 11.

$$\frac{511}{150}-\left(\frac{11}{4}-\frac{3\times 8+1}{8}-\frac{2\times 6+1}{6}\right)$$

Multiply 3 and 8 to get 24.

$$\frac{511}{150}-\left(\frac{11}{4}-\frac{24+1}{8}-\frac{2\times 6+1}{6}\right)$$

Add 24 and 1 to get 25.

$$\frac{511}{150}-\left(\frac{11}{4}-\frac{25}{8}-\frac{2\times 6+1}{6}\right)$$

Least common multiple of 4 and 8 is 8. Convert \frac{11}{4} and \frac{25}{8} to fractions with denominator 8.

$$\frac{511}{150}-\left(\frac{22}{8}-\frac{25}{8}-\frac{2\times 6+1}{6}\right)$$

Since \frac{22}{8} and \frac{25}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{511}{150}-\left(\frac{22-25}{8}-\frac{2\times 6+1}{6}\right)$$

Subtract 25 from 22 to get -3.

$$\frac{511}{150}-\left(-\frac{3}{8}-\frac{2\times 6+1}{6}\right)$$

Multiply 2 and 6 to get 12.

$$\frac{511}{150}-\left(-\frac{3}{8}-\frac{12+1}{6}\right)$$

Add 12 and 1 to get 13.

$$\frac{511}{150}-\left(-\frac{3}{8}-\frac{13}{6}\right)$$

Least common multiple of 8 and 6 is 24. Convert -\frac{3}{8} and \frac{13}{6} to fractions with denominator 24.

$$\frac{511}{150}-\left(-\frac{9}{24}-\frac{52}{24}\right)$$

Since -\frac{9}{24} and \frac{52}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{511}{150}-\frac{-9-52}{24}$$

Subtract 52 from -9 to get -61.

$$\frac{511}{150}-\left(-\frac{61}{24}\right)$$

The opposite of -\frac{61}{24} is \frac{61}{24}.

$$\frac{511}{150}+\frac{61}{24}$$

Least common multiple of 150 and 24 is 600. Convert \frac{511}{150} and \frac{61}{24} to fractions with denominator 600.

$$\frac{2044}{600}+\frac{1525}{600}$$

Since \frac{2044}{600} and \frac{1525}{600} have the same denominator, add them by adding their numerators.

$$\frac{2044+1525}{600}$$

Add 2044 and 1525 to get 3569.

$$\frac{3569}{600}$$

Factor

$$\frac{43 \cdot 83}{3 \cdot 2 ^ {3} \cdot 5 ^ {2}} = 5\frac{569}{600} = 5.948333333333333$$