Solve 7/6+1/4+3/2+4/8+frac{8}{4}+frac{8}{4}

$$\frac { 7 } { 6 } + \frac { 1 } { 4 } + \frac { 3 } { 2 } + \frac { 4 } { 8 } + \frac { 8 } { 4 } + \frac { 8 } { 4 }$$

Evaluate

$$\frac{89}{12}\approx 7.416666667$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{14}{12}+\frac{3}{12}+\frac{3}{2}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{14}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{14+3}{12}+\frac{3}{2}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Add 14 and 3 to get 17.

$$\frac{17}{12}+\frac{3}{2}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Least common multiple of 12 and 2 is 12. Convert \frac{17}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{17}{12}+\frac{18}{12}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{17}{12} and \frac{18}{12} have the same denominator, add them by adding their numerators.

$$\frac{17+18}{12}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Add 17 and 18 to get 35.

$$\frac{35}{12}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{35}{12}+\frac{1}{2}+\frac{8}{4}+\frac{8}{4}$$

Least common multiple of 12 and 2 is 12. Convert \frac{35}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{35}{12}+\frac{6}{12}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{35}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{35+6}{12}+\frac{8}{4}+\frac{8}{4}$$

Add 35 and 6 to get 41.

$$\frac{41}{12}+\frac{8}{4}+\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$\frac{41}{12}+2+\frac{8}{4}$$

Convert 2 to fraction \frac{24}{12}.

$$\frac{41}{12}+\frac{24}{12}+\frac{8}{4}$$

Since \frac{41}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{41+24}{12}+\frac{8}{4}$$

Add 41 and 24 to get 65.

$$\frac{65}{12}+\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$\frac{65}{12}+2$$

Convert 2 to fraction \frac{24}{12}.

$$\frac{65}{12}+\frac{24}{12}$$

Since \frac{65}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{65+24}{12}$$

Add 65 and 24 to get 89.

$$\frac{89}{12}$$

Factor

$$\frac{89}{2 ^ {2} \cdot 3} = 7\frac{5}{12} = 7.416666666666667$$