Solve 1+1/1+2+1/1+2+3=

$$1 + \frac { 1 } { 1 + 2 } + \frac { 1 } { 1 + 2 + 3 } =$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Add 1 and 2 to get 3.

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

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 1 to get 4.

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

Add 1 and 2 to get 3.

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

Add 3 and 3 to get 6.

$$\frac{4}{3}+\frac{1}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{8}{6}+\frac{1}{6}$$

Since \frac{8}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{6}$$

Add 8 and 1 to get 9.

$$\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$