Solve 1/2*3+1/3*4+1/4*5+1/5*6

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Multiply 3 and 4 to get 12.

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

Least common multiple of 6 and 12 is 12. Convert \frac{1}{6} and \frac{1}{12} to fractions with denominator 12.

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

Since \frac{2}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

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

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

Multiply 4 and 5 to get 20.

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

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

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

Since \frac{5}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

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

Add 5 and 1 to get 6.

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

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{1}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$\frac{3}{10}+\frac{1}{30}$$

Least common multiple of 10 and 30 is 30. Convert \frac{3}{10} and \frac{1}{30} to fractions with denominator 30.

$$\frac{9}{30}+\frac{1}{30}$$

Since \frac{9}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{30}$$

Add 9 and 1 to get 10.

$$\frac{10}{30}$$

Reduce the fraction \frac{10}{30} to lowest terms by extracting and canceling out 10.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$