Solve 5/3+9/8+5/16+2/9

$$\frac { 5 } { 3 } + \frac { 9 } { 8 } + \frac { 5 } { 16 } + \frac { 2 } { 9 }$$

Evaluate

$$\frac{479}{144}\approx 3.326388889$$

Solution Steps

Least common multiple of 3 and 8 is 24. Convert \frac{5}{3} and \frac{9}{8} to fractions with denominator 24.

$$\frac{40}{24}+\frac{27}{24}+\frac{5}{16}+\frac{2}{9}$$

Since \frac{40}{24} and \frac{27}{24} have the same denominator, add them by adding their numerators.

$$\frac{40+27}{24}+\frac{5}{16}+\frac{2}{9}$$

Add 40 and 27 to get 67.

$$\frac{67}{24}+\frac{5}{16}+\frac{2}{9}$$

Least common multiple of 24 and 16 is 48. Convert \frac{67}{24} and \frac{5}{16} to fractions with denominator 48.

$$\frac{134}{48}+\frac{15}{48}+\frac{2}{9}$$

Since \frac{134}{48} and \frac{15}{48} have the same denominator, add them by adding their numerators.

$$\frac{134+15}{48}+\frac{2}{9}$$

Add 134 and 15 to get 149.

$$\frac{149}{48}+\frac{2}{9}$$

Least common multiple of 48 and 9 is 144. Convert \frac{149}{48} and \frac{2}{9} to fractions with denominator 144.

$$\frac{447}{144}+\frac{32}{144}$$

Since \frac{447}{144} and \frac{32}{144} have the same denominator, add them by adding their numerators.

$$\frac{447+32}{144}$$

Add 447 and 32 to get 479.

$$\frac{479}{144}$$

Factor

$$\frac{479}{2 ^ {4} \cdot 3 ^ {2}} = 3\frac{47}{144} = 3.326388888888889$$