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

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

Evaluate

$$\frac{29}{6}\approx 4.833333333$$

Solution Steps

Multiply 8 and 3 to get 24.

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

Add 24 and 2 to get 26.

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

Multiply 4 and 2 to get 8.

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

Add 8 and 1 to get 9.

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

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

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

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

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

Subtract 27 from 52 to get 25.

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

Multiply 5 and 4 to get 20.

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

Add 20 and 3 to get 23.

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

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

$$\frac{50}{12}+\frac{69}{12}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

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

$$\frac{50+69}{12}-\frac{1\times 3+1}{3}-\left(\frac{3\times 6+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

Add 50 and 69 to get 119.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

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

$$\frac{119}{12}-\frac{16}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

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

$$\frac{119-16}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

Subtract 16 from 119 to get 103.

$$\frac{103}{12}-\left(\frac{3\times 6+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

Multiply 3 and 6 to get 18.

$$\frac{103}{12}-\left(\frac{18+1}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

Add 18 and 1 to get 19.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{2\times 4+1}{4}-\frac{1\times 3+2}{3}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{8+1}{4}-\frac{1\times 3+2}{3}\right)$$

Add 8 and 1 to get 9.

$$\frac{103}{12}-\left(\frac{19}{6}+\frac{9}{4}-\frac{1\times 3+2}{3}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{19}{6} and \frac{9}{4} to fractions with denominator 12.

$$\frac{103}{12}-\left(\frac{38}{12}+\frac{27}{12}-\frac{1\times 3+2}{3}\right)$$

Since \frac{38}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{103}{12}-\left(\frac{38+27}{12}-\frac{1\times 3+2}{3}\right)$$

Add 38 and 27 to get 65.

$$\frac{103}{12}-\left(\frac{65}{12}-\frac{1\times 3+2}{3}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{103}{12}-\left(\frac{65}{12}-\frac{3+2}{3}\right)$$

Add 3 and 2 to get 5.

$$\frac{103}{12}-\left(\frac{65}{12}-\frac{5}{3}\right)$$

Least common multiple of 12 and 3 is 12. Convert \frac{65}{12} and \frac{5}{3} to fractions with denominator 12.

$$\frac{103}{12}-\left(\frac{65}{12}-\frac{20}{12}\right)$$

Since \frac{65}{12} and \frac{20}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103}{12}-\frac{65-20}{12}$$

Subtract 20 from 65 to get 45.

$$\frac{103}{12}-\frac{45}{12}$$

Since \frac{103}{12} and \frac{45}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103-45}{12}$$

Subtract 45 from 103 to get 58.

$$\frac{58}{12}$$

Reduce the fraction \frac{58}{12} to lowest terms by extracting and canceling out 2.

$$\frac{29}{6}$$

Factor

$$\frac{29}{2 \cdot 3} = 4\frac{5}{6} = 4.833333333333333$$