Solve [1/7+8/5+10/4+16/3+frac{40}{2}+25]

$$[ \frac { 1 } { 7 } + \frac { 8 } { 5 } + \frac { 10 } { 4 } + \frac { 16 } { 3 } + \frac { 40 } { 2 } + 25 ]$$

Evaluate

$$\frac{11461}{210}\approx 54.576190476$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{1}{7} and \frac{8}{5} to fractions with denominator 35.

$$\frac{5}{35}+\frac{56}{35}+\frac{10}{4}+\frac{16}{3}+\frac{40}{2}+25$$

Since \frac{5}{35} and \frac{56}{35} have the same denominator, add them by adding their numerators.

$$\frac{5+56}{35}+\frac{10}{4}+\frac{16}{3}+\frac{40}{2}+25$$

Add 5 and 56 to get 61.

$$\frac{61}{35}+\frac{10}{4}+\frac{16}{3}+\frac{40}{2}+25$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{61}{35}+\frac{5}{2}+\frac{16}{3}+\frac{40}{2}+25$$

Least common multiple of 35 and 2 is 70. Convert \frac{61}{35} and \frac{5}{2} to fractions with denominator 70.

$$\frac{122}{70}+\frac{175}{70}+\frac{16}{3}+\frac{40}{2}+25$$

Since \frac{122}{70} and \frac{175}{70} have the same denominator, add them by adding their numerators.

$$\frac{122+175}{70}+\frac{16}{3}+\frac{40}{2}+25$$

Add 122 and 175 to get 297.

$$\frac{297}{70}+\frac{16}{3}+\frac{40}{2}+25$$

Least common multiple of 70 and 3 is 210. Convert \frac{297}{70} and \frac{16}{3} to fractions with denominator 210.

$$\frac{891}{210}+\frac{1120}{210}+\frac{40}{2}+25$$

Since \frac{891}{210} and \frac{1120}{210} have the same denominator, add them by adding their numerators.

$$\frac{891+1120}{210}+\frac{40}{2}+25$$

Add 891 and 1120 to get 2011.

$$\frac{2011}{210}+\frac{40}{2}+25$$

Divide 40 by 2 to get 20.

$$\frac{2011}{210}+20+25$$

Convert 20 to fraction \frac{4200}{210}.

$$\frac{2011}{210}+\frac{4200}{210}+25$$

Since \frac{2011}{210} and \frac{4200}{210} have the same denominator, add them by adding their numerators.

$$\frac{2011+4200}{210}+25$$

Add 2011 and 4200 to get 6211.

$$\frac{6211}{210}+25$$

Convert 25 to fraction \frac{5250}{210}.

$$\frac{6211}{210}+\frac{5250}{210}$$

Since \frac{6211}{210} and \frac{5250}{210} have the same denominator, add them by adding their numerators.

$$\frac{6211+5250}{210}$$

Add 6211 and 5250 to get 11461.

$$\frac{11461}{210}$$

Factor

$$\frac{73 \cdot 157}{2 \cdot 3 \cdot 5 \cdot 7} = 54\frac{121}{210} = 54.576190476190476$$