Solve 8+7/2+6/3+5/4+4/5+frac{3}{6}+frac{2}{7}+frac{1}{8}

$$8 + \frac { 7 } { 2 } + \frac { 6 } { 3 } + \frac { 5 } { 4 } + \frac { 4 } { 5 } + \frac { 3 } { 6 } + \frac { 2 } { 7 } + \frac { 1 } { 8 }$$

Evaluate

$$\frac{4609}{280}\approx 16.460714286$$

Solution Steps

Convert 8 to fraction \frac{16}{2}.

$$\frac{16}{2}+\frac{7}{2}+\frac{6}{3}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Since \frac{16}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{16+7}{2}+\frac{6}{3}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Add 16 and 7 to get 23.

$$\frac{23}{2}+\frac{6}{3}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Divide 6 by 3 to get 2.

$$\frac{23}{2}+2+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{23}{2}+\frac{4}{2}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Since \frac{23}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{23+4}{2}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Add 23 and 4 to get 27.

$$\frac{27}{2}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Least common multiple of 2 and 4 is 4. Convert \frac{27}{2} and \frac{5}{4} to fractions with denominator 4.

$$\frac{54}{4}+\frac{5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Since \frac{54}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{54+5}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Add 54 and 5 to get 59.

$$\frac{59}{4}+\frac{4}{5}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Least common multiple of 4 and 5 is 20. Convert \frac{59}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{295}{20}+\frac{16}{20}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Since \frac{295}{20} and \frac{16}{20} have the same denominator, add them by adding their numerators.

$$\frac{295+16}{20}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Add 295 and 16 to get 311.

$$\frac{311}{20}+\frac{3}{6}+\frac{2}{7}+\frac{1}{8}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{311}{20}+\frac{1}{2}+\frac{2}{7}+\frac{1}{8}$$

Least common multiple of 20 and 2 is 20. Convert \frac{311}{20} and \frac{1}{2} to fractions with denominator 20.

$$\frac{311}{20}+\frac{10}{20}+\frac{2}{7}+\frac{1}{8}$$

Since \frac{311}{20} and \frac{10}{20} have the same denominator, add them by adding their numerators.

$$\frac{311+10}{20}+\frac{2}{7}+\frac{1}{8}$$

Add 311 and 10 to get 321.

$$\frac{321}{20}+\frac{2}{7}+\frac{1}{8}$$

Least common multiple of 20 and 7 is 140. Convert \frac{321}{20} and \frac{2}{7} to fractions with denominator 140.

$$\frac{2247}{140}+\frac{40}{140}+\frac{1}{8}$$

Since \frac{2247}{140} and \frac{40}{140} have the same denominator, add them by adding their numerators.

$$\frac{2247+40}{140}+\frac{1}{8}$$

Add 2247 and 40 to get 2287.

$$\frac{2287}{140}+\frac{1}{8}$$

Least common multiple of 140 and 8 is 280. Convert \frac{2287}{140} and \frac{1}{8} to fractions with denominator 280.

$$\frac{4574}{280}+\frac{35}{280}$$

Since \frac{4574}{280} and \frac{35}{280} have the same denominator, add them by adding their numerators.

$$\frac{4574+35}{280}$$

Add 4574 and 35 to get 4609.

$$\frac{4609}{280}$$

Factor

$$\frac{11 \cdot 419}{2 ^ {3} \cdot 5 \cdot 7} = 16\frac{129}{280} = 16.460714285714285$$