Solve 3/4+2/5+8/7+3/8

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

Evaluate

$$\frac{747}{280}\approx 2.667857143$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{15}{20}+\frac{8}{20}+\frac{8}{7}+\frac{3}{8}$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+8}{20}+\frac{8}{7}+\frac{3}{8}$$

Add 15 and 8 to get 23.

$$\frac{23}{20}+\frac{8}{7}+\frac{3}{8}$$

Least common multiple of 20 and 7 is 140. Convert \frac{23}{20} and \frac{8}{7} to fractions with denominator 140.

$$\frac{161}{140}+\frac{160}{140}+\frac{3}{8}$$

Since \frac{161}{140} and \frac{160}{140} have the same denominator, add them by adding their numerators.

$$\frac{161+160}{140}+\frac{3}{8}$$

Add 161 and 160 to get 321.

$$\frac{321}{140}+\frac{3}{8}$$

Least common multiple of 140 and 8 is 280. Convert \frac{321}{140} and \frac{3}{8} to fractions with denominator 280.

$$\frac{642}{280}+\frac{105}{280}$$

Since \frac{642}{280} and \frac{105}{280} have the same denominator, add them by adding their numerators.

$$\frac{642+105}{280}$$

Add 642 and 105 to get 747.

$$\frac{747}{280}$$

Factor

$$\frac{3 ^ {2} \cdot 83}{2 ^ {3} \cdot 5 \cdot 7} = 2\frac{187}{280} = 2.6678571428571427$$