Solve 4/5+3/4+2/3+1/2

$$\frac { 4 } { 5 } + \frac { 3 } { 4 } + \frac { 2 } { 3 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{163}{60}\approx 2.716666667$$

Solution Steps

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

$$\frac{16}{20}+\frac{15}{20}+\frac{2}{3}+\frac{1}{2}$$

Since \frac{16}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{16+15}{20}+\frac{2}{3}+\frac{1}{2}$$

Add 16 and 15 to get 31.

$$\frac{31}{20}+\frac{2}{3}+\frac{1}{2}$$

Least common multiple of 20 and 3 is 60. Convert \frac{31}{20} and \frac{2}{3} to fractions with denominator 60.

$$\frac{93}{60}+\frac{40}{60}+\frac{1}{2}$$

Since \frac{93}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{93+40}{60}+\frac{1}{2}$$

Add 93 and 40 to get 133.

$$\frac{133}{60}+\frac{1}{2}$$

Least common multiple of 60 and 2 is 60. Convert \frac{133}{60} and \frac{1}{2} to fractions with denominator 60.

$$\frac{133}{60}+\frac{30}{60}$$

Since \frac{133}{60} and \frac{30}{60} have the same denominator, add them by adding their numerators.

$$\frac{133+30}{60}$$

Add 133 and 30 to get 163.

$$\frac{163}{60}$$

Factor

$$\frac{163}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{43}{60} = 2.716666666666667$$