Solve (82/3-41/2)+(53/4-11/3)-(3frac{1}{6}+2frac{7}{17})

$$( 8 \frac { 2 } { 3 } - 4 \frac { 1 } { 2 } ) + ( 5 \frac { 3 } { 4 } - 1 \frac { 1 } { 3 } ) - ( 3 \frac { 1 } { 6 } + 2 \frac { 7 } { 17 } )$$

Evaluate

$$\frac{613}{204}\approx 3.004901961$$

Solution Steps

Multiply 8 and 3 to get 24.

$$\frac{24+2}{3}-\frac{4\times 2+1}{2}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 24 and 2 to get 26.

$$\frac{26}{3}-\frac{4\times 2+1}{2}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Multiply 4 and 2 to get 8.

$$\frac{26}{3}-\frac{8+1}{2}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 8 and 1 to get 9.

$$\frac{26}{3}-\frac{9}{2}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{26}{3} and \frac{9}{2} to fractions with denominator 6.

$$\frac{52}{6}-\frac{27}{6}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Since \frac{52}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-27}{6}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Subtract 27 from 52 to get 25.

$$\frac{25}{6}+\frac{5\times 4+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Multiply 5 and 4 to get 20.

$$\frac{25}{6}+\frac{20+3}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 20 and 3 to get 23.

$$\frac{25}{6}+\frac{23}{4}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{25}{6} and \frac{23}{4} to fractions with denominator 12.

$$\frac{50}{12}+\frac{69}{12}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Since \frac{50}{12} and \frac{69}{12} have the same denominator, add them by adding their numerators.

$$\frac{50+69}{12}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 50 and 69 to get 119.

$$\frac{119}{12}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{119}{12}-\frac{3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 3 and 1 to get 4.

$$\frac{119}{12}-\frac{4}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Least common multiple of 12 and 3 is 12. Convert \frac{119}{12} and \frac{4}{3} to fractions with denominator 12.

$$\frac{119}{12}-\frac{16}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Since \frac{119}{12} and \frac{16}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{119-16}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Subtract 16 from 119 to get 103.

$$\frac{103}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 17+7}{17}\right)$$

Multiply 3 and 6 to get 18.

$$\frac{103}{12}-\left(\frac{18+1}{6}+\frac{2\times 17+7}{17}\right)$$

Add 18 and 1 to get 19.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{2\times 17+7}{17}\right)$$

Multiply 2 and 17 to get 34.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{34+7}{17}\right)$$

Add 34 and 7 to get 41.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{41}{17}\right)$$

Least common multiple of 6 and 17 is 102. Convert \frac{19}{6} and \frac{41}{17} to fractions with denominator 102.

$$\frac{103}{12}-\left(\frac{323}{102}+\frac{246}{102}\right)$$

Since \frac{323}{102} and \frac{246}{102} have the same denominator, add them by adding their numerators.

$$\frac{103}{12}-\frac{323+246}{102}$$

Add 323 and 246 to get 569.

$$\frac{103}{12}-\frac{569}{102}$$

Least common multiple of 12 and 102 is 204. Convert \frac{103}{12} and \frac{569}{102} to fractions with denominator 204.

$$\frac{1751}{204}-\frac{1138}{204}$$

Since \frac{1751}{204} and \frac{1138}{204} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1751-1138}{204}$$

Subtract 1138 from 1751 to get 613.

$$\frac{613}{204}$$

Factor

$$\frac{613}{2 ^ {2} \cdot 3 \cdot 17} = 3\frac{1}{204} = 3.0049019607843137$$