Solve 1/1*2+1/2*3+1/3*4+1/4*5+frac{1}{5*6}=

$$\frac{ 1 }{ 1 \times 2 } + \frac{ 1 }{ 2 \times 3 } + \frac{ 1 }{ 3 \times 4 } + \frac{ 1 }{ 4 \times 5 } + \frac{ 1 }{ 5 \times 6 } =$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{2}+\frac{1}{6}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{3}{6}+\frac{1}{6}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{6}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Add 3 and 1 to get 4.

$$\frac{4}{6}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Multiply 3 and 4 to get 12.

$$\frac{2}{3}+\frac{1}{12}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{8}{12}+\frac{1}{12}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Since \frac{8}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{12}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Add 8 and 1 to get 9.

$$\frac{9}{12}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}$$

Multiply 4 and 5 to get 20.

$$\frac{3}{4}+\frac{1}{20}+\frac{1}{5\times 6}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{1}{20} to fractions with denominator 20.

$$\frac{15}{20}+\frac{1}{20}+\frac{1}{5\times 6}$$

Since \frac{15}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{20}+\frac{1}{5\times 6}$$

Add 15 and 1 to get 16.

$$\frac{16}{20}+\frac{1}{5\times 6}$$

Reduce the fraction \frac{16}{20} to lowest terms by extracting and canceling out 4.

$$\frac{4}{5}+\frac{1}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$\frac{4}{5}+\frac{1}{30}$$

Least common multiple of 5 and 30 is 30. Convert \frac{4}{5} and \frac{1}{30} to fractions with denominator 30.

$$\frac{24}{30}+\frac{1}{30}$$

Since \frac{24}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{24+1}{30}$$

Add 24 and 1 to get 25.

$$\frac{25}{30}$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$